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Don L. Boyer and Xiuzhang Zhang

Abstract

With the aim of developing increasingly realistic physical models of the interaction of ocean currents with isolated seamounts, laboratory experiments concerning the flow of an oscillatory current past a cosine-squared body of revolution in the presence of background rotation and stratification are considered. The pertinent parameters governing the motion are the Rossby, temporal Rossby, Burger and Ekman numbers, the ratio of the magnitude of the oscillatory velocity component to the mean current and various geometrical parameters. With the exception that the present experiments distort the vertical coordinate, the studies are conducted in regions of parameter space of relevance to the real ocean; future communications will investigate relatively undistorted geometries.

The experiments demonstrate that three fundamentally different flow regimes can be identified and that these are highly sensitive to the value of the Rossby number, Ro. These include, (i) at low Ro a regime in which the flow is fully attached to the obstacle for all phases of the flow cycle, (ii) at moderate Ro a regime in which eddies are attached to the lee side of the topographic feature and, (iii) at high Ro flows in which eddies are shed from the obstacle. Various flow regime diagrams are presented.

Emphasis is given to those aspects of the motion that are related to the unsteady nature of the free stream current. For example, for sufficiently small Rossby numbers, it is shown that fluid parcels advecting over the top of the obstacle exhibit anticyclonic loops similar to those observed recently for diurnal tidal flow past Fieberling Guyot.

Quantitative measures of the size of the leeside bubble region for the attached leeside eddies flow regime, eddy separation distances for the eddy shedding regime, particle residence times for fluid parcels advecting over the topography and upwelling and downwelling measures on the upstream side of the obstacle are presented as functions of the various system parameters.

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Xiuzhang Zhang and Don L. Boyer

Abstract

Pure oscillatory flow of a rotating, linearly stratified fluid in the vicinity of an isolated topography of revolution is considered in the laboratory. The pertinent dimensionless parameters governing the motion are the Rossby (Ro), temporal Rossby (Rot), Burger (S), and Ekman (E) numbers and geometrical length-scale ratios. Experiments are considered for fixed S, E and geometry and ranges of Ro and Rot given by 0.003 ≤ Ro ≤ 0.03 and 0.2 ≤ Rot ≤ 2.4. A Rot against Ro regime diagram is developed, which includes the following flow classifications: (i) attached flow (AF), (ii) tidal oscillation loops (TOL), (iii) trapped waves-anticyclonic/cyclonic residual current (WAC), (iv) trapped waves-anticyclonic residual current (WA), (v) attached eddies (AE), and (vi) vortex shedding (VS).

For all flow regimes a rectified mean anticyclonic motion is observed in the vicinity of the topography. For superinertial frequencies (i.e., Rot > 1), a resonance phenomenon enhances the streamwise speed near the obstacle well beyond the corresponding velocity in the undisturbed flow; this flow enhancement is strongest at levels above the summit of the obstacle. The resonance phenomenon, as evidenced by the streamwise and cross-stream sizes of the observed tidal oscillation loops normalized with the undisturbed tidal displacement, is quantified at various streamwise locations for a series of experiments with fixed geometry, Ro=0.013, S=1.0, and various Ro, in the range 0.6≤ Rot≤2.4. These experiments demonstrate amplification peaks near Rot∼1.0 and 2.0. For subinertial frequencies (i.e., Rot < 1), the rectified flow is bottom trapped in the sense that the mean anticyclonic flow is strongest near the obstacle and decreases at higher elevations. The laboratory observations are shown to depict some of the qualitative aspects of recent observations of oceanic motions in the vicinity of Fieberling Guyot; in particular, upper-level enhancement of superinertial components and bottom trapping of subinertial ones.

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Don L. Boyer and Lijun Tao

Abstract

This study is an experimental investigation of impulsively started, linearly stratified flow over long ridges of triangular and cosine-squared cross sections. The experiments employ a rigid-lid boundary confining the fluid from above. Emphasis is given to the temporal development, as well as to the fully established character of the wake. Both qualitative and quantitative measures of the characteristics of the flow are introduced and thew are studied for a wide range of the system parameters, which include the internal Froude number, F i Reynolds number, Re ridge height to width ratio, G> d and ridge height to fluid depth ratio, G h

The governing equations for the laboratory experiments are related to those of the atmosphere. Flow regime diagrams based on the mode of the vertical wave structure are presented and the relationship of the observations to linear theory discussed. For the lowest vertical wave mode the constant phase lines of the Ice waves have a vertical slope implying total reflection of the waves by the rigid lid. At higher wave modes the constant phase lines slope upstream, indicating that some of the upward propagating momentum flux is absorbed by the lid. Experiments are presented for certain ranges of dimensionless parameter space which show the lee wave field breaking into turbulence and in certain cases subsequently relarminarizing.

Observables in the tee wave pattern are introduced, including a normalized wavelength, λ/D, and wave amplitude, a/hdimensioniess downstream distance to which significant oscillatory motion in the wake occurs, L/D, and a normalized vertical location of the principal rotor, z r/h, and measurements of these for a range of system parameters are presented.

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Xiuzhang Zhang and Don L. Boyer

Abstract

A laboratory study has been conducted on the deflection of steady and oscillatory free stream currents impinging on two model seamounts of identical shape. The laboratory model includes the effects of background rotation (f-plane) and stratification (linear). The flows are generated by towing obstacles through a fluid medium that is otherwise at rest with respect to an observer fixed with the rotating frame. The system behavior is investigated as a function of the normalized obstacle separation distance, G = G */D, and angle, θ between the line connecting the obstacle centers and the free-stream direction; here G * is the obstacle center-to-center separation distance and D is the base width of one of the obstacles. The temporal Rossby (for oscillatory cases), Burger, and Ekman numbers and the remaining geometrical parameters are fixed for all of the experiments; characteristic flow variations with the Rossby number, R 0, are investigated.

For the ranges of parameters considered, two characteristic flows are observed with the particular details of the motions depending strongly on G and θ. The first, generally occurring at small R 0, is an attached leeside eddy regime in which eddies are attached to the lee of the topographic features and for which the general flow field is steady. The second, at higher R 0, is an eddy-shedding regime in which eddy structures are periodically formed in the vicinity of the obstacles and shed downstream. Some comments are made on the possible importance of the flow in the vicinity of Fieberling Guyot as it might be affected by its neighbors Fieberling II Seamount and Hoke Guyot.

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Don L. Boyer and Rui-Rong Chen

Abstract

An analysis concerning the modelling of large-scale atmospheric motions past orographic features in a linearly stratified rotating laboratory experiment is conducted; it is concluded that for an ƒ-plane model the similarity criteria include. matching the Rossby, Burger and Ekman numbers as well as a mountain height function normalized on the fluid depth. The fluid depth to topographic width parameter is not of zeroth order importance, and this allows for the use of distorted laboratory topographies; i.e., the laboratory model can employ exaggerated vertical to horizontal length scale ratios.

Experiments are conducted for the westerly f-plane flow over a model of the Rocky Mountains for a range of parameters appropriate for the atmosphere. Horizontal streamline patterns at various depths and at ranges of the system parameters are presented and analyzed quantitatively. The experiments demonstrate ~ qualitative agreement concerning the ridge over the mountain, the downstream trough to the ease of the mountains, and the general orientation of the ridge and trough. The experiments also show that relative to an observer moving with the mean wind, a closed cyclonic eddy is found to the southeast of the central portion of the mountains. This cyclonic disturbance is located and farther to the northeast as the Rossby number is increased. Furthemore, a stationary anticyclonic vortex is located along the crest just to the north of the mountain center, the location of this anticyclone is relatively insensitive to the Rossby number.

Experiments are also presented for vertical cross-section motions in the southern. central and northern regions of the model. These demonstrate the nature of the wake pattern, especially the vertical motion field Finally, experiments concerning the eastward advection of a trough with a cut-off low over the central portions of the model am presented. These show a weak northeasterly drift of the cut-off low upstream of the mountains and a sharp veer to the south on passing the mountain crest; the core of the cut-off low accelerates in passing over the mountains and then decelerates in the lee. These laboratory results are qualitatively similar to atmospheric observations of the advection of cut-off low across the Rocky Mountains.

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Don L. Boyer and Rui-Rong Chen

Abstract

The dimensionless governing equations and boundary conditions for the atmosphere are compared with those for a linearly stratified rotating dishpan laboratory experiment; by doing so a set of similarity criteria are determined. Model experiments on the effects of Greenland, the Rocky Mountains and Tibet on a uniform shear zonal flow in the Northern Hemisphere are presented. The laboratory model qualitatively simulates such semipermanent features of the Northern Hemisphere circulation as the Aleutian and Icelandic lows, the ridgesand troughs in the vicinity of the Rocky Mountains and Tibet and the shedding of the "southwest eddy" in the lee of Tibet.

Although the background flow is steady, the large-scale disturbances caused by the mountains are unsteady and have an inherent periodicity equal to the time required for a fluid parcel to make a single 'circuit around the dishpan (globe). The strengths of the Aleutian and Icelandic lows, for example, oscillate with this Iiod; the lows are out of phase in the sense that when one is weak the other is strong and vice versa. A number of other correlations between various regions of the flow field are also noted.

Removal of the model of Tibet does not greatly affect ihe qualitative nature of the general flow pattern. For example, the Aleutian and Icelandic lows remain as distinct entities, although their strengths and locations are altered somewhat, and the general character of the flow in the vicinity of the Rocky Mountains remains essentially unchanged. On the other hand, removal of the Rocky Mountains eliminates the Aleutian and Icelandic lows as separate entities. The joint effect ofthe Rocky Mountains and Tibet is to deflect the streamlines in the higherlatitudes toward the north, thus causing deeper Aleutian and Icelandic lows and locations of these features which are more similar to observations in the atmosphere than if either of these features is absent. The experiments show in a quite straightforward fashion the important effects mountains have on the formation of some of the semipermanent features of the Northern Hemisphere.

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Don L. Boyer, Dale B. Haidvogel, and Nicolas Pérenne

Abstract

An integrated set of laboratory and numerical-model experiments has been conducted to understand the development of residual circulation surrounding a coastal canyon and to explore further the degree to which laboratory experiments can provide useful benchmark datasets for numerical models of the coastal ocean. The use of an idealized shear-stress boundary condition along the coastal floor in the numerical model gives good quantitative agreement with the laboratory results for the zeroth-order, time-dependent flow and good qualitative agreement for the higher-order [i.e., O(Ro), where Ro (the Rossby number) is small] time-mean flow. The quantitative agreement for the latter, however, is not within estimates of laboratory uncertainties. It is shown that the use of a no-slip condition along the floor improves the model away from the canyon boundaries, but the enhanced viscosities needed to obtain numerical stability give boundary layers that are too wide along the coastline. The laboratory and numerical-model results are used to investigate the trends of a number of flow diagnostics with changes in the governing parameters. A scaling argument to estimate the characteristic strength of the horizontal component of the time-mean or residual velocity U1 leads to the relation U1/u 0 ∼ [Ro(h S/ h D)−1 Ro−1tBu−1/2Ek−1/2], where u 0 is the amplitude of the oscillatory background flow at the shelfbreak level, (h S/h D) is the ratio of the depth of the shelf to that of the deep ocean, Rot is the temporal Rossby number, Bu is the Burger number, and Ek is the Ekman number. Laboratory and numerical data support this scaling. The model-to-model comparisons indicate that, for the range of parameters investigated, upwelling dominates the residual flow patterns in the vicinity of the shelf break and above. This study supports the notion that a closely coupled laboratory–numerical model investigation can lead to results that are more reliable than those obtained by either approach alone.

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Nicolas Pérenne, Dale B. Haidvogel, and Don L. Boyer

Abstract

Different modeling approaches are applied to the same geophysical flow in order to assess the ability of laboratory models to provide useful benchmarks in the development of oceanic numerical models. The test case considered here—that of the flow driven by an oscillatory forcing over a submarine canyon—involves background rotation, density stratification, and steep topography. Velocity fields measured by particle-tracking velocimetry and time series of density fluctuations are directly compared to the corresponding outputs from a high-order finite-element numerical ocean model.

Quantitative comparison of the laboratory and numerical models shows good overall agreement in the structure and magnitude of the strongest residual currents, which occur at the level of the shelf break in the configuration presented here. The associated residual vorticity field is also structurally consistent between the two models, although the residual divergence is not. Residual currents higher up and lower down in the water column are weaker than at the shelf break, and the agreement between the laboratory and numerical models is less good at these levels, possibly indicative of the controlling influence of the surface and bottom boundary layers.

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Rui-Rong Chen, Don L. Boyer, and Lijun Tao

Abstract

Laboratory experiments concerned with surface cooling, were conducted to simulate the surface wind patterns and the free atmosphere general circulation in the vicinity of Antarctica. The principal dynamical similarity parameter is shown to be ROT/S, where RoT is the thermal Rossby number and S the Burger number. At parameter values appropriate to the atmosphere, the physical model experiments led to a surface drainage flow and an accompanying polar cyclone that had characteristics similar to atmospheric observations. The simulated polar cyclone contained two low centers and planetary wavelike structures. The interior streamlines near the cyclone centers tended to follow the continental height contours. In the laboratory simulations, eastward-propagating wave troughs were periodically generated in the vicinity of 110°E and developed maximum strengths in the vicinity of the Ross Ice Shelf at 160°W before dissipating by 70°W. Jets in the polar cyclone were observed over regions of the model Antarctic continent having large slope. The boundary drainage flows spread out from the interior of the continent and concentrated in several valleys leading to the oceans. On approaching the model ocean, the drainage flows tended to move around the edge of the continent in an anticlockwise pattern (i.e., an anticyclone) with anticyclonic spiral tongues spreading to the surrounding ocean regions. Experiments conducted by varying RoT and S, while fixing RoT/S, demonstrated that the strength and areal extent of the polar cyclone do not vary greatly in what is in effect a change of season. The results demonstrated that the thermal forcing of the Antarctic continent and the unique nature of the Antarctic orography are important features in determining the principal characteristics of the continental surface winds and the general circulation of the high-latitude Southern Hemisphere atmosphere.

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Jacques Verron, Dominique Renouard, Gabriel Chabert D'Hieres, Thong Nguyen, Henri Didelle, and Don L. Boyer

Abstract

Alongshore oscillatory flows over an elongated topographic feature next to a vertical wall for a homogeneous, rotating fluid were investigated by means of numerical and laboratory experiments. The physical experiments were conducted in the Grenoble 13-m diameter rotating tank, in which an elongated obstacle of limited longitudinal extent was placed along the vertical sidewall. The background oscillating motion was obtained by periodically varying the platform angular velocity. Fluid motions were visualized and quantified by direct velocity measurements and particle tracking. The numerical model employed was a tridimensional model developed by Haidvogel et al. It consists of the traditional primitive equations, that is, the Navier-Stokes equations for a rotating fluid with the addition of the hydrostatic, Boussinesq, and incompressibility approximations. (The experiments described here employ the homogeneous version.) The numerical formulation uses finite differences in the horizontal and spectral representation in the vertical dimensions.

Both the laboratory and numerical experiments show that in the range of dimensionless parameters considered, two distinct flow regimes, based on general properties of the rectified flow patterns observed, can be defined. It is further shown that the flow regime designation depends principally on the magnitude of the temporal Rossby number, Rot, defined as the ratio of the flow oscillation to the background rotation frequency. Good qualitative and quantitative agreement is found between the laboratory experiments and the numerical model for such observables as the spatial distribution of rectified flow patterns. Several other flow observables are defined and their relation with the system parameters delineated.

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