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.

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.

Climatology of the Sierra Nevada Mountain-Wave Events

2008 ◽  
Vol 136 (2) ◽  
pp. 757-768 ◽  
Author(s):  
Vanda Grubišić ◽  
Brian J. Billings
Keyword(s):  
Sierra Nevada ◽  
Cloud Formation ◽  
Wave Form ◽  
Mountain Range ◽  
Mountain Wave ◽  
Single Wave ◽  
Sierra Nevada Mountain ◽  
Lee Waves ◽  
Lee Wave ◽  
Wave Trains

Abstract This note presents a satellite-based climatology of the Sierra Nevada mountain-wave events. The data presented were obtained by detailed visual inspection of visible satellite imagery to detect mountain lee-wave clouds based on their location, shape, and texture. Consequently, this climatology includes only mountain-wave events during which sufficient moisture was present in the incoming airstream and whose amplitude was large enough to lead to cloud formation atop mountain-wave crests. The climatology is based on data from two mountain-wave seasons in the 1999–2001 period. Mountain-wave events are classified in two types according to cloud type as lee-wave trains and single wave clouds. The frequency of occurrence of these two wave types is examined as a function of the month of occurrence (October–May) and region of formation (north, middle, south, or the entire Sierra Nevada range). Results indicate that the maximum number of mountain-wave events in the lee of the Sierra Nevada occurs in the month of April. For several months, including January and May, frequency of wave events displays substantial interannual variability. Overall, trapped lee waves appear to be more common, in particular in the lee of the northern sierra. A single wave cloud on the lee side of the mountain range was found to be a more common wave form in the southern Sierra Nevada. The average wavelength of the Sierra Nevada lee waves was found to lie between 10 and 15 km, with a minimum at 4 km and a maximum at 32 km.

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.

scholarly journals High-Resolution Simulations of Lee Waves and Downslope Winds over the Sierra Nevada during T-REX IOP 6

2012 ◽  
Vol 51 (7) ◽  
pp. 1333-1352 ◽  
Author(s):  
Peter Sheridan ◽  
Simon Vosper
Keyword(s):  
High Resolution ◽  
Sierra Nevada ◽  
Cross Sections ◽  
Weather Prediction ◽  
Vertical Motion ◽  
Owens Valley ◽  
Downslope Winds ◽  
Lee Waves ◽  
Rotor Experiment ◽  
Intensive Observation

AbstractThe downslope windstorm during intensive observation period (IOP) 6 was the most severe that was detected during the Terrain-Induced Rotor Experiment (T-REX) in Owens Valley in the Sierra Nevada of California. Cross sections of vertical motion in the form of a composite constructed from aircraft data spanning the depth of the troposphere are used to link the winds experienced at the surface to the changing structure of the mountain-wave field aloft. Detailed analysis of other observations allows the role played by a passing occluded front, associated with the rapid intensification (and subsequent cessation) of the windstorm, to be studied. High-resolution, nested modeling using the Met Office Unified Model (MetUM) is used to study qualitative aspects of the flow and the influence of the front, and this modeling suggests that accurate forecasting of the timing and position of both the front and strong mountaintop winds is crucial to capture the wave dynamics and accompanying windstorm. Meanwhile, far ahead of the front, simulated downslope winds are shallow and foehnlike, driven by the thermal contrast between the upstream and valley air mass. The study also highlights the difficulties of capturing the detailed interaction of weather systems with large and complex orography in numerical weather prediction.

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.

scholarly journals The Intense Lee-Wave Rotor Event of Sierra Rotors IOP 8

2007 ◽  
Vol 64 (12) ◽  
pp. 4178-4201 ◽  
Author(s):  
Vanda Grubišić ◽  
Brian J. Billings
Keyword(s):  
Sierra Nevada ◽  
Large Amplitude ◽  
Forced Flow ◽  
Mountain Range ◽  
Wave Rotor ◽  
Owens Valley ◽  
Mountain Waves ◽  
Downslope Wind ◽  
Lee Wave ◽  
Strong Control

Abstract A large-amplitude lee-wave rotor event observationally documented during Sierra Rotors Project Intensive Observing Period (IOP) 8 on 24–26 March 2004 in the lee of the southern Sierra Nevada is examined. Mountain waves and rotors occurred over Owens Valley in a pre-cold-frontal environment. In this study, the evolution and structure of the observed and numerically simulated mountain waves and rotors during the event on 25 March, in which the horizontal circulation associated with the rotor was observed as an opposing, easterly flow by the mesonetwork of surface stations in Owens Valley, are analyzed. The high-resolution numerical simulations of this case, performed with the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) run with multiple nested-grid domains, the finest grid having 333-m horizontal spacing, reproduced many of the observed features of this event. These include small-amplitude waves above the Sierra ridge decoupled from thermally forced flow within the valley, and a large-amplitude mountain wave, turbulent rotor, and strong westerlies on the Sierra Nevada lee slopes during the period of the observed surface easterly flow. The sequence of the observed and simulated events shows a pronounced diurnal variation with the maximum wave and rotor activity occurring in the early evening hours during both days of IOP 8. The lee-wave response, and thus indirectly the appearance of lee-wave rotor during the core IOP 8 period, is found to be strongly controlled by temporal changes in the upstream ambient wind and stability profiles. The downstream mountain range exerts strong control over the lee-wave horizontal wavelength during the strongest part of this event, thus exhibiting the control over the cross-valley position of the rotor and the degree of strong downslope wind penetration into the valley.

Response of Atmospheric Convection to Vertical Wind Shear: Cloud-System-Resolving Simulations with Parameterized Large-Scale Circulation. Part II: Effect of Interactive Radiation

2015 ◽  
Vol 73 (1) ◽  
pp. 199-209 ◽  
Author(s):  
Usama Anber ◽  
Shuguang Wang ◽  
Adam Sobel
Keyword(s):  
Wind Shear ◽  
Large Scale ◽  
Lower Boundary ◽  
Vertical Wind Shear ◽  
Surface Fluxes ◽  
Vertical Wind ◽  
Radiative Heating ◽  
Vertical Shear ◽  
Large Scale Circulation ◽  
Lower Boundary Condition

Abstract The authors investigate the effects of cloud–radiation interaction and vertical wind shear on convective ensembles interacting with large-scale dynamics in cloud-resolving model simulations, with the large-scale circulation parameterized using the weak temperature gradient approximation. Numerical experiments with interactive radiation are conducted with imposed surface heat fluxes constant in space and time, an idealized lower boundary condition that prevents wind–evaporation feedback. Each simulation with interactive radiation is compared to a simulation in which the radiative heating profile is held constant in the horizontal and in time and is equal to the horizontal-mean profile from the interactive-radiation simulation with the same vertical shear profile and surface fluxes. Interactive radiation is found to reduce mean precipitation in all cases. The magnitude of the reduction is nearly independent of the vertical wind shear but increases with surface fluxes. Deep shear also reduces precipitation, though by approximately the same amount with or without interactive radiation. The reductions in precipitation due to either interactive radiation or deep shear are associated with strong large-scale ascent in the upper troposphere, which more strongly exports moist static energy and is quantified by a larger normalized gross moist stability.

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.

scholarly journals LES of Laminar Flow in the PBL: A Potential Problem for Convective Storm Simulations

2016 ◽  
Vol 144 (5) ◽  
pp. 1841-1850 ◽  
Author(s):  
Paul M. Markowski ◽  
George H. Bryan
Keyword(s):  
Lower Boundary ◽  
Vertical Wind Shear ◽  
Surface Friction ◽  
Vertical Wind ◽  
Lower Boundary Condition ◽  
Near Surface ◽  
Severe Storms ◽  
Turbulent Eddies ◽  
Wind Profiles ◽  
Tornadic Storms

In idealized simulations of convective storms, which are almost always run as large-eddy simulations (LES), the planetary boundary layers (PBLs) are typically laminar (i.e., they lack turbulent eddies). When compared with turbulent simulations, theory, or simulations with PBL schemes, the typically laminar LES used in the severe-storms community produce unrealistic near-surface vertical wind profiles containing excessive vertical wind shear when the lower boundary condition is nonfree slip. Such simulations are potentially problematic given the recent interest within the severe storms community in the influence of friction on vorticity generation within tornadic storms. Simulations run as LES that include surface friction but lack well-resolved turbulent eddies thus probably overestimate friction’s effects on storms.

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.

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