Abstract

Supercritical flow interaction occurring in the marine boundary layer between closely spaced coastal capes is investigated with a mesoscale numerical prediction model. As an extension of previous work, the U.S. Navy’s Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS) is used to perform idealized model simulations with marine layers of varying upstream Froude number to elucidate the different flow responses for a single convex bend. The impact upon the supercritical flow of introducing a series of closely spaced coastal bends is then investigated. The expansion fan is significantly reduced in magnitude and size by the formation of a compression wave at a blocking, concave bend approximately 150 km downstream. Building upon the idealized marine layer response, real-data forecasts are then examined for several time periods of supercritical flow interaction between Cape Blanco, Oregon, and Cape Mendocino, California.

Observations from the Coastal Waves 1996 (CW96) field program were collected in the vicinity of these capes on several days during June–July of 1996. Aircraft measurements on three CW96 flights provide model validation and show ample evidence of supercritical phenomena, while buoy data along the Oregon and California coastline indicate substantial diurnal variability in the marine environment. GOES-9 satellite imagery reveals preferred regions of clearing in the coastal stratus deck downwind of convex coastal bends, which is consistent with supercritical expansion fan dynamics.

Real-data COAMPS forecasts of summertime marine layer flow between these major capes indicate that the supercritical flow features, and their degree of interaction, vary diurnally. Diurnal oscillations in the upstream Froude number and flow direction driven by the sea–land-breeze circulation enhance or diminish the expansion fan in the lee of Cape Blanco, thereby altering the flow conditions encountering the concave turn at Cape Mendocino. In a manner similar to that produced in the idealized simulations, a compression jump forms due to the impact of highly supercritical flow within the Cape Blanco expansion fan upon the Cape Mendocino terrain. The compression wave becomes detached and propagates northward during the afternoon in response to a reduction in upstream Froude number. This propagating compression wave occurred in all three days of the study. The findings presented here demonstrate that supercritical flow responses about several closely spaced coastal bends cannot be analyzed independently.

1. Introduction

The California coastal zone is an area rich in a variety of mesoscale flows. Frequently the summertime synoptic regime dominating the northern Pacific favors strong northerly low-level winds along the west coast of the United States within a shallow, inversion-capped, nearly saturated marine boundary layer. Since the coastal terrain height is generally well above that of the strong temperature inversion capping the marine layer, low-level flow is blocked and channeled along the coast and readily modulated by topographic features such as capes, points, bays, and valleys. Around several of California’s coastal bends for example, particularly abrupt spatial and temporal variations in marine layer depth and velocity have been observed and associated with the dynamics of supercritical flow. Supercritical flow occurs when the Froude number, a dimensionless quantity given by the ratio of the fluid speed to the phase speed of internal gravity waves, is greater than unity. Perturbations are confined to downstream propagation in a supercritical regime so that the flow responds to topographic forcing in a predictable manner. Furthermore, blocked flow can develop transcritical regimes wherein the Froude number transitions through unity, and thus local regions of both super- and subcritical flow exist.

Even slight adjustments in marine layer structure can dramatically affect local atmospheric conditions. Spatial variations in the marine layer depth and low-level winds for example impact the marine layer stratus and their associated radiative properties. Visible satellite imagery over northern California during the warm season often depicts preferred clearing in scalloped regions downwind of convex bends in the coastline. A striking example of this horizontal variability is shown in Fig. 1 valid ∼0000 UTC 17 July 1998. Observations and modeling have shown that these regions contain an accelerated and thinned marine layer consistent with the characteristics of supercritical expansion fans. Conversely, blocked flow on the upwind side of capes and points often remain cloudy throughout the day. Additionally, the accelerated flow and cyclonic turning of the surface wind field in an expansion fan have been associated with enhanced stress and stress curl that may drive localized oceanic upwelling (Zemba and Friehe 1987; Enriquez and Friehe 1995).

Fig. 1.

GOES-9 visible satellite imagery over northern California valid 2345 UTC (1645 LT) 16 Jul 1998 showing scalloped regions of clearing in the lee of convex coastal bends.

Fig. 1.

GOES-9 visible satellite imagery over northern California valid 2345 UTC (1645 LT) 16 Jul 1998 showing scalloped regions of clearing in the lee of convex coastal bends.

In the past several decades, coastal flow dynamics has been the subject of several observational field experiments and modeling studies devised to investigate the behavior of orographically modulated marine layer flow. Gill (1977) first associated the coastal marine layer with hydraulic control in his study of propagating coastally trapped disturbances off southern Africa. Along the U.S. west coast, observations collected during the 1981 and 1982 Coastal Ocean Dynamics Experiment revealed stationary features in the marine layer, such as expansion fans and compression jumps, which were directly tied to changes in coastal topography (Beardsley et al. 1987). Winant et al. (1988) provides a theoretical description using the early work of Ippen (1951) who applied the concepts and analytic developments of gas dynamics to high-velocity, channeled fluid. That analogy can be used to describe the behavior of the atmospheric marine layer bounded laterally by coastal topography. Samelson’s (1992) idealized, shallow-water modeling study of supercritical flow around a turning lateral boundary found that the inviscid expansion fan pattern in the wind field becomes elliptical in shape when surface friction is added. From a shallow-water modeling study of transcritical flow performed by Rogerson (1999), expansion fans were found to halt or severely attenuate the propagation of coastally trapped wind reversals that tend to travel against the prevailing northerly flow bringing a cooling surge of fog up the coast.

Recently, the Coastal Waves 1996 (CW96) experiment was conducted along the west coast of the United States during the months of June and July 1996 to investigate dynamic processes in the marine layer associated with topographic forcing. In addition to special surface and buoy data, extensive aircraft measurements were collected aboard the National Center for Atmospheric Research C-130 Hercules, including scanning aerosol backscatter lidar data. From these data and mesoscale model fields, a June–July climatological mean marine layer structure is described by Dorman et al. (2000). Rogers et al. (1998) give a summary of the field study and, along with Dorman et al. (1999), provide evidence of supercritical expansion fan phenomena from the aircraft data.

Burk et al. (1999) conducted an idealized modeling study using a fully stratified mesoscale numerical model with a simplified coastal barrier and homogeneous initial conditions designed to be consistent with a shallow-water model of supercritical flow. In the present study, we utilize their idealized simulations for which a marine layer of specified background Froude number is channeled along a linear coastal “wall” containing one (or more) well-defined bend angle(s). The most dramatic marine layer response was found to occur for the transcritical flow regime in which the Froude number transitions through unity around the bend. Further, unlike shallow-water model solutions, they find that large adjustments take place in the stratified layer above the inversion as it responds to the orographic bend and to the marine layer below. Tjernström (1999) and Tjernström and Grisogono (2000) use a hydrostatic meso-γ-scale model to study supercritical flow around Cape Mendocino and Point Sur during the CW96 experiment. Their results from several idealized numerical simulations indicate that the expansion fan is a highly robust feature.

Real-data modeling studies have also been employed to describe the temporal and spatial complexity of the coastal marine layer in a littoral setting. Burk and Thompson (1996) and Holt (1996) investigate the dynamics of the summertime low-level jet off the U.S. west coast using the navy’s hydrostatic regional model, the Navy Operational Regional Atmospheric Prediction System. Their studies highlight the influence of diurnal and topographic forcing on the coastal jet structure, intensity, and position. Further, Burk and Thompson (1996) discuss the relative importance of supercritical expansion fan flow around Cape Mendocino versus leeside downslope acceleration over the Cape.

While there have been several previous investigations, generally idealized to some degree, of supercritical flow around a single coastal bend or cape, in the present study we address a significantly more complex dynamical situation involving flow interaction between adjacent capes. In particular we focus on northerly flow rounding Cape Blanco, Oregon, in a supercritical expansion fan that interacts with Cape Mendocino, California. These capes are spaced ∼250 km apart, and represent significant convex and concave coastal bends embedded within coastal orography having elevation well above the depth of the adjacent marine layer. As we will demonstrate, in the absence of any synoptic-scale changes, the expansion fan around Cape Blanco undergoes substantial diurnal variation in shape, areal extent, and intensity. When this Cape Blanco fan is at its maximum extent, the enhanced supercritical flow is strongly blocked by the Cape Mendocino headland and an oblique compression jump, or shock, is created within the flow.

Using an idealized model simulation, Burk et al. (1999) also examine supercritical flow interaction between two convex coastal bends separated by a concave bend. In that study, the supercritical flow around the first convex bend is strongly blocked by a downstream concave bend and undergoes a compression jump transition to subcritical flow. Recently, Burk and Haack (2000) presented a real-data modeling study of supercritical marine layer flow transitioning to a cloud-topped undular bore as the flow is blocked by California’s Monterey Peninsula. In this paper, we build upon the previous idealized and more realistic studies to examine the complex, diurnally varying interplay of supercritical flow between two prominent coastal capes. Section 2 describes the Coupled Ocean/Atmospheric Mesoscale Prediction System (COAMPS; Hodur 1997) that is used in this investigation. Section 3 discusses the synoptic setting and observations of three real-data case studies for which aircraft measurements were collected offshore of southern Oregon/northern California in conjunction with the CW96 experiment. In section 4, we present the COAMPS model results from idealized simulations of supercritical and transcritical flow, while section 5 summarizes the COAMPS results from the real-data CW96 cases. The high spatial and temporal resolution fields from the mesoscale model case studies, as well as from several sensitivity tests, allow detailed examination of the marine layer response to variations in coastal orography. Concluding remarks are presented in section 6.

2. Model description

COAMPS consists of a nonhydrostatic, fully compressible atmospheric model coupled to a hydrostatic ocean model via the exchange of surface fluxes. In this investigation, we use only the atmospheric component of COAMPS, while the oceanic model undergoes further development and testing. The atmospheric model contains a relocatable, multinested, horizontally staggered grid structure with each inner grid increasing in resolution by three times that of the parent grid. Irregularly spaced vertical levels are defined using a terrain-following sigma-z coordinate system. Sound waves are treated with a semi-implicit time-splitting integration scheme.

The model’s physical parameterization schemes include explicit moist physics (Rutledge and Hobbs 1983), cumulus convection (Kain and Fritsch 1990), long- and shortwave radiation (Harshvardhan et al. 1987), surface exchange (Louis et al. 1982), and level-2.5 turbulence closure (Mellor and Yamada 1982). COAMPS permits idealized or real-data case studies. Idealized simulations are typically initialized by simplified, user-specified surface fields and homogeneous vertical profiles, while real-data studies are initialized from surface databases and first-guess fields interpolated from the Navy Operational Global Atmospheric Prediction System (NOGAPS) modified by automated data processing observations. During real-data forecasts, outer mesh boundary conditions are updated every 6 h using the NOGAPS fields, and inner mesh lateral boundaries are one-way interactive using the Davies (1976) method. Hodur (1997) gives a more complete COAMPS model description.

For the purposes of this study, Cape Mendocino is positioned near the middle of the horizontal grid meshes, which are rotated ∼30° west of north so that the y axis aligns nearly parallel to the coastline south of the cape. Simulations are run with three nested grids having horizontal resolutions of 45, 15, and 5 km and containing 30 vertical levels where more than half the levels are placed in the lowest kilometer with average vertical spacing of ∼50 m. The three model domains are displayed in Fig. 2 with grid 3 enlarged showing terrain elevation. The locations of five nearshore National Data Buoy Center (NDBC) buoys, cross section A–B, several geographical locations, and the asterisk are indicated for later reference. Marine layer and mesoscale detail are established in the prognostic fields by beginning the simulations 36 h before the period of interest while performing intermittent data assimilation updates. This preforecast consists of initialization from NOGAPS fields followed by two 12-h data assimilation update cycles. Surface characteristics are specified from a 1° land use database, a sea surface temperature analysis is performed on each of the model grids, and terrain height data is interpolated from a 100-m resolution database. We analyze COAMPS fields for the three real-data case studies from 12-h forecasts beginning at 1200 UTC on 7 June, 12 June, and 1 July 1996, which coincide with times during which three CW96 flights were conducted in the study area.

Fig. 2.

Horizontal model domains for COAMPS real-data Jun–Jul 1996 case studies of marine layer flow along the southern Oregon–northern California coast. The inner nest (grid 3) is enlarged and shows terrain elevations (m, shaded). Locations of five nearshore NDBC buoys, cross section A–B, several geographical locations, and the asterisk are indicated for later reference. The dotted line east of Cape Mendocino represents the straightened coastline used in sensitivity test S2 (see Fig. 20b).

Fig. 2.

Horizontal model domains for COAMPS real-data Jun–Jul 1996 case studies of marine layer flow along the southern Oregon–northern California coast. The inner nest (grid 3) is enlarged and shows terrain elevations (m, shaded). Locations of five nearshore NDBC buoys, cross section A–B, several geographical locations, and the asterisk are indicated for later reference. The dotted line east of Cape Mendocino represents the straightened coastline used in sensitivity test S2 (see Fig. 20b).

3. Synoptic conditions and observations

In their June 1996 monthly average of the CW96 observational and model data, Dorman et al. (2000) characterize the coastal marine atmospheric boundary layer (MABL) as gradually thinning from Cape Blanco to Santa Barbara with wind speed increasing south of the cape. They found that supercritical flow begins along southern Oregon with supercritical enhancement in the lee of every major cape.

An example of the observed, cross-shore MABL structure sampled during the CW96 experiment along C-130 aircraft transects L1, L2, and L3 near Cape Mendocino is shown in Fig. 3. These contoured composites of potential temperature and wind speed, from data taken between 2100 and 0000 UTC 7 June 1996, describe the cross-coast MABL structure upwind and downwind of this prominent blocking terrain feature. The expansion fan signature of supercritical flow is reviewed in section 4 and characterized here by the thinning and acceleration of the MABL downwind of the cape in L3. The moist MABL is strongly capped and slopes toward the coast where the inversion sharpens and lowers confining a low-level jet of maximum speed ∼27 m s−1. Note also, the much deeper and slower marine layer in the blocked flow upwind of the cape in L1 producing a subcritical marine layer in this region.

Fig. 3.

CW96 aircraft transects of potential temperature (K) in column 1 and wind speed (m s−1) in column 2 from flight legs (a) L1, (b) L2, and (c) L3, valid 2100–0000 UTC 7 Jun 1996. The white lines indicate the aircraft sawtooth and horizontal flight legs. The transect locations are shown on the map inset.

Fig. 3.

CW96 aircraft transects of potential temperature (K) in column 1 and wind speed (m s−1) in column 2 from flight legs (a) L1, (b) L2, and (c) L3, valid 2100–0000 UTC 7 Jun 1996. The white lines indicate the aircraft sawtooth and horizontal flight legs. The transect locations are shown on the map inset.

Warm season climatological fields for the eastern Pacific are given by Mass and Bond (1996). They depict a weak 500-mb trough along the west coast of the United States and a sea level pressure distribution consisting of a subtropical high in the eastern Pacific near 35°N, 145°W and a thermal low over the southwestern United States. The 850-mb winds are northerly along the coast and attain maximum speeds near 10 m s−1. The three cases presented here do not differ significantly from the general climatological pattern although each has subtle variations in the synoptic conditions that lead to somewhat differing strengths and orientation of the low-level wind field along the coast. Figure 4 displays the COAMPS grid 1 mean sea level pressure pattern and 10-m wind barbs valid at 1800 UTC for each case. Surface observations and the positions of the synoptic high and low pressure centers are indicated in each plot. Beardsley et al.’s (1987) conceptual model describing coastal MABL flow in the eastern North Pacific suggests, as one might expect, that the position of maximum surface winds along the northern California coast is due in part to the relative positions of these pressure centers.

Fig. 4.

COAMPS grid 1 6-h forecasts of sea level pressure (hPa) and 10-m wind barbs (full barb = 5 m s−1) overlaid with surface observations valid 1800 UTC (a) 7 Jun, (b) 12 Jun, and (c) 1 Jul 1996. The H and L indicate the positions of the synoptic high and low pressure centers. The modeled 10-m winds are compared to NDBC buoy measurements in Table 1.

Fig. 4.

COAMPS grid 1 6-h forecasts of sea level pressure (hPa) and 10-m wind barbs (full barb = 5 m s−1) overlaid with surface observations valid 1800 UTC (a) 7 Jun, (b) 12 Jun, and (c) 1 Jul 1996. The H and L indicate the positions of the synoptic high and low pressure centers. The modeled 10-m winds are compared to NDBC buoy measurements in Table 1.

As seen in Fig. 4, on 7 June low pressure over Alaska has forced the subtropical high farther south than the other two days. Consequently, the low-level coastal flow along the Washington–Oregon coast is more westerly and significantly weaker. On 12 June, with the intensification of the subtropical high, the horizontal pressure gradient is considerably stronger than on the other two days giving rise to MABL winds that are several meters per second faster. On 1 July, significant warming in the California Central Valley and along the central and southern California coast has shifted the thermal low westward, and that coupled with ridging in the Pacific Northwest produces offshore coastal flow in Oregon and northern California.

Near-surface velocities at the NDBC buoy locations shown in Fig. 2 are reported in Table 1 for each case at 1200 and 0000 UTC from observations and from COAMPS grid 1 initial and 12-h forecasts. Generally, modeled and observed wind speeds agree to within 2.0 m s−1 and most wind directions are within 10° of one another. Slightly larger differences occur in velocity at buoy 30 and in direction at buoy 27 except in light wind conditions for which directional agreement is poor. Note the strengthening and westerly shift in the surface winds throughout the day in both the observations and model at all locations except buoy 30. At this buoy, located just offshore of Cape Mendocino, the opposite trend occurs in the low-level winds whereby the flow weakens and becomes more northerly during the day. In section 5 we associate this trend with the diurnal variations in the supercritical flow between Cape Blanco and Cape Mendocino. The westerly shift in wind direction at all other nearshore buoys results from the coupling of the diurnally varying, thermally direct, cross-coast sea–land breeze with the prevailing, primarily northerly flow. By creating a significant cross-coast component to the flow direction, this diurnally driven feature can be important in determining the turning angle of the flow and, hence, in predicting the magnitude of the downwind supercritical flow response.

Table 1.

Observed 5-m and modeled grid 1, 10-m wind direction and speed (m s−1) at NDBC buoys 41, 29, 50, 27, and 30. Buoy locations are labeled in Fig. 2.

Observed 5-m and modeled grid 1, 10-m wind direction and speed (m s−1) at NDBC buoys 41, 29, 50, 27, and 30. Buoy locations are labeled in Fig. 2.
Observed 5-m and modeled grid 1, 10-m wind direction and speed (m s−1) at NDBC buoys 41, 29, 50, 27, and 30. Buoy locations are labeled in Fig. 2.

During the forecast period, satellite imagery also reveals consistent trends in the evolution of the marine cloud field. Three mid- to late-morning Geostationary Operational Environmental Satellite-9 (GOES-9) images are displayed in Fig. 5 from each of the three real-data case studies: 1754 UTC (∼1100 LT) 7 and 12 June, and 1554 UTC (∼0900 LT) 1 July 1996. Scalloped regions of clearing tend to occur first in the lee of convex coastal bends, particularly south of Cape Blanco, and along Shelter Cove south of Cape Mendocino, while the clouds on the northern flank of Cape Mendocino persist throughout the day. The cloudy areas in the coastal zone correspond to blocked MABL flow that has been elevated and adiabatically cooled. Described in section 5, the grid 3 (Δx = 5 km) COAMPS forecast fields indicate that this blocked flow behaves in a manner consistent with the hydrodynamics of a shallow-water compression wave.

Fig. 5.

GOES-9 visible satellite imagery over northern California valid 1754 UTC (1054 LT) (a) 7 Jun, (b) 12 Jun, and (c) 1554 UTC (0854 LT) 1 Jul 1996.

Fig. 5.

GOES-9 visible satellite imagery over northern California valid 1754 UTC (1054 LT) (a) 7 Jun, (b) 12 Jun, and (c) 1554 UTC (0854 LT) 1 Jul 1996.

The large-scale synoptic conditions coupled with the local marine layer structure upwind of Cape Blanco provide an estimate of the background Froude number. The position and strength of the subtropical high, relative to the continental thermal low, determine the general orientation and magnitude of the low-level wind field, and so may also determine where supercritical flow begins along the coast.

4. Idealized simulations

Prior to investigating the full complexity of flow interaction between capes, we analyze simpler, more idealized scenarios. We utilize the fully stratified COAMPS model with idealized initial conditions and a simplified coastal barrier representative of those generally used in shallow-water modeling. These results are an extension of the work of Burk et al. (1999). In their study, shallow-water principles are applied quantitatively first for a single convex bend and then for a triple (convex, concave, convex) bend configuration to demonstrate the marine layer interaction between closely spaced capes. Here we examine in detail specific differences between a supercritical and transcritical MABL in an idealized setting to reduce uncertainties associated with real-data case studies for which mountain wave affects, synoptic evolution, diurnal forcing, and irregular topography present additional challenges. Building upon the simplified, idealized mesoscale model results and shallow-water hydrodynamic theory, we anticipate that these dynamical responses are also present in the more realistic coastal environment, albeit we no longer expect quantitative agreement with hydrodynamic theory.

a. Single convex bend

Shallow-water theory of supercritical channel flow requires that the marine layer upstream of a bend be uniform, steady state, inviscid, and vertically bounded. The Froude number is defined as Fr = V/(gh)1/2, where g′ = gΔθ/θ is the reduced gravity, Δθ is the potential temperature jump across the inversion, and h, V and θ are the fluid depth, speed, and potential temperature, respectively. In idealized depictions, Δθ often is represented by a first-order discontinuity, whereas for a continuously stratified coastal MABL determination of the inversion is more ambiguous. From COAMPS, we estimate the inversion base from the lowest level for which the potential temperature gradient is greater than 0.02°C m−1, and the inversion top by the height at which the gradient again falls below 0.02°C m−1. The layer depth h is taken as the height midway between inversion base and top, and the inversion strength Δθ is the difference between the potential temperature at the inversion top and the average mixed layer potential temperature. These choices are based on examination of numerous model profiles.

The initial model fields are horizontally homogeneous consisting of northerly flow with a low-level wind maximum of 15 m s−1 in a 425-m-deep well-mixed MABL of 285-K potential temperature. Setting the initial surface fluxes to zero and eliminating radiation so as to remove the diurnal forcing further simplified these simulations. The Froude number characterizing the MABL criticality is controlled in these simulations by specifying the strength of the inversion, Δθ. Two simulations are presented corresponding to different inversion strengths: a fully supercritical case for which Δθ = 5 K, Fr1 = 1.5, and a transcritical case for which Δθ = 20 K, Fr1 = 0.8. A thorough description of these simulations is given in Burk et al. (1999).

In determining the supercritical flow response for shallow-water flow, one needs only to know the Froude number and speed of the incoming flow, and the bend angle of the wall. However, in a fully stratified, rotating atmosphere having frictional turning and thermally driven cross-coast circulations in the MABL, the upstream flow direction may contain a significant coast-perpendicular component, such that the bounding wall is not an accurate measure of the flow’s actual turning angle. Therefore, in estimating this angle for a particular coastal bend, we use the curvature of the flow (streamlines) ϕ±, rather than the angle of the lateral barrier. To obtain the curvature, we choose the closest nearshore streamline that continues around the bend from a height representative of mid-MABL flow. Since the choice of this height is somewhat arbitrary, we allow uncertainty of ±2.5° in our estimate of ϕ±. This value is determined by inspection of the variability in streamline orientation with height. The closest streamline rounding the bend is selected since those nearer to the coast are slowed due to friction within the lateral wall boundary layer and therefore may not be supercritical.

We utilize hydrodynamics principles given by Ippen (1951) to describe the flow channeled along a 2-km-high lateral barrier containing a single convex bend of ∼26°. Horizontal fields from the fully supercritical (Δθ = 5 K) case are shown in Fig. 6: marine layer depth (Fig. 6a), marine layer averaged wind speed overlaid with 200-m streamlines (Fig. 6b), and model-computed Froude number (Fig. 6c). The streamlines turn ϕ± ≈ −15° ± 2.5°, for which the negative angle represents a convex turn away from the upstream flow. Downwind of the bend, the MABL shallows to less than 275 m and accelerates to a speed of 18 m s−1. As a result, the local Froude number increases to a maximum value of ∼2.5.

Fig. 6.

Idealized COAMPS simulation of supercritical flow (inversion strength Δθ = 5 K) encountering a single convex bend (a) layer depth (m), (b) layer-averaged wind speed (m s−1) and 200-m streamlines, and (c) Froude number. The bold arrow is the upwind flow direction, ϕ±, is the curvature of the streamlines, and α is the Mach angle (α ≅ 40° for Fr1 = 1.5) indicated by the dotted line.

Fig. 6.

Idealized COAMPS simulation of supercritical flow (inversion strength Δθ = 5 K) encountering a single convex bend (a) layer depth (m), (b) layer-averaged wind speed (m s−1) and 200-m streamlines, and (c) Froude number. The bold arrow is the upwind flow direction, ϕ±, is the curvature of the streamlines, and α is the Mach angle (α ≅ 40° for Fr1 = 1.5) indicated by the dotted line.

The background Froude number is Fr1 = 1.5 yielding a leading Mach angle of α = sin−1(1/Fr) = 42°. The corresponding Mach line is drawn (dotted line) with respect to the upwind streamlines and matches quite well to the initial transition in MABL depth in Fig. 6a. It represents the stationary position of propagating internal gravity waves initiated at the barrier and denotes the leading edge of the supercritical expansion fan. Transitions in layer-averaged wind speed, however, tend to be more elliptical than that of a classical expansion fan (Fig. 6b), in agreement with Samelson’s (1992) shallow-water model results that include surface friction. Interestingly, flow acceleration begins upwind of the bend indicating that some modes are propagating upwind against the supercritical flow, presumably in the stratified layer above the MABL.

The expected downwind values of marine layer wind speed and height are determined from conservation of mass and momentum and use of the Bernoulli theorem, which states that the total energy along a streamline is conserved. For shallow-water flow the Bernoulli constant is given by B = h + V2/(2g′). Variations in h/B or Fr as a function of turning angle ϕ = ϕ1 + ϕ± are graphically displayed in Fig. 7, where ϕ1 = 3 tan−1(⁠3/Fr21 − 1⁠) − tan−1(1/Fr21 − 1⁠). This expression for ϕ1 is given as Eq. (10b) in Ippen (1951). For given upstream conditions, downstream values of layer depth and wind speed may be obtained by knowing ϕ. In this case, h1 ≈ 425 m, V1 ≈ 13 m s−1, g′ ≈ 0.172 m s−2, and ϕ± ≈ −15° ± 2.5°. The initial angle ϕ1 ≈ 57° corresponds to Fr1 ≈ 1.5, so that the total turning angle ϕ is in the range 39.5°–44.5°, giving downstream values of h2/B = 0.23–0.285 and Fr2 = 2.25–2.60 from Fig. 7. This estimate of Fr2 is in good agreement with the model-computed maximum. With the Bernoulli constant, B ≈ 916 m, determined from upwind conditions, a range of predicted downwind characteristics from shallow-water theory are obtained: h2 = 211–261 m and V2 = 15.0–15.6 m s−1. While the MABL depths in the expansion fan appear to be consistent with shallow-water theory, layer-averaged wind speeds are larger by ∼3 m s−1.

Fig. 7.

Integration solutions to the rate equations representing the general supercritical flow response to a bend in the lateral barrier: values of Fr and h/B vs the total turning angle ϕ = ϕ1 + ϕ±. See text for details. [From Ippen’s (1951)  Fig. 3. (Reproduced by permission of the American Society of Civil Engineers).]

Fig. 7.

Integration solutions to the rate equations representing the general supercritical flow response to a bend in the lateral barrier: values of Fr and h/B vs the total turning angle ϕ = ϕ1 + ϕ±. See text for details. [From Ippen’s (1951)  Fig. 3. (Reproduced by permission of the American Society of Civil Engineers).]

In comparing the model results to the frictionless hydrodynamics theory, one would expect a model having viscosity and turbulent mixing to produce a weaker acceleration around the bend as is obtained by Samelson’s (1992) viscous shallow-water model (his Fig. 4). On the contrary, here we obtain flow enhancement. This additional acceleration results from a substantial horizontal pressure gradient (∼1 mb over 150 km) that is present in the stratified layer above the MABL. In allowing for upper-level stratification, the viscous, shallow-water similarity solutions described by Burk et al. (1999, their Figs. 21 and 22) produce a thinner layer with considerably faster flow speeds than the theoretical predictions. Similarly COAMPS idealized simulations yield notably faster wind speeds but layer depths only slightly shallower than theory. Thus in the more general modeling framework that includes frictional effects and upper-level stratification, but still highly idealized model settings, layer depths tend to agree well with the hydrodynamics theory while layer speeds tend to be faster.

For comparison, horizontal fields for the transcritical (Δθ = 20 K) case are shown in Fig. 8. The stronger inversion strength produces a subcritical upwind Froude number, Fr1 = 0.8, that transitions through critical in a line nearly perpendicular to the coastline. Note in Fig. 8a the gradual transition in layer depth at much broader angles than in the Δθ = 5 K case (Fig. 6a). Moreover, substantially greater flow acceleration is present downwind of the bend with maximum speeds approaching 25 m s−1, nearly double the upwind value (Fig. 8b). Initial marine layer adjustments occur in the subcritical regime upstream due to flow divergence and local pressure gradient imbalances that are associated with the sloping inversion. The thinning and acceleration of the MABL rounding the bend leads to an increase in the local Froude number. When the flow reaches the critical value Fr = 1, the Mach angle is 90°. This angle (dotted line in Fig. 8a) is in good agreement with the modeled marine layer transitions in this case.

Fig. 8.

As in Fig. 6 except for transcritical flow (inversion strength Δθ = 20 K).

Fig. 8.

As in Fig. 6 except for transcritical flow (inversion strength Δθ = 20 K).

Variations in MABL wind speed and depth within an expansion fan lead, in turn, to changes in Froude number that impact the rate equations when integrated over the total turning angle [Ippen 1951; Eqs. (7) and (8)]. For MABLs having similar upstream conditions but different inversion strengths (i.e., different background Froude numbers Fr1 due to differing g′ values), the rate of change in layer speed is greatest throughout the turn for less supercritical flows (larger g′). And, the rate of change of layer depth is greatest at the leading Mach wave for less supercritical flows. However, in cases characterized by large Fr1 (smaller g′), upon integration through the fan, the rate of change of layer depth can become greater than the rate of change of layer speed. Consequently, near-critical and transcritical cases generally produce greater accelerations than do highly supercritical cases, but do not necessarily produce shallower expansion fans. As predicted by the theory and in the case modeled here, the transcritical expansion fan (Fig. 8) is broader and generates considerably greater acceleration with only slightly more shallowing than the fully supercritical case (Fig. 6). Similarly, in simulating flow over a mountain barrier, Durran (1986) found more vigorous lee wave activity and downslope wind storms develop in transcritical regimes.

b. Triple (convex, concave, convex) bend

In this section a series of bend angles are embedded in the idealized coastal “wall” to more closely mimic the topographic forcing associated with Cape Blanco and Cape Mendocino, but for idealized, homogeneous, steady-state marine layer flow. In this simulation, two convex bends are situated approximately 120 km apart, with a concave bend in between about 80 km south of the first bend. Each bend makes a 26.6° angle with the terrain orientation immediately upwind. The blocking affect of the concave bend creates a compression jump where the layer may undergo an abrupt transition termed an oblique shock. This feature represents a flow state change to the subcritical regime where the Froude number, when computed using the velocity normal to the shock, transitions through unity. Here we use the total wind speed to compute Froude numbers, so that the value may be greater than unity on either side of an oblique jump.

For concave bends, integration of the rate equations yields functions relating the incoming Froude number Fr1 and turning angle ϕ, to the shock angle β, shock strength h2/h1 (where h1 and h2 are the layer depths upstream and downstream of the shock respectively), and downstream Froude number Fr2. The relationship between these quantities is graphically displayed in Fig. 9 where, given the value of any two parameters, the other two may be determined (Ippen 1951). From Fig. 9a note that two shock angle solutions are possible. Weak shocks occur at smaller β and typically have Fr2 > 1.0.

Fig. 9.

Integration solutions to the rate equations representing the supercritical flow response to a concave bend [from Ippen’s (1951)  Fig. 8 (reproduced by permission of the American Society of Civil Engineers)]: values of upstream Froude number Fr1 for (a) bend angle ϕ vs shock angle β, (b) shock strength h2/h1 vs shock angle β, (c) bend angle ϕ vs downstream Froude number Fr2, and (d) shock strength h2/h1 vs downstream Froude number Fr2.

Fig. 9.

Integration solutions to the rate equations representing the supercritical flow response to a concave bend [from Ippen’s (1951)  Fig. 8 (reproduced by permission of the American Society of Civil Engineers)]: values of upstream Froude number Fr1 for (a) bend angle ϕ vs shock angle β, (b) shock strength h2/h1 vs shock angle β, (c) bend angle ϕ vs downstream Froude number Fr2, and (d) shock strength h2/h1 vs downstream Froude number Fr2.

The transcritical flow response to a triple-bend configuration is shown by Burk et al. (1999) to produce expansion fans about the two convex bends with a region of flow deceleration and flow reversal upwind of the concave bend. The deceleration in low-level winds coincides with an abruptly elevated marine layer and downwind subcritical regime characteristic of a compression jump whose stationary position is denoted by the critical Froude number contour. The upwind expansion fan has maximum Froude number Fr = 1.8 (Burk et al.’s Fig. 13) indicating that these conditions cannot support an attached oblique shock using the hydrodynamics relations of Fig. 9a. In this case, the shock becomes detached and may move away from its point of origin. No longer constrained by the topographic bend angle, these detached shocks are curved, being normal to the flow at the coast and approaching the Mach angle far offshore where the perturbations are weak. The model fields (Burk et al.’s Figs. 12 and 13) depict a detached shock feature where the sharp transition in Froude number to subcritical occurs ∼35 km upwind of the concave bend.

As shown in Figs. 7 and 13 of Burk et al. (1999), adding a downwind blocking terrain feature significantly alters the expansion fan. In the single-bend case, the expansion fan covers a much larger footprint (as measured by the Fr = 1.6 contour) extending roughly 170 km downwind compared to only ∼60 km in the triple-bend simulation. Further, the maximum Froude number in the triple-bend simulation is about one-half the value produced by a single convex bend for the same upstream conditions. The Froude number is weaker primarily because V2 is lower, the maximum speed in the expansion fan being ∼25% less than that of the single bend, rather than from deeper h2. Modification of this magnitude to the upstream expansion fan provides evidence of supercritical flow interaction between closely spaced coastal bends. Having explored the hydrodynamic character of the marine layer in fully stratified, but idealized, flows, we now utilize these concepts in analyzing more realistic coastal marine flow along complex topography in real-data forecast situations.

5. Real-data studies

In this section we explore supercritical flow interactions forced by the orographic complex along coastal Oregon and northern California, consisting of three major coastal bends: a 30° convex bend at Cape Blanco, and ∼250 km to the south, a 30° concave and 40° convex bend combination forming Cape Mendocino. The 12-h COAMPS forecasts valid 1200–0000 UTC 7 and 12 June, and 1 July 1996 are analyzed first from the grid 2 (Δx = 15 km) domain to obtain an overview of the synoptic settings, background flow conditions and marine layer responses. We then examine in detail the daytime variability from the inner grid 3 (Δx = 5 km) domain of 12 June. Marine layer “responses” to changes in coastal orientation for layer depth (Δh), layer-averaged wind speed (ΔV), and Froude number (ΔFr) are measured by the difference between the maximum/minimum value (h2, V2, Fr2) in the expansion fan (compression jump) and the average upwind value (h1, V1, Fr1) within ∼50 km of the coastline.

Figure 10 shows marine layer depth (shaded), layer-averaged wind speed (contoured), and 185-m streamlines from grid 2 for each case. Regions of accelerated flow extend southwestward from the coast with localized maxima in the lee of the two major convex turns at Cape Blanco and Cape Mendocino. These local marine layer responses to topographic forcing are embedded within a larger-scale marine layer acceleration that begins well upwind of the northernmost convex bend. The upwind acceleration results from an enhancement of the synoptic pressure gradient by coastal baroclinity. Holt (1996) and Burk and Thompson (1996) examine the dynamics of the coastal low-level jet formed at the top of the sloping, baroclinic MABL along the U.S. west coast. They find that the coastal mountain range acts to intensify and concentrate high momentum flow into a low-level jet. When fully developed, this jet takes on a width comparable to the Rossby deformation radius, which is of the order 100 km (Holt 1996). Thus, thermal wind considerations and the orientation of the synoptic-scale pressure pattern with respect to the coastal orography act to broadly determine the location and strength of the coastal jet. The coastal baroclinity produces a thinning MABL and speed increase but without the alongcoast variability associated with supercritical flow dynamics, and also defines the upwind marine environment that encounters a bend in the coastline.

Fig. 10.

COAMPS grid 2 12-h forecasts of marine layer depth (m, shaded), layer-averaged wind speed (m s−1, contoured), and 185-m streamlines valid 0000 UTC (a) 8 Jun, (b) 13 Jun, and (c) 2 Jul 1996.

Fig. 10.

COAMPS grid 2 12-h forecasts of marine layer depth (m, shaded), layer-averaged wind speed (m s−1, contoured), and 185-m streamlines valid 0000 UTC (a) 8 Jun, (b) 13 Jun, and (c) 2 Jul 1996.

Although the pattern of coastal flow acceleration is rather similar on each day, considerable differences are present in the overall marine layer depth field. Along the coast, however, minimum depths consistently occur in the local expansion fan regions south of Cape Blanco and Cape Mendocino, and maximum depths occur in the blocked flow north of Cape Mendocino, often extending well offshore and downwind. Note that this location also corresponds to flow deceleration, which is consistent with the observational analysis of automated surface stations presented by Dorman et al. (2000), who report a June 1996 mean speed north of Cape Mendocino that is about one-third slower than surrounding coastal stations. As shown by the 0000 UTC horizontal distribution of Froude number for each case (Fig. 11), the deeper, slower marine layer just north of Cape Mendocino leads to a considerable reduction in Fr in this region, in some cases transitioning through unity. The Fr pattern and magnitude for the 12 June and 1 July cases agree well with those computed from aircraft observations (Rogers et al. 1998, their Fig. 11) revealing similar enhancement/reduction of Froude number in the same coastal areas.

Fig. 11.

As in Fig. 10 except for Froude number.

Fig. 11.

As in Fig. 10 except for Froude number.

The background flow on 7 June yields an upwind Froude number near ∼0.5 that transitions through unity around Cape Blanco, whereas the background flow on the other two days is supercritical. Hence this 7 June real-data case is comparable to the idealized simulation of transcritical flow (Fig. 8). In examining the combined effect of the Cape Blanco–Cape Mendocino orographic complex, a stronger marine layer response is generated on 7 June than on the other two days. The marine layer wind speed gradually accelerates from 10 m s−1 upwind of Cape Blanco to 22 m s−1 in the lee of Cape Mendocino (Fig. 10a), while the layer depth thins by ∼200 m. Tjernström and Grisogono’s (2000) numerical simulation of the 7 June case produces an expansion fan in the lee of Cape Mendocino that is similar to that shown here; however, direct comparisons are not possible since their model is driven by highly idealized initial conditions and uniform, steady-state boundary values.

The blocked MABL response north of Cape Mendocino is more clearly seen in the grid 3 fields, having horizontal resolution of Δx = 5 km. Shown in Fig. 12 is the grid 3, 10-m wind field for the three cases valid 0000 UTC. Similar to the idealized, triple-bend results, the sharp gradient in wind speed and flow deflection north of Cape Mendocino is characteristic of a compression jump. Near-surface wind speeds drop by half their maximum value across this gradient.

Fig. 12.

COAMPS grid 3 12-h forecasts of 10-m wind speed (m s−1) and arrows valid 0000 UTC (a) 8 Jun, (b) 13 Jun, and (c) 2 Jul 1996.

Fig. 12.

COAMPS grid 3 12-h forecasts of 10-m wind speed (m s−1) and arrows valid 0000 UTC (a) 8 Jun, (b) 13 Jun, and (c) 2 Jul 1996.

Comparison of COAMPS fields with available aircraft measurements indicates generally good agreement. As an example aircraft transect L3 and COAMPS cross sections of potential temperature, relative humidity, and wind speed valid 2100–2200 UTC 1 July 1996 are shown in Fig. 13. The flight track is located south of Cape Blanco, which marks the northernmost major convex turn in the Pacific coastal barrier. The COAMPS grid 3, 9-h forecast cross sections indicate reasonably good agreement in inversion strength, marine layer thickness, and temperatures in the expansion fan region, as well as in the strength and location of the low-level jet. COAMPS representation of the MABL’s vertical structure is generally consistent with aircraft transects in all three real-data case studies. In the model, however, wind speeds at 850 mb and ∼100 km offshore on 12 June are overestimated by a few meters per second and marine layer depths are underpredicted by 200–300 m. The modeled 10-m winds on 12 June at Cape Mendocino and 1 July at Cape Blanco tend to be a few meters per second slower than observed but have velocity patterns around the respective capes similar to the aircraft measurements reported by Dorman et al. (2000, Fig. 5). The speed increase is ΔV ≈ 12 m s−1 around Cape Mendocino on 12 June and ΔV ≈ 8 m s−1 around Cape Blanco on 1 July indicating the presence of supercritical features in the flow: compression jumps along concave portions of the orography and expansion fans south of convex bends.

Fig. 13.

Cross sections of CW96 aircraft observations in column 1 and COAMPS grid 3 9-h forecast fields in column 2 of (a) potential temperature (K), (b) relative humidity (%), and (c) wind speed (m s−1) valid 2100–2200 UTC 1 Jul 1996. The cross-section location is shown in the map inset.

Fig. 13.

Cross sections of CW96 aircraft observations in column 1 and COAMPS grid 3 9-h forecast fields in column 2 of (a) potential temperature (K), (b) relative humidity (%), and (c) wind speed (m s−1) valid 2100–2200 UTC 1 Jul 1996. The cross-section location is shown in the map inset.

Statistics of the measured and modeled average marine layer structure upwind and downwind of the two capes are given in Table 2. The upwind average includes nine cross-shore points: three upwind of Cape Blanco from 1 July (flight leg L2), and six upwind of Cape Mendocino—three from 7 June (L1), three from 12 June (L2). The downwind average includes nine cross-shore points: three downwind of Cape Blanco from 1 July (L3), and six downwind of Cape Mendocino—three from 7 June (L3), three from 12 June (L4). At each point from the aircraft transects and collocated COAMPS cross sections, a comparison of the estimated marine layer wind speed V, depth h, potential temperature θ, inversion strength Δθ, and Froude number Fr are made. These statistics indicate a model bias for slightly weaker marine layer winds and shallower layer thickness than observed, which when combined produce a slight bias toward higher Froude numbers. These differences however, are in the range of uncertainty contained within the sampling of the aircraft measurements.

Table 2.

Average marine layer characteristics at nine points upwind and nine points downwind of Cape Blanco and Cape Mendocino from C-130 flight data and COAMPS forecasts for the three case studies. (See text for details.)

Average marine layer characteristics at nine points upwind and nine points downwind of Cape Blanco and Cape Mendocino from C-130 flight data and COAMPS forecasts for the three case studies. (See text for details.)
Average marine layer characteristics at nine points upwind and nine points downwind of Cape Blanco and Cape Mendocino from C-130 flight data and COAMPS forecasts for the three case studies. (See text for details.)

a. Diurnal variability

Despite the variability in synoptic conditions, the supercritical flow patterns within the Cape Blanco–Cape Mendocino orographic complex are quite similar on each of the three days studied. The Cape Blanco expansion fan undergoes substantial diurnal oscillation causing an attached, oblique shock north of Cape Mendocino to become detached near 1800 UTC. During the next 6 h, the shock moves ∼40 km upwind (north) due to changes in upwind Froude number and flow direction. The 12 June case is shown as an example of the marine layer evolution.

The grid 3 marine layer depth (color shading), layer-averaged wind speed (contoured), and 185-m streamlines are shown in Fig. 14 valid 1200, 1800, and 0000 UTC 12 June 1996. Froude numbers at these times are depicted in Fig. 15. The expansion fan signature is evident downwind of the two capes where the marine layer is shallower and faster than the upstream and offshore MABL. However, the leading Mach angle determined from the upwind Froude number Fr1 is not apparent in the real-data MABL depth field as it was in the idealized case. In fact layer depths are quite inhomogeneous in the coastal zone being an average of the inversion base and top and, therefore, sensitive to variations in either or both of these heights. For this reason, we are unable to correlate initial transitions in marine layer depth to the hydrodynamic estimate of the leading Mach angle. Additionally, the reduction in Fr1 from 2.0 to 1.75 during the 12-h period would cause the shallow-water expansion fan to broaden by only ∼5°, which is within our range of uncertainty and not likely to produce a perceptible impact upon the shape of the modeled expansion fan.

Fig. 14.

For 12 Jun 1996 the COAMPS grid 3 (a) initial 1200 UTC, (b) 6-h forecast valid 1800 UTC, and (c) 12-h forecast valid 0000 UTC forecasts of marine layer depth (m, color shading), layer-averaged wind speed (m s−1, contoured), and 185-m streamlines. The arrows denote the flow direction and the dotted blue lines denote the estimated positions of the compression jump.

Fig. 14.

For 12 Jun 1996 the COAMPS grid 3 (a) initial 1200 UTC, (b) 6-h forecast valid 1800 UTC, and (c) 12-h forecast valid 0000 UTC forecasts of marine layer depth (m, color shading), layer-averaged wind speed (m s−1, contoured), and 185-m streamlines. The arrows denote the flow direction and the dotted blue lines denote the estimated positions of the compression jump.

Fig. 15.

As in Fig. 14 except for Froude number.

Fig. 15.

As in Fig. 14 except for Froude number.

The integrated downstream flow response about Cape Blanco may be estimated from hydraulic theory as demonstrated in section 4 for idealized cases. At 1200 UTC, using Fr1 ≈ 2.0 we compute ϕ1 ≈ 48°. From Fig. 7 with approximately 15° of turning in the streamlines and a Bernoulli constant B ≈ 1437 m (h1 ≈ 500 m, V1 ≈ 16 m s−1, g′ ≈ 0.137), downstream conditions are obtained: Fr2 ≈ 3.1, h2 ≈ 245 m, and V2 ≈ 18 m s−1. Comparing these values with magnitudes in the Cape Blanco expansion fan, we find expansion fan behavior in this real-data case that is consistent with that of the idealized case. The modeled coastal flow tends to agree with hydraulic predictions of downwind Froude number (Fr2 ≈ 3.0) and layer depth (h2 ≈ 200 m) but forecasts wind speeds that are considerably faster (V2 ≈ 24 m s−1) than theory. Expansion fan calculations done at 1800 and 0000 UTC reveal similar modeled MABL behavior. As noted in section 4, the enhanced acceleration results from the mesoscale pressure gradient imposed above the MABL that thereby prevents strict applications of Bernoulli conservation.

The modeled fields indicate a reduction in the magnitude of the Cape Blanco expansion fan Froude number during the 12-h period. From hydraulic theory, lower Fr1 would tend to increase the expansion fan Froude number if all other upstream conditions remain the same. However, the curvature of the prevailing northerly flow shifts from an offshore nocturnal land breeze at 1200 UTC to an onshore sea breeze. This diurnal shift in flow direction reduces the effective turning angle around Cape Blanco by 5°–10°. At 0000 UTC, reduced turning produces a less supercritical and deeper expansion fan (Fr1 ≈ 2.5, h2 ≈ 300 m) than 12 h earlier, but with the same downstream speed (V2 ≈ 24 m s−1). These modeled values again agree well with hydraulic predictions in terms of Froude number and layer depth but produce a faster flow field. Similar to the onshore shift in flow direction shown here, Samelson (1992) oriented the large-scale pressure gradient parallel to the coast downstream rather than upstream of the bend. He reported weaker acceleration in his shallow-water expansion fan, while here, based upon minimum/maximum values within the expansion fan, we find that at the mass field responds to a reduction in curvature rather than the momentum field.

Although the acceleration around Cape Blanco remains nearly constant during the day, the location of the wind maximum shifts to the north and closer to the coast. As found by Burk and Thompson (1996), we obtain a similar diurnal movement of the MABL wind maximum: offshore during the night and nearshore during peak heating. Thus, in terms of Froude number, the Cape Blanco expansion fan obtains its largest magnitude and downwind extent during the nighttime as the offshore land breeze creates greater flow curvature around the cape. Conversely, the expansion fan weakens and contracts during the day as the flow curvature around Cape Blanco is reduced by the onshore sea-breeze flow.

The diurnal shift in streamline orientation, schematically drawn in Fig. 16, occurs on each of the three days studied. Note that while the flow curvature around Cape Blanco lessens in the afternoon, the flow north of Cape Mendocino becomes more strongly blocked and deflected. Thus, the flow curvature around this cape increases during the afternoon behaving in the opposite sense as that around Cape Blanco. The June 1996 diurnal trends in wind speed and direction at several buoys are shown in Fig. 17. These measurements also indicate substantial diurnal variability that supports the model trends in the low-level wind field. Near 1200 UTC, buoy wind speeds tend to be a minimum except at buoy 30 offshore of Cape Mendocino where it peaks at night. Moreover, the wind direction at buoy 30 remains northerly during the day while it becomes more westerly at all the other nearshore locations. This diurnal shift in low-level winds impact the turning angles around the two coastal capes, and although data from a few buoys is far from conclusive, the deviations at buoy 30 provides some support for the nocturnal enlargement of the Cape Blanco expansion fan.

Fig. 16.

Schematic depiction of the diurnal variation in the Cape Blanco expansion fan (shading), MABL streamlines (solid lines), and compression jump (dotted lines) at 1200 (dark, bold) and 0000 UTC (light, thin) around Cape Blanco and Cape Mendocino. The expansion fan contracts between 1200 and 0000 UTC.

Fig. 16.

Schematic depiction of the diurnal variation in the Cape Blanco expansion fan (shading), MABL streamlines (solid lines), and compression jump (dotted lines) at 1200 (dark, bold) and 0000 UTC (light, thin) around Cape Blanco and Cape Mendocino. The expansion fan contracts between 1200 and 0000 UTC.

Fig. 17.

Jun 1996 diurnal trend in (a) wind speed (m s−1) and (b) direction (°, positive angles are east of north and negative angles are west or north) at five nearshore buoy locations shown in Fig. 2.

Fig. 17.

Jun 1996 diurnal trend in (a) wind speed (m s−1) and (b) direction (°, positive angles are east of north and negative angles are west or north) at five nearshore buoy locations shown in Fig. 2.

The expansion fan downwind of Cape Mendocino does not exhibit nearly as much diurnal variability as does the Cape Blanco expansion fan, despite substantial variation in upstream conditions. The shape and magnitude of the enhanced region of supercritical flow in the lee of Cape Mendocino (Fr = 1.5 contour; Fig. 15) and the character of the marine layer (Fig. 14) in this region remain relatively unchanged throughout the forecast. Because the upstream marine layer is dramatically altered in addition to the upstream Froude number, the response south of Cape Mendocino differs from the idealized simulations in which upstream Froude number was controlled solely by changing the inversion strength. A deeper, slower upstream MABL at 0000 UTC offsets the effect of the increase in flow curvature to cause a nearly constant expansion fan around Cape Mendocino over the 12-h period. Hence, the diurnal shift in flow direction is again found to be a major contributor in the expansion fan response south of this cape.

While the Cape Blanco expansion fan diminishes both in size and magnitude and the Cape Mendocino fan remains relatively unchanged, an expanding area of subcritical flow (Fr < 1.0) develops upwind of Cape Mendocino (Fig. 15c) during the 12-h period. This subcritical regime forms by the abrupt lifting and deceleration of the MABL associated with the compression jump that emanates from the blocking terrain north of Cape Mendocino. The vertical structure of this jump is shown in Fig. 18 by cross sections of potential temperature (contoured) and wind speed (shaded) taken through Cape Mendocino along path A–B shown in Fig. 2. MABL characteristics are sharply altered ∼50–75 km upwind of the cape where wind speeds near the middle of the layer decrease as much as 15 m s−1 and layer depths rise over 400 m. Over and downwind of the cape, mountain gravity wave activity is also apparent in the cross sections with strong localized leeside subsidence. As is evident in the 296-K isopleth, this effect also varies diurnally but is largely confined to a narrow zone ∼10 km downwind of the coastline.

Fig. 18.

The 12 Jun 1996 COAMPS grid 3 (a) initial 1200 UTC, (b) 6-h forecast valid 1800 UTC, and (c) 12-h forecast valid 0000 UTC cross sections of potential temperature (K, contoured) and wind speed (m s−1, shaded). Cross-section location A–B is shown in Fig. 2. The hatching indicates terrain.

Fig. 18.

The 12 Jun 1996 COAMPS grid 3 (a) initial 1200 UTC, (b) 6-h forecast valid 1800 UTC, and (c) 12-h forecast valid 0000 UTC cross sections of potential temperature (K, contoured) and wind speed (m s−1, shaded). Cross-section location A–B is shown in Fig. 2. The hatching indicates terrain.

In response to diurnal changes within the Cape Blanco expansion fan, the compression jump also undergoes dramatic variation. The position and shape of this jump, as well as the changing character of the Cape Blanco expansion fan, are schematically depicted in Fig. 16 at 1200 and 0000 UTC. Between 1200 and 1800 UTC the MABL deepens substantially just north of Cape Mendocino, and from 1800 to 0000 UTC the shock moves upstream nearly doubling the size of the subcritical regime in its wake. Over short spatial scales where Coriolis turning can be neglected, the modeled jump feature can be described approximately from shallow-water hydrodynamics using the diagrams of Fig. 9. We estimate ϕ for concave bends from the topographic bend angle with respect to the direction of the incoming flow. In this case, the angle of the streamlines to the Cape Mendocino headlands is ϕ ≈ 30° and a maximum value of the Froude number in the Cape Blanco expansion fan is Fr1 ≈ 3.0 at 1200 UTC. Thus, Fig. 9a indicates that a shock angle of β ≈ 57° is to be expected. From Fig. 9c, these values of Fr1 and ϕ yield a downwind Froude number, Fr2 ≈ 1.1. Finally, using the upwind and downwind Froude numbers Fr1 and Fr2 in Fig. 9d, one obtains a shock strength of h2/h1 ≈ 3.0.

Although strictly appropriate for shallow-water channel flow, these hydrodynamics characteristics closely approximate the jump simulated by the model at 1200 UTC. The linear region of decelerated, elevated flow north of Cape Mendocino is oriented at about 55° to the upwind streamlines (dotted line in Fig. 14a). This region corresponds to a downwind Froude number in the range 1.0–1.5, in good agreement with the hydrodynamics prediction. The strength of the jump forecast by COAMPS is estimated from Fig. 18a using the 288-K isopleth. Although admittedly only a rough estimate, a modeled shock strength of h2/h1 ≈ 550 m/175 m ≈ 3.1 is obtained, very near the computed value from Fig. 9d.

Between 1200 and 1800 UTC, the maximum Froude number in the Cape Blanco expansion fan decreases to Fr1 ≈ 2.5. For ϕ ≈ 30°, values of Fr1 > 2.5 are required to maintain an attached shock. In this case since the incoming Froude number is still supercritical, the shock becomes detached. Note the curved transition region north of Cape Mendocino in Fig. 14b oriented at 90° to the flow direction near the coast (dotted line). The jump extends more than 50 km offshore where it attains an orientation well represented by the Mach angle α = sin−1(1/2.5) ≈ 25°. On the northern flank of Cape Mendocino in Fig. 15b, Froude numbers are near 1.0 and the shock strength has diminished slightly from its 1200 UTC value (Fig. 18).

By 0000 UTC, Froude numbers in the Cape Blanco expansion fan continue to decrease and the curved, detached shock propagates nearly 50 km to the north. The region of subcritical flow has expanded well upwind, while the shock strength continues to weaken. During the 12-h period, layer depths along the coast increase about 200 m with the greatest deepening occurring behind the compression jump. The grid 3 horizontal distribution of integrated cloud liquid water shown in Fig. 19 valid 1200, 1800, and 0000 UTC indicates that this area is a preferential region of enhanced stratus and marine fog. The modeled cloud cover at 1800 UTC is quite consistent with that shown in the GOES-9 visible satellite image (Fig. 5b) taken at nearly the same time. The model also predicts clear regions in both of the expansion fans throughout the forecast in conjunction with the areas of lowest inversion height.

Fig. 19.

As in Fig. 14 except for integrated cloud liquid water (kg m−2).

Fig. 19.

As in Fig. 14 except for integrated cloud liquid water (kg m−2).

b. Sensitivity tests

In this section the results of two sensitivity tests are described. In the first test, S1, the impact of diurnal forcing on coastal MABL dynamics including the interaction of supercritical flow between the two major capes is investigated. This test is accomplished by holding the sea–ground surface temperatures (Tsfc) fixed at their 1200 UTC (0500 LST) distribution throughout the 12-h forecast. This time was selected because the land–sea temperature contrast is small. In the second test, S2, the Cape Mendocino terrain is eliminated to determine the extent to which the blocking is able to influence upwind marine layer conditions. These sensitivity tests are performed only on the 12 June case.

For sensitivity test S1, contours of marine layer averaged wind speed and 185-m streamlines are shown in Fig. 20a valid 0000 UTC 13 June 1996. During this simulation, marine layer wind speed patterns remain generally unchanged from the 1200 UTC field (Fig. 14a). The wind speed maximum south of Cape Blanco has the same magnitude and long downwind footprint at 0000 UTC as it did at 1200 UTC that strongly impacts the concave bend at Cape Mendocino. In contrast to the control at 0000 UTC, the Cape Blanco expansion fan does not contract to the north or shift nearer to the coastline in S1. Since it is absent here, we conclude that the contraction of the Cape Blanco speed maximum in the control run is dependent upon the diurnal variation in baroclinic forcing. This diurnally varying MABL adjustment in turn affects the supercritical flow response along the blocking orography of Cape Mendocino.

Fig. 20.

Marine layer averaged wind speed (m s−1) and 185-m streamlines valid 0000 UTC 13 Jun 1996 for (a) sensitivity test S1, ground temperatures held constant at the 1200 UTC value, and (b) sensitivity test S2, Cape Mendocino removed and coastline straightened as shown by the dotted line in Fig. 2.

Fig. 20.

Marine layer averaged wind speed (m s−1) and 185-m streamlines valid 0000 UTC 13 Jun 1996 for (a) sensitivity test S1, ground temperatures held constant at the 1200 UTC value, and (b) sensitivity test S2, Cape Mendocino removed and coastline straightened as shown by the dotted line in Fig. 2.

Since both the shape and magnitude of the Cape Blanco expansion fan are altered by elimination of the diurnal wave, so is the nature of the flow interaction with Cape Mendocino and the resultant compression jump north of the cape. The expansion fan does not diminish in strength and thereby allow the upwind movement of the jump as occurred in the control (Fig. 14c). The sharp transition in MABL winds associated with the jump remains hugging the terrain north of Cape Mendocino. These results suggest that diurnal forcing significantly modulates MABL responses along the coast, as well as supercritical flow interaction between closely spaced capes.

In sensitivity test S2, to further investigate the impact of the blocking effect of Cape Mendocino on the Cape Blanco expansion fan, the Cape Mendocino terrain is removed west of the dotted line drawn in Fig 2, replacing it with water of the same temperature as that surrounding the cape. The coastline is made linear from north of Rocky Point to Shelter Cove. The MABL fields for S2 are generated from a 24-h forecast beginning 0000 UTC 12 June 1996, 12 h earlier than the control run to allow the marine layer adequate time to adjust to the elimination of the cape. In this test, ground temperatures evolve through their normal diurnal cycle.

Figure 20b shows contours of marine layer averaged wind speed and 185-m streamlines valid 0000 UTC 13 June 1996 for sensitivity test S2. The areal extent of marine layer acceleration south of Cape Blanco, indicated by the 20 m s−1 contour, extends south of 40° latitude to a distance ∼100 km farther than in the control simulation and through the region that comprises the Cape Mendocino terrain in the control. Hence when the blocking orography of Cape Mendocino is present, the supercritical flow around Cape Blanco, as modified by both diurnal and synoptic forcing, directly interacts with the topographic protrusion. As in the control run, diurnal effects cause the onshore shift in flow orientation around Cape Blanco, and the contraction and movement of the speed maximum to the north and nearer to the coast. Additionally, some topographic blocking occurs along the coastal barrier despite the absence of Cape Mendocino due to the impact of the onshore sea breeze. For this reason, flow deceleration is still present in S2 along the coast. However, more noteworthy are the southerly extent of the Cape Blanco expansion fan and the absence of the diurnally varying compression jump when Cape Mendocino is eliminated from the coastal orography.

The results of the sensitivity tests and the control run are summarized in Fig. 21. This figure shows time series from 1200 to 0000 UTC of Froude number, MABL-averaged wind speed, and depth at the point north of Cape Mendocino indicated by the asterisk in Fig. 2. After ∼1800 UTC, the advancement of the compression wave north of the cape causes the marine layer to deepen and slow in the control, while considerably less temporal changes occur in the two sensitivity tests. Note also that without diurnal forcing or a blocking terrain feature, the Froude number stays near 2.0, but rapidly approaches unity after ∼2000 UTC in the control. Hence, the combined influences of supercritical flow dynamics modulated by the diurnally varying sea breeze promote the movement of the compression wave.

Fig. 21.

Time series from 1200 to 0000 UTC 12 Jun 1996 of (a) Froude number, (b) marine layer averaged wind speed (m s−1), and (c) depth (m) at the point denoted by the asterisk in Fig. 2 for the control (solid line), sensitivity test S1 (dashed line), and sensitivity test S2 (triangles).

Fig. 21.

Time series from 1200 to 0000 UTC 12 Jun 1996 of (a) Froude number, (b) marine layer averaged wind speed (m s−1), and (c) depth (m) at the point denoted by the asterisk in Fig. 2 for the control (solid line), sensitivity test S1 (dashed line), and sensitivity test S2 (triangles).

6. Discussion and conclusions

In this paper we have extended the earlier modeling studies of marine layer flow along a varying lateral barrier by contrasting supercritical and transcritical flow phenomena in idealized settings and then investigating real-data MABL responses along complex orographic coastlines. The idealized simulations, performed with the U.S. Navy’s mesoscale model COAMPS, reveal a quite different MABL character about a convex turning coastline for supercritical versus transcritical upstream conditions. As expected from hydrodynamics theory, the thinning and acceleration of the MABL follow a narrower Mach angle in the supercritical case and the MABL develops greater accelerations in the transcritical case. Moreover, the influence of turbulent viscosity and upper-level stratification produces a marine layer response that agrees well with simple hydrodynamics theory in terms of layer depth but tends to produce faster speeds. This additional MABL acceleration is generated by an enhancement to the local pressure gradient induced by the stratification and baroclinicity aloft.

Real-data COAMPS forecasts are performed on three days during the CW96 field experiment conducted off the U.S. west coast during the months of June and July 1996. Validation of the modeled MABL structure is accomplished through comparison with aircraft transects, buoy and surface station observations, and satellite imagery that provide quite good agreement in the coastal zone. These real-data studies contain an inner grid of horizontal resolution Δx = 5 km that is centered over the coast in northern California to simulate the MABL responses between closely space topographic features. Cape Blanco and Cape Mendocino are situated ∼250 km apart and represent a complex of bend angles embedded within steep, blocking coastal terrain. From modeling results produced by the differing atmospheric conditions on the three days in June–July, and from two sensitivity tests, we determine the affects of diurnal forcing on the supercritical flow response between the two capes, and the degree of blocking imposed on the MABL by Cape Mendocino.

The blocking associated with the concave bend creates a compression jump whose character is highly dependent upon upwind conditions. These upwind conditions are established by the expansion fan around Cape Blanco that varies substantially over the 12-h period between 1200 and 0000 UTC. The downwind footprint and the strength of the Cape Blanco expansion fan, as measured by the change in Froude number around the bend, is greatest during the early morning hours and lessens during the day as thermal forcing enhances onshore flow and reduces the effective turning angle around the bend. From hydrodynamics theory, a smaller turning angle produces a weaker response. Thus, we find that the orientation of the streamlines within the marine layer, rather than the topographic bend angle itself, more accurately describes the MABL’s supercritical response expected from hydrodynamics theory.

The reduction in Cape Blanco’s expansion fan Froude number during the period causes the attached, oblique shock north of Cape Mendocino at 1200 UTC to become detached and curved by 1800 UTC, and to move ∼40 km upwind by 0000 UTC. The modeled behavior, as well as the character of the shock, agrees with the theory. Comparison to the values obtained from the hydrodynamic integration diagrams of Ippen (1951) indicates reasonable agreement in shock strength, shock orientation, and downwind Froude number at 1200 UTC when the modeled compression jump is attached.

The first sensitivity test, S1, reveals that without the diurnal heating cycle the Cape Blanco expansion fan remains strong throughout the period and the compression jump remains close to the terrain. Sensitivity test S2 shows that without the blocking orography of Cape Mendocino, while diurnal forcing still causes a shift in maximum winds to the north and close to shore, the downwind footprint of the Cape Blanco expansion fan extends ∼150 km farther than in the control.

Burk and Haack (2000) show how supercritical flow in an expansion fan, coupled with a sea breeze, interacts with blocking orography to produce a striking, cloud-topped undular bore. Such flow interaction is similar to that observed and modeled along the Cape Blanco–Cape Mendocino orographic complex. This interaction demonstrates the supercritical flow responses about closely spaced coastal bends cannot be analyzed by independently modeling the effect upon the MABL of each bend separately.

Acknowledgments

The NRL team development of COAMPS, led by Drs. Richard Hodur and James Doyle, was vital to this study. Observational data were kindly provided by Richard Lind of the Naval Postgraduate School and the creators of the CW96 Web site: http://penarth.ucsd.edu/cw96/cw96_prop_rev.htm including Drs. Linda Ström and Ian Brooks. Constructive comments by the three reviewers were very helpful. This work was supported by the Office of Naval Research, Program Element 0601153N.

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Footnotes

Corresponding author address: Tracy Haack, Marine Meteorology Division, Naval Research Laboratory, 7 Grace Hopper Ave., Monterey, CA 93943-5502.