scholarly journals Orographic Drag Associated with Lee Waves Trapped at an Inversion

2013 ◽  
Vol 70 (9) ◽  
pp. 2930-2947 ◽  
Author(s):  
Miguel A. C. Teixeira ◽  
José Luis Argaín ◽  
Pedro M. A. Miranda
Keyword(s):  
Numerical Simulations ◽  
Mixed Boundary ◽  
Single Layer ◽  
Temperature Inversion ◽  
Static Stability ◽  
Wave Drag ◽  
Low Level ◽  
Flow Parameters ◽  
Lee Waves ◽  
Lee Wave

Abstract The drag produced by 2D orographic gravity waves trapped at a temperature inversion and waves propagating in the stably stratified layer existing above are explicitly calculated using linear theory, for a two-layer atmosphere with neutral static stability near the surface, mimicking a well-mixed boundary layer. For realistic values of the flow parameters, trapped-lee-wave drag, which is given by a closed analytical expression, is comparable to propagating-wave drag, especially in moderately to strongly nonhydrostatic conditions. In resonant flow, both drag components substantially exceed the single-layer hydrostatic drag estimate used in most parameterization schemes. Both drag components are optimally amplified for a relatively low-level inversion and Froude numbers Fr ≈ 1. While propagating-wave drag is maximized for approximately hydrostatic flow, trapped-lee-wave drag is maximized for l2a = O(1) (where l2 is the Scorer parameter in the stable layer and a is the mountain width). This roughly happens when the horizontal scale of trapped lee waves matches that of the mountain slope. The drag behavior as a function of Fr for l2H = 0.5 (where H is the inversion height) and different values of l2a shows good agreement with numerical simulations. Regions of parameter space with high trapped-lee-wave drag correlate reasonably well with those where lee-wave rotors were found to occur in previous nonlinear numerical simulations including frictional effects. This suggests that trapped-lee-wave drag, besides giving a relevant contribution to low-level drag exerted on the atmosphere, may also be useful to diagnose lee-rotor formation.

Dissipating and reflecting internal waves

2021 ◽  
Author(s):  
Callum J. Shakespeare ◽  
Brian K. Arbic ◽  
Andrew McC. Hogg
Keyword(s):  
Numerical Simulations ◽  
Linear Theory ◽  
Internal Waves ◽  
Energy Flux ◽  
Internal Tide ◽  
Internal Tides ◽  
Linear Wave ◽  
Lee Waves ◽  
Lee Wave ◽  
Upper Boundary

AbstractInternal waves generated at the seafloor propagate through the interior of the ocean, driving mixing where they break and dissipate. However, existing theories only describe these waves in two limiting cases. In one limit, the presence of an upper boundary permits bottom-generated waves to reflect from the ocean surface back to the seafloor, and all the energy flux is at discrete wavenumbers corresponding to resonant modes. In the other limit, waves are strongly dissipated such that they do not interact with the upper boundary and the energy flux is continuous over wavenumber. Here, a novel linear theory is developed for internal tides and lee waves that spans the parameter space in between these two limits. The linear theory is compared with a set of numerical simulations of internal tide and lee wave generation at realistic abyssal hill topography. The linear theory is able to replicate the spatially-averaged kinetic energy and dissipation of even highly non-linear wave fields in the numerical simulations via an appropriate choice of the linear dissipation operator, which represents turbulent wave breaking processes.

Forcing of oceanic mean flows by dissipating internal tides

2012 ◽  
Vol 708 ◽  
pp. 250-278 ◽  
Author(s):  
Nicolas Grisouard ◽  
Oliver Bühler
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Wave Drag ◽  
Perturbation Series ◽  
Internal Tides ◽  
Time Averaging ◽  
Mean Flow ◽  
Wave Source ◽  
Lee Waves ◽  
Lee Wave

AbstractWe present a theoretical and numerical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by the oscillatory flow of a barotropic tide over undulating topography and are also subject to dissipation. This extends the classic lee-wave drag problem of atmospheric wave–mean interaction theory to a more complicated oceanographic setting, because now the steady lee waves are replaced by oscillatory internal tides and, most importantly, because now the three-dimensional oceanic mean flow is defined by time averaging over the fast tidal cycles rather than by the zonal averaging familiar from atmospheric theory. Although the details of our computation are quite different, we recover the main action-at-a-distance result from the atmospheric setting, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, we derive an explicit expression for the effective mean force at leading order using a perturbation series in small wave amplitude within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and then compute the effective mean force numerically in a number of idealized examples with simple topographies.

Lee waves in a stratified flow Part 1. Thin barrier

1968 ◽  
Vol 32 (3) ◽  
pp. 549-567 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Dynamic Pressure ◽  
Separation Of Variables ◽  
Stratified Flow ◽  
Wave Drag ◽  
Variational Approximations ◽  
Lee Waves ◽  
Lee Wave ◽  
Thin Barrier

The lee-wave amplitudes and wave drag for a thin barrier in a two-dimensional stratified flow in which the upstream dynamic pressure and density gradient are constant (Long's model) are determined as functions of barrier height and Froude number for a channel of finite height and for a half-space. Variational approximations to these quantities are obtained and validated by comparison with the earlier results of Drazin & Moore (1967) for the channel and with the results of an exact solution for the half-space, as obtained through separation of variables. An approximate solution of the integral equation for the channel also is obtained through a reduction to a singular integral equation of potential theory. The wave drag tends to increase with decreasing wind speed, but it seems likely that the flow is unstable in the region of high drag. The maximum attainable drag coefficient consistent with stable lee-wave formation appears to be roughly two and almost certainly less than three.

A Procedure For Studying Mountain Effects at Low Levels

1954 ◽  
Vol 35 (9) ◽  
pp. 412-416 ◽  
Author(s):  
Uwe Radok
Keyword(s):  
Temperature Inversion ◽  
Point Of View ◽  
Air Pressure ◽  
The Other ◽  
Lapse Rate ◽  
Temperature Lapse Rate ◽  
Low Level ◽  
Lee Waves ◽  
Low Levels ◽  
Mountainous Country

A representative picture, from the aeronautical point of view, of vertical currents above mountainous country is obtained by letting these currents act on an aircraft set to fly horizontally in still air. Pressure and temperature traces recorded by such an aircraft give the effective vertical velocities and some idea of the temperature lapse rate in the undisturbed stream. Two sets of results are given for illustration. One shows low-level lee waves which were caused presumably by a temperature inversion; the other is a case of strong turbulence side by side with a smooth wave, in which downdrafts reached 1600 ft/min in an 18-knot wind.

Numerical simulations of stratified inviscid flow over a smooth obstacle

1994 ◽  
Vol 260 ◽  
pp. 1-22 ◽  
Author(s):  
Kevin G. Lamb
Keyword(s):  
Numerical Simulations ◽  
Wave Breaking ◽  
Finite Depth ◽  
Inviscid Flow ◽  
Wave Drag ◽  
Experimental Results ◽  
Buoyancy Frequency ◽  
Lee Waves ◽  
Boussinesq Fluid ◽  
Good Agreement

Results of numerical simulations of the flow of a non-rotating, inviscid, Boussinesq fluid over smooth two-dimensional obstacles are described. The fluid has finite depth and a rigid lid. Far upstream of the obstacle the horizontal velocity and buoyancy frequency are uniform. Comparisons with linear theory for small-amplitude obstacles are made and the long-time behaviour is compared with steady-state Long's model solutions. Comparisons with the time-dependent results of Baines (1979) are done. For Froude numbers between ½ and 1 the obstacle amplitude is varied in order to determine the amplitudes needed to initiate wave breaking. These results are compared with the predictions of Long's model and with the experimental results of Baines (1977) showing good agreement with the latter. It is found that wave breaking occurs for amplitudes significantly lower than Long's model predicts for a large range of Froude numbers. This is shown to be the result of the generation of large-amplitude lee waves with wavelengths longer than that of stationary lee waves, but not long enough to propagate upstream. The behaviour of these waves is coupled to the generation of both longer mode-one waves which do propagate upstream from the obstacle and to mode-two waves which propagate against the flow as they are advected downstream. It is also coupled to oscillations in the wave drag. The periods of the wave drag oscillations are compared to experimental results showing good agreement with cases for which oscillations have been observed. The behaviour of these large transient lee waves is compared with the theoretical results contained in Grimshaw & Yi (1991), showing some similarities. As the Froude number approaches 0.5 the breaking behaviour is no longer due to these large waves, with the result that wave breaking occurs much later.

Lee-Wave Resonances over Double Bell-Shaped Obstacles

2009 ◽  
Vol 66 (5) ◽  
pp. 1205-1228 ◽  
Author(s):  
Vanda Grubišić ◽  
Ivana Stiperski
Keyword(s):  
Sierra Nevada ◽  
Lower Boundary ◽  
Vertical Wind Shear ◽  
Separation Distance ◽  
Wave Drag ◽  
Owens Valley ◽  
Lower Boundary Condition ◽  
Atmospheric Structure ◽  
Lee Waves ◽  
Lee Wave

Abstract Lee-wave resonance over double bell-shaped obstacles is investigated through a series of idealized high-resolution numerical simulations with the nonhydrostatic Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) model using a free-slip lower boundary condition. The profiles of wind speed and stability as well as terrain derive from observations of lee-wave events over the Sierra Nevada and Inyo Mountains from the recently completed Terrain-Induced Rotor Experiment (T-REX). Numerical experiments show that double bell-shaped obstacles promote trapped lee waves that are in general shorter than those excited by an isolated ridge. While the permissible trapped lee-wave modes are determined by the upstream atmospheric structure, primarily vertical wind shear, the selected lee-wave wavelengths for two obstacles that are close or equal in height are dictated by the discrete terrain spectrum and correspond to higher harmonics of the primary orographic wavelength, which is equal to the ridge separation distance. The exception is the smallest ridge separation distance examined, one that corresponds to the Owens Valley width and is closest to the wavelength determined by the given upstream atmospheric structure, for which the primary lee-wave and orographic wavelengths were found to nearly coincide. The influence two mountains exert on the overall lee-wave field is found to persist at very large ridge separation distances. For the nonlinear nonhydrostatic waves examined, the ridge separation distance is found to exert a much stronger control over the lee-wave wavelengths than the mountain half-width. Positive and negative interferences of lee waves, which can be detected through their imprint on wave drag and wave amplitudes, were found to produce appreciable differences in the flow structure mainly over the downstream peak, with negative interference characterized by a highly symmetric flow pattern leading to a low drag state.

scholarly journals Improving Nonlinear and Nonhydrostatic Ocean Lee Wave Drag Parameterizations

2020 ◽  
Vol 50 (9) ◽  
pp. 2417-2435
Author(s):  
Frederick T. Mayer ◽  
Oliver B. Fringer
Keyword(s):  
Steady State ◽  
Characteristic Time ◽  
Wave Theory ◽  
Wave Drag ◽  
Characteristic Time Scale ◽  
Time Varying ◽  
Global Circulation ◽  
Global Circulation Models ◽  
Lee Waves ◽  
Lee Wave

AbstractOcean lee waves occur on length scales that are smaller than the grid scale of global circulation models (GCMs). Therefore, such models must parameterize the drag associated with launching lee waves. This paper compares the lee wave drag predicted by existing parameterizations with the drag measured in high-resolution nonhydrostatic numerical simulations of a lee wave over periodic sinusoidal bathymetry. The simulations afford a time-varying glimpse at the nonlinear and nonhydrostatic oceanic lee wave spinup process and identify a characteristic time scale to reach steady state. The maximum instantaneous lee wave drag observed during the spinup period is found to be well predicted by linear lee wave theory for all hill heights. In steady state, the simulations demonstrate the applicability of parameterizing the drag based on applying linear theory to the lowest overtopping streamline of the flow (LOTS), as is currently employed in GCMs. However, because existing parameterizations are based only on the height of the LOTS, they implicitly assume hydrostatic flow. For hills tall enough to trap water in their valleys, the simulations identify a set of nonhydrostatic processes that can result in a reduction of the lee wave drag from that given by hydrostatic parameterizations. The simulations suggest implementing a time-dependent nonhydrostatic version of the LOTS-based parameterization of lee wave drag and demonstrate the remarkable applicability of linear lee wave theory to oceanic lee waves.

The Triggering of Orographic Rainbands by Small-Scale Topography

2007 ◽  
Vol 64 (5) ◽  
pp. 1530-1549 ◽  
Author(s):  
Daniel J. Kirshbaum ◽  
George H. Bryan ◽  
Richard Rotunno ◽  
Dale R. Durran
Keyword(s):  
Flow Direction ◽  
Cross Flow ◽  
Leading Edge ◽  
Static Stability ◽  
Precipitation Event ◽  
Small Scale ◽  
Band Formation ◽  
Lee Waves ◽  
Lee Wave ◽  
Orographic Cloud

Abstract The triggering of convective orographic rainbands by small-scale topographic features is investigated through observations of a banded precipitation event over the Oregon Coastal Range and simulations using a cloud-resolving numerical model. A quasi-idealized simulation of the observed event reproduces the bands in the radar observations, indicating the model’s ability to capture the physics of the band-formation process. Additional idealized simulations reinforce that the bands are triggered by lee waves past small-scale topographic obstacles just upstream of the nominal leading edge of the orographic cloud. Whether a topographic obstacle in this region is able to trigger a strong rainband depends on the phase of its lee wave at cloud entry. Convective growth only occurs downstream of obstacles that give rise to lee-wave-induced displacements that create positive vertical velocity anomalies wc and nearly zero buoyancy anomalies bc as air parcels undergo saturation. This relationship is quantified through a simple analytic condition involving wc, bc, and the static stability N 2m of the cloud mass. Once convection is triggered, horizontal buoyancy gradients in the cross-flow direction generate circulations that align the bands parallel to the flow direction.

The impact of lee waves on the Southern Ocean circulation

2021 ◽  
Author(s):  
Luwei Yang ◽  
Maxim Nikurashin ◽  
Andrew McC. Hogg ◽  
Bernadette M. Sloyan
Keyword(s):  
Southern Ocean ◽  
Ocean Circulation ◽  
Turbulent Mixing ◽  
Wave Drag ◽  
Global Ocean ◽  
Mixing Effects ◽  
Lee Waves ◽  
Lee Wave ◽  
Eddy Field ◽  
The Impact

AbstractLee waves play an important role in transferring energy from the geostrophic eddy field to turbulent mixing in the Southern Ocean. As such, lee waves can impact the Southern Ocean circulation and modulate its response to changing climate through their regulation on the eddy field and turbulent mixing. The drag effect of lee waves on the eddy field and the mixing effect of lee waves on the tracer field have been studied separately to show their importance. However, it remains unclear how the drag and mixing effects act together to modify the Southern Ocean circulation. In this study, a lee wave parameterization that includes both lee wave drag and its associated lee-wave-driven mixing is developed and implemented in an eddy-resolving idealized model of the Southern Ocean to simulate and quantify the impacts of lee waves on the Southern Ocean circulation. The results show that lee waves enhance the baroclinic transport of the Antarctic Circumpolar Current (ACC) and strengthen the lower overturning circulation. The impact of lee waves on the large-scale circulation are explained by the control of lee wave drag on isopycnal slopes through their effect on eddies, and by the control of lee-wave-driven mixing on deep stratification and water mass transformation. The results also show that the drag and mixing effects are coupled such that they act to weaken one another. The implication is that the future parameterization of lee waves in global ocean and climate models should take both drag and mixing effects into consideration for a more accurate representation of their impact on the ocean circulation.

A closure for lee wave drag on the large-scale ocean circulation

2021 ◽  
Author(s):  
Carsten Eden ◽  
Dirk Olbers ◽  
Thomas Eriksen
Keyword(s):  
Large Scale ◽  
Surface Wind ◽  
Wave Drag ◽  
Ocean Model ◽  
Mean Flow ◽  
Model Simulations ◽  
Energy Transfers ◽  
Lee Waves ◽  
Lee Wave ◽  
The Mean

AbstractA new, energetically and dynamically consistent closure for the lee wave drag on the large scale circulation is developed and tested in idealized and realistic ocean model simulations. The closure is based on the radiative transfer equation for internal gravity waves, integrated over wavenumber space, and consists of two lee wave energy compartments for up-and downward propagating waves, which can be co-integrated in an ocean model. Mean parameters for vertical propagation, mean-ow interaction, and the vertical wave momentum flux are calculated assuming that the lee waves stay close to the spectral shape given by linear theory of their generation.Idealized model simulations demonstrate how lee waves are generated and interact with the mean flow and contribute to mixing, and document parameter sensitivities. A realistic eddy-permitting global model at 1/10° resolution coupled to the new closure yields a globally integrated energy flux of 0.27 TW into the lee wave field. The bottom lee wave stress on the mean flow can be locally as large as the surface wind stress and can reach into the surface layer. The interior energy transfers by the stress are directed from the mean flow to the waves, but this often reverses, for example in the Southern Ocean in case of shear reversal close to the bottom. The global integral of the interior energy transfers from mean ow to waves is 0.14 TW, while 0.04 TW is driving the mean ow, but this share depends on parameter choices for non-linear effects.

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