Wave Ducting in a Stratified Shear Flow over a Two-Dimensional Mountain. Part I: General Linear Criteria

Wang, Ting-An; Lin, Yuh-Lang

doi:10.1175/1520-0469(1999)056<0412:wdiass>2.0.co;2

Cited by 28 publications

(29 citation statements)

References 37 publications

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“…This implies that waves with a wavenumber vector perpendicular to the mean flow (k = 0 and l = 0) are totally absorbed, no matter how low Ri c is, whereas the attenuation of waves with wavenumber vectors parallel to the mean flow (l = 0) is similar to that of 2D waves. Following Lindzen and Tung [75], but carrying out a more systematic exploration of parameter space, [76,77] used linear theory to address wave ducting, and its implications for downslope windstorms, in flow over 2D mountains. They treated cases where both Ri c > 0.25, and thus the critical level absorbs upward propagating waves in accordance with (47), and cases where Ri c < 0.25, where the waves are unattenuated, but instead amplified by the critical level, in what has been termed "overreflection" [75].…”

Section: Total Critical Levelsmentioning

confidence: 99%

“…Using a piecewise-linear wind profile qualitatively similar to (55), Wang and Lin [76,77] studied the implications of wave ducting for downslope windstorms and high-drag states. They found that, at least in the linear regime, wave reflections at the shear discontinuities existing below and above the critical level (whose intensity is controlled by Ri c ) rather than at the critical level itself determine the wave response, with wind and drag maxima at the surface attained when (58) is fulfilled, where now z 1 is the height of the lowest shear discontinuity.…”

Section: Partial Wave Reflection and Resonancementioning

confidence: 99%

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The physics of orographic gravity wave drag

Teixeira

2014

Front. Phys.

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The drag and momentum fluxes produced by gravity waves generated in flow over orography are reviewed, focusing on adiabatic conditions without phase transitions or radiation effects, and steady mean incoming flow. The orographic gravity wave drag is first introduced in its simplest possible form, for inviscid, linearized, non-rotating flow with the Boussinesq and hydrostatic approximations, and constant wind and static stability. Subsequently, the contributions made by previous authors (primarily using theory and numerical simulations) to elucidate how the drag is affected by additional physical processes are surveyed. These include the effect of orography anisotropy, vertical wind shear, total and partial critical levels, vertical wave reflection and resonance, non-hydrostatic effects and trapped lee waves, rotation and nonlinearity. Frictional and boundary layer effects are also briefly mentioned. A better understanding of all of these aspects is important for guiding the improvement of drag parametrization schemes.

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Section: Total Critical Levelsmentioning

confidence: 99%

Section: Partial Wave Reflection and Resonancementioning

confidence: 99%

The physics of orographic gravity wave drag

Teixeira

2014

Front. Phys.

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“…Two-layer linear model and its solution: lowlevel wind shear case Similar to Wang and Lin (1999), the linear governing equations for a 2-D, steady-state, non-rotating and hydrostatic flow over orography are given as follows:…”

Section: P U B L I S H E D B Y T H E I N T E R N a T I O N A L M E T mentioning

confidence: 99%

Low-level vertical wind shear effects on the gravity wave breaking over an isolated two-dimensional orography

Bao

Tan

2012

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C T Flow regimes of dry, stratified flow passing over an isolated two-dimensional (2-D) orography mainly concentrate at two stagnation points. One occurs on the upslope of the orography owing to flow blocking; another is related to gravity wave breaking (GWB) over the leeside. Smith (1979) put forward a hypothesis that the occurring of GWB is suppressed when the low-level vertical wind shear (VWS) exceeds some value. In the present study, a theoretical solution in a two-layer linear model of orographic flow with a VWS over a bellshaped 2-D orography is developed to investigate the effect of VWS on GWB's occurring over a range of surface Froude number Fr 0 0U 0 /Nh (U 0 is surface wind speed, h is orography height and N is stability parameter), over which the GWB occurs first and the upstream flow blocking is excluded. Based on previous simulations and experiments, the range of surface Froude number selected is 0.6 5 Fr 0 52.0. Based on this solution, the conditions of surface wind speed (U 0 ) and one-to-one matching critical VWS (Du c ) for GWB's occurring are discussed. Over the selected range of Fr 0 , GWB's occurring will be suppressed if the VWS (Du) is larger than Du c at given U 0 . Moreover, there is a maximum value of Du c over the selected range of Fr 0 , which is labelled as Du max , and its matching surface wind speed by U 0m . Once the Du is larger than Du max , the flow will pass over the orography without GWB's occurring. That means, over the selected range of Fr 0 , the flow regime of 2-D orographic flow related to GWB occurring primarily will be absent when Du ! Du max , regardless of the value for U 0 . In addition, the vertical profile of atmospheric stability and height of VWS could result in different features of mountain wave, which leads to different Du c and Du max for the GWB's occurring. The possible inaccuracy of estimated Du c in the present linear model is also discussed.

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“…They also stressed the role of the Richardson number in the shear layer as a key parameter of the flow, with an importance much beyond that of delaying the onset of high-drag states. Grimshaw and Smyth (1986) suggested that high-drag states may begin with linear resonance, and Wang and Lin (1999a) found that, when the Richardson number is above 0.25, the influence of what goes on above a critical level is very limited. So, in this study a very simple linear model is proposed, which may help to elucidate how the high-drag states are initiated.…”

Section: Introductionmentioning

confidence: 99%

Resonant gravity‐wave drag enhancement in linear stratified flow over mountains

Teixeira

Miranda

Argaín

et al. 2005

Quart J Royal Meteoro Soc

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SUMMARYHigh-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z 1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z 1 , and the Richardson number, Ri, in the shear layer. The drag oscillates as z 1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z 1 . Drag maxima correspond to constructive interference of the upward-and downward-propagating waves in the region z < z 1 , while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z 1 increases as Ri decreases. The critical level, z c , plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

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Wave Ducting in a Stratified Shear Flow over a Two-Dimensional Mountain. Part I: General Linear Criteria

Cited by 28 publications

References 37 publications

The physics of orographic gravity wave drag

The physics of orographic gravity wave drag

Low-level vertical wind shear effects on the gravity wave breaking over an isolated two-dimensional orography

Resonant gravity‐wave drag enhancement in linear stratified flow over mountains

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