The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Teixeira, Miguel A. C.; Yu, Chau Lam

doi:10.1016/j.euromechflu.2014.02.004

Cited by 17 publications

(22 citation statements)

References 29 publications

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“…Currently, the representation of the momentum flux depletion with height that forces the deceleration of the largescale atmospheric circulation is based on a monochromatic wave formulation (which does not represent the effects of critical level filtering by directional wind shear). An approach akin those suggested by Shutts and Gadian [81], Teixeira and Miranda [85] and Teixeira and Yu [88], or an extension of it to higher wave amplitudes, would improve consistency with current treatments of the surface drag in parameterizations (e.g., [15]). …”

Section: Discussionmentioning

confidence: 99%

“…Very recently, Teixeira and Yu [88] extended the model of Teixeira and Miranda [85] to mountains with an elliptical horizontal cross-section, bringing it one step closer to a concrete parametrization proposal. They also developed the necessary theory for the situation where the wind turns non-monotonically with height or by an angle larger than 180 o , where there is more than one critical level per wavenumber of the wave spectrum.…”

Section: Partial Critical Levels In Flow Over 3d Mountainsmentioning

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: Discussionmentioning

confidence: 99%

Section: Partial Critical Levels In Flow Over 3d Mountainsmentioning

confidence: 99%

The physics of orographic gravity wave drag

Teixeira

2014

Front. Phys.

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“…The intrinsic group velocity vector is

(c_{g 1}, c_{g 2}, c_{g 3}) = ({\overset{ω}{true}}_{k}, {\overset{ω}{true}}_{l}, {\overset{ω}{true}}_{m})

, where the subscripts k , l , m denote partial derivatives. The notation here is that the sign of m is chosen to be the opposite sign of

\overset{ω}{true}

for upward propagating waves with c g 3 >0, as in the Fourier formulations of Pulido and Rodas [] and Teixeira and Yu [].…”

Section: Formulationmentioning

confidence: 99%

A stationary phase solution for mountain waves with application to mesospheric mountain waves generated by Auckland Island

et al. 2017

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A relatively general stationary phase solution is derived for mountain waves from localized topography. It applies to hydrostatic, nonhydrostatic, or anelastic dispersion relations, to arbitrary localized topography, and to arbitrary smooth vertically varying background temperature and vector wind profiles. A simple method is introduced to compute the ray Jacobian that quantifies the effects of horizontal geometrical spreading in the stationary phase solution. The stationary phase solution is applied to mesospheric mountain waves generated by Auckland Island during the Deep Propagating Gravity Wave Experiment. The results are compared to a Fourier solution. The emphasis is on interpretations involving horizontal geometrical spreading. The results show larger horizontal geometrical spreading for nonhydrostatic waves than for hydrostatic waves in the region directly above the island; the dominant effect of horizontal geometrical spreading in the lower ∼30 km of the atmosphere, compared to the effects of refraction and background density variation; and the enhanced geometrical spreading due to directional wind in the approach to a critical layer in the mesosphere.

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“…Under the linear theory approximation, critical levels never lead to any wave reflection, but rather either transmit or absorb the waves, as shown originally by Booker and Bretherton () and further elaborated on by Teixeira and Miranda (), Xu et al . (; ; ), and Teixeira and Yu (). However, as nonlinearity increases, this situation is thought to change, as suggested by various studies (Breeding, ; Clark and Peltier, ; Smith, ).…”

Section: Introductionmentioning

confidence: 97%

Reflection of nonlinear mountain waves by critical levels: behaviour of the reflection coefficient

Teixeira

Argaín

2020

Quart J Royal Meteoro Soc

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Critical levels, where the wind vanishes in the atmosphere, are of key importance for gravity wave drag parametrization. The reflectivity of these levels to mountain waves is investigated here using a combination of high‐resolution numerical simulations and insights from linear theory. A methodology is developed for relating the reflection coefficient R of 2D hydrostatic orographic gravity waves to the extrema of the associated drag as a function of an independent flow parameter. This method is then used to infer the variation of the reflection coefficient with flow nonlinearity. To isolate the effect of critical levels, a wind profile with negative shear is adopted, which is characterized by its Richardson number Ri and the dimensionless mountain height Nh0/U0, based on the mountain height h0, Brunt‐Väisälä frequency N and surface incoming wind speed U0. Subject to the assumptions of linear theory, the drag is shown to be modified by wave refraction and reflection. The modulation of the drag by wave reflection is used to derive the reflection coefficient from the drag diagnosed from the numerical simulations. Despite considerable uncertainty, the critical level is found to have an R that first increases with Nh0/U0 for low values of this parameter, and for stronger nonlinearity saturates to a value of about 0.6. The flow configuration in this saturated regime is characterized in the case of high‐drag states by constructive wave interference, resembling downslope windstorms. Wave reflection by critical levels enhances the flow nonlinearity and the associated drag amplification, more than doubling it for values of Nh0/U0 as low as 0.12. These results emphasize the need to represent this process in orographic gravity wave drag parametrizations, and suggest a possible way of doing it using a prescribed critical level reflection coefficient, derived using the present methodology.

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The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Cited by 17 publications

References 29 publications

The physics of orographic gravity wave drag

The physics of orographic gravity wave drag

A stationary phase solution for mountain waves with application to mesospheric mountain waves generated by Auckland Island

Reflection of nonlinear mountain waves by critical levels: behaviour of the reflection coefficient

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