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Christoph Schär
and
Dale R. Durran

Abstract

The flow of a nonrotating atmosphere with uniform stratification and wind speed past an isolated three-dimensional topographic obstacle is investigated with a nonhydrostatic numerical model having a free-slip lower boundary. When the mountain is sufficiently high, the transient development of a quasi-steady flow occurs in two phases. During the first phase, which occurs over a dimensionless time of O(1), the flow is essentially inviscid and adiabatic, and potential vorticity (PV) is conserved. The transient evolution of the flow during the second phase, which occurs over a dimensionless time of O(10) to O(100), is controlled by dissipation and is accompanied by the generation of PV anomalies.

Two cases are examined in which the flow is forced to remain left–right symmetric with respect to the axis of the incident flow. In the first, the dimensionless mountain height NH/U is 1.5, and gravity waves break over the mountain. In the second, NH/U = 3, and a quasi-steady recirculating wake containing a doublet of positive and negative vortices develops in the lee. In both cases potential vorticity anomalies are generated by dissipation, although the sources of dissipation are different in each case. The net effect of the dissipation on the PV budget is, nevertheless, similar as may be understood from the generalized Bernoulli theorem that equates the generation of potential vorticity fluxes to the development of a Bernoulli function gradient on quasi-steady isentropic surfaces. In these experiments a Bernoulli deficit develops either from strong localized dissipation in the wave-breaking region (dominant for NH/U = 1.5), or as the result of weak dissipation throughout the elongated wake (dominant for NH/U = 3).

Oscillating von Kármán vortex streets appear if the flows are allowed to develop asymmetries with respect to the axis of the incident flow. It is shown that the transition into the vortex shedding regime is associated with an absolute instability of the symmetrical wake, which feeds upon the shear present at the edges of the wake. The most unstable global normal mode is diagnosed numerically and shows strong similarities with the corresponding mode in shallow-water theory. The doubling time of the instability is a few hours, which is consistent with the rapid formation of observed atmospheric vortex streets. The individual vortices in the fully developed vortex street are quasi-balanced warm-core vortices that are associated with both PV and surface potential temperature anomalies.

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Louisa B. Nance
and
Dale R. Durran

Abstract

The generation of nonstationary trapped mountain lee waves through nonlinear wave dynamics without any concomitant change in the background flow is investigated by conducting two-dimensional mountain wave simulations. These simulations demonstrate that finite-amplitude lee-wave patterns can exhibit temporal variations in local wavelength and amplitude, even when the background flow is perfectly steady. For moderate amplitudes, a nonlinear wave interaction involving the stationary trapped wave and a pair of nonstationary waves appears to be responsible for the development of nonstationary perturbations on the stationary trapped wave. This pair of nonstationary waves consists of a trapped wave and a vertically propagating wave, both having horizontal wavelengths approximately twice that of the stationary trapped wave. As the flow becomes more nonlinear, the nonstationary perturbations involve a wider spectrum of horizontal wavelengths and may dominate the overall wave pattern at wave amplitudes significantly below the threshold required to produce wave breaking. Sensitivity tests in which the wave propagation characteristics of the basic state are modified without changing the horizontal wavelength of the stationary trapped wave indicate these nonstationary perturbations are absent when the background flow does not support nonstationary trapped waves with horizontal wavelengths approximately twice that of the stationary trapped mode. These sensitivity tests also show that a second nonstationary trapped wave can assume the role of the nonstationary vertically propagating wave when the Scorer parameter in the upper layer is reduced below the threshold that will support the vertically propagating wave. In this case, a resonant triad composed of three trapped waves appears to be responsible for the development of nonstationary perturbations.

The simulations suggest that strongly nonlinear wave dynamics can generate a wider range of nonstationary trapped modes than that produced by temporal variations in the background flow. It is suggested that the irregular variations in lee-wave wavelength and amplitude observed in real atmospheric flows and the complex fluctuations above a fixed point that are occasionally found in wind profiler observations of trapped lee waves are more likely to be generated by nonlinear wave dynamics than changes in the background flow.

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James D. Doyle
and
Dale R. Durran

Abstract

The development of rotor flow associated with mountain lee waves is investigated through a series of high-resolution simulations with the nonhydrostatic Coupled Ocean–Atmospheric Mesoscale Prediction System (COAMPS) model using free-slip and no-slip lower boundary conditions. Kinematic considerations suggest that boundary layer separation is a prerequisite for rotor formation. The numerical simulations demonstrate that boundary layer separation is greatly facilitated by the adverse pressure gradients associated with trapped mountain lee waves and that boundary layer processes and lee-wave-induced perturbations interact synergistically to produce low-level rotors. Pairs of otherwise identical free-slip and no-slip simulations show a strong correlation between the strength of the lee-wave-induced pressure gradients in the free-slip simulation and the strength of the reversed flow in the corresponding no-slip simulation.

Mechanical shear in the planetary boundary layer is the primary source of a sheet of horizontal vorticity that is lifted vertically into the lee wave at the separation point and carried, at least in part, into the rotor itself. Numerical experiments show that high shear in the boundary layer can be sustained without rotor development when the atmospheric structure is unfavorable for the formation of trapped lee waves. Although transient rotors can be generated with a free-slip lower boundary, realistic rotors appear to develop only in the presence of surface friction.

In a series of simulations based on observational data, increasing the surface roughness length beyond values typical for a smooth surface (z 0 = 0.01 cm) decreases the rotor strength, although no rotors form when free-slip conditions are imposed at the lower boundary. A second series of simulations based on the same observational data demonstrate that increasing the surface heat flux above the lee slope increases the vertical extent of the rotor circulation and the strength of the turbulence but decreases the magnitude of the reversed rotor flow.

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Daniel J. Kirshbaum
and
Dale R. Durran

Abstract

Radar images and numerical simulations of three shallow convective precipitation events over the Coastal Range in western Oregon are presented. In one of these events, unusually well-defined quasi-stationary banded formations produced large precipitation enhancements in favored locations, while varying degrees of band organization and lighter precipitation accumulations occurred in the other two cases. The difference between the more banded and cellular cases appeared to depend on the vertical shear within the orographic cap cloud and the susceptibility of the flow to convection upstream of the mountain. Numerical simulations showed that the rainbands, which appeared to be shear-parallel convective roll circulations that formed within the unstable orographic cap cloud, developed even over smooth mountains. However, these banded structures were better organized, more stationary, and produced greater precipitation enhancement over mountains with small-scale topographic obstacles. Low-amplitude random topographic roughness elements were found to be just as effective as more prominent subrange-scale peaks at organizing and fixing the location of the orographic rainbands.

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Daniel J. Kirshbaum
and
Dale R. Durran

Abstract

The three-dimensional structure of shallow orographic convection is investigated through simulations performed with a cloud-resolving numerical model. In moist flows that overcome a given topographic barrier to form statically unstable cap clouds, the organization of the convection depends on both the atmospheric structure and the mechanism by which the convection is initiated. Convection initiated by background thermal fluctuations embedded in the flow over a smooth mountain (without any small-scale topographic features) tends to be cellular and disorganized except that shear-parallel bands may form in flows with strong unidirectional vertical shear. The development of well-organized bands is favored when there is weak static instability inside the cloud and when the dry air surrounding the cloud is strongly stable. These bands move with the flow and distribute their cumulative precipitation evenly over the mountain upslope.

Similar shear-parallel bands also develop in flows where convection is initiated by small-scale topographic noise superimposed onto the main mountain profile, but in this case stronger circulations are also triggered that create stationary rainbands parallel to the low-level flow. This second dominant mode, which is less sensitive to the atmospheric structure and the strength of forcing, is triggered by lee waves that form over small-scale topographic bumps near the upstream edge of the main orographic cloud. Due to their stationarity, these flow-parallel bands can produce locally heavy precipitation amounts.

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Saša Gaberšek
and
Dale R. Durran

Abstract

Numerical simulations are conducted of geostrophically balanced flow over an isolated mountain cut by a horizontal gap. The relative importance of the along-gap synoptic-scale pressure gradient and terrain-induced mesoscale circulations for the generation of gap winds was examined by changing the direction of the synoptic-scale wind relative to the topography. In all cases, the forcing associated with mesoscale circulations generated by the mountain was at least as significant as the synoptic-scale pressure gradient. In the cases where a component of the large-scale flow was directed perpendicular to the ridge, the dynamics were dominated by either the vertical momentum fluxes due to mountain lee waves or by mesoscale pressure gradients associated with upstream blocking or lee troughing. Mesoscale circulations were also important when the large-scale flow was parallel to the ridge because surface friction turned the low-level winds toward the high pressure side of the ridge, partially blocking the flow and enhancing the along-gap pressure gradient.

The flow in the interior of a very long uniform gap was also simulated for a case with the synoptic-scale winds parallel to the ridge so that the synoptic-scale pressure gradient was down the gap. The flow in the interior of the long gap was not horizontal and not in a simple dynamical balance between acceleration, the pressure gradient force, and surface friction. Even the flow in the lowest 150 m was gradually subsiding. Subsidence and lateral momentum flux convergence at low levels near the center of the gap were important contributors to the mass and along-gap momentum budgets.

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James D. Doyle
and
Dale R. Durran

Abstract

The internal structure and dynamics of rotors that form in the lee of topographic ridges are explored using a series of high-resolution eddy-resolving numerical simulations. Surface friction generates a sheet of horizontal vorticity along the lee slope that is lifted aloft by the mountain lee wave at the boundary layer separation point. Parallel-shear instability breaks this vortex sheet into small intense vortices or subrotors.

The strength and evolution of the subrotors and the internal structure of the main large-scale rotor are substantially different in 2D and 3D simulations. In 2D, the subrotors are less intense and are ultimately entrained into the larger-scale rotor circulation, where they dissipate and contribute their vorticity toward the maintenance of the main rotor. In 3D, even for flow over a uniform infinitely long barrier, the subrotors are more intense, and primarily are simply swept downstream past the main rotor along the interface between that rotor and the surrounding lee wave. The average vorticity within the interior of the main rotor is much weaker and the flow is more chaotic.

When an isolated peak is added to a 3D ridge, systematic along-ridge velocity perturbations create regions of preferential vortex stretching at the leading edge of the rotor. Subrotors passing through such regions are intensified by stretching and may develop values of the ridge-parallel vorticity component well in excess of those in the parent, shear-generated vortex sheet. Because of their intensity, such subrotor circulations likely pose the greatest hazard to aviation.

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Patrick A. Reinecke
and
Dale R. Durran

Abstract

A parameter widely used to predict topographic flow blocking is the nondimensional mountain height or, synonymously, the inverse Froude number. Predictions using this parameter are based on the morphology of flows with uniform upstream static stability and wind speed, which rarely occur in the real world. The appropriateness of applying this theory in the presence of nontrivial background stability is therefore investigated using a numerical model. Two methods were considered to estimate the low-level stability, averaging the Brunt–Väisälä frequency below the crest and using the bulk change in θ between the ground and crest level.

No single best method emerged for estimating the upstream static stability and thereby mapping the simulations with inversions onto the set of solutions with constant stratification. Instead, the best method depended on the application at hand. To predict the onset of flow stagnation, averaging the low-level stability worked best, while to predict low-level flow diversion the bulk estimate of low-level stability was most appropriate. These results are consistent across a range of inversion thicknesses and strengths. In addition, it is shown that variations in static stability above the mountain crest have little impact on flow blocking.

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Craig C. Epifanio
and
Dale R. Durran

Abstract

Numerical simulations of nonrotating flow with uniform basic wind and stability past long three-dimensional (3D) ridges are compared to the corresponding two-dimensional (2D) limit to reveal the importance of 3D effects. For mountain heights smaller than the threshold for breaking waves, the low-level flow over the interior of the ridge is well described by 2D theory when the horizontal aspect ratio β is roughly 10 or greater. By contrast, in flows with wave breaking significant discrepancies between 2D and 3D results remain apparent even for β = 12.

It is found that the onset of wave breaking and the transition to the high-drag state is accompanied in 3D by an abrupt increase in deflection of the low-level flow around the ridge. The increased flow deflection is produced at least in part by upstream-propagating columnar disturbances forced by the transition to the high-drag state. The deflection of the incident flow reduces the amplitude of the mountain wave aloft relative to 2D and acts as a negative feedback on the surface form drag. As a result, the nonlinear enhancement of the surface drag associated with wave breaking for a ridge with β = 7.5 is found to be roughly half the enhancement obtained for a 2D ridge.

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Dale R. Durran
and
Joseph B. Klemp

Abstract

Numerical mountain wave simulations have documented that intense lee-slope winds frequently arise when wave-overturning occurs above the mountain. Explanations for this amplification process have been proposed by Clark and Peltier in terms of a resonance produced by linear-wave reflections from a self-induced critical layer, and by Smith in terms of solutions to Long's equation for flow beneath a stagnant well-mixed layer. In this paper, we evaluate the predictions of these theories through numerical mountain-wave simulations in which the level of wave-overturning is fixed by a critical layer in the mean flow. The response of the simulated flow to changes in the critical-layer height and the mountain height is in good agreement with Smith's theory. A comparison of Smith's solution with shallow-water theory suggests that the strong lee-slope winds associated with wave-overturning are caused by a continuously stratified analog to the transition from subcritical to supercritical flow in conventional hydraulic theory.

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