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.

/pdf/the-physics-of-orographic-gravity-wave-drag-504ljv99bt.pdf

The physics of orographic gravity wave drag

The impact of horizontal propagation of mountain waves on the orographic gravity wave drag (OGWD) in the stratosphere and lower mesosphere of the Northern Hemisphere is evaluated for the first time. Using a fine-resolution (1 arc min) terrain and 2.5°×2.5° European Centre for Medium-Range Weather Forecasts ERA-Interim reanalysis data during 2011–2016, two sets of OGWD are calculated offline according to a traditional parameterization scheme (without horizontal propagation) and a newly proposed scheme (with horizontal propagation). In both cases, the zonal mean OGWDs show similar spatial patterns and undergo a notable seasonal variation. In winter, the OGWD is mainly distributed in the upper stratosphere and lower mesosphere of middle to high latitudes, whereas the summertime OGWD is confined in the lower stratosphere. Comparison between the two sets of OGWD reveal that the horizontal propagation of mountain waves tends to decrease (increase) the OGWD in the lower stratosphere (middle to upper stratosphere and lower mesosphere). Consequently, including the horizontal propagation of mountain waves in the parameterization of OGWD can reduce the excessive OGWD in the lower stratosphere and strengthen the insufficient gravity wave forcing in the mesosphere, which are the known problems of traditional OGWD schemes. The impact of horizontal propagation is more prominent in winter than in summer, with the OGWD in western Tibetan Plateau, Rocky Mountains, and Greenland notably affected.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2017JD027528

Impacts of Horizontal Propagation of Orographic Gravity Waves on the Wave Drag in the Stratosphere and Lower Mesosphere

Mountain-wave turbulence in the presence of directional wind shear over the Rocky Mountains in Colorado is investigated. Pilot reports (PIREPs) are used to select cases in which moderate or severe turbulence encounters were reported in combination with significant directional wind shear in the upstream sounding from Grand Junction, Colorado (GJT). For a selected case, semi-idealized numerical simulations are carried out using the WRF-ARW atmospheric model, initialized with the GJT atmospheric sounding and a realistic but truncated orography profile. To isolate the role of directional wind shear in causing wave breaking, sensitivity tests are performed to exclude the variation of the atmospheric stability with height, the speed shear, and the mountain amplitude as dominant wave breaking mechanisms. Significant downwind transport of instabilities is detected in horizontal flow cross sections, resulting in mountain-wave-induced turbulence occurring at large horizontal distances from the first wave br...

/pdf/mountain-wave-turbulence-in-the-presence-of-directional-wind-5alumlh9a4.pdf

Mountain-Wave Turbulence in the Presence of Directional Wind Shear over the Rocky Mountains

Mountain wave breaking, and the resulting potential for the generation of turbulence in the atmosphere, is investigated using numerical simulations of idealized, nearly hydrostatic atmospheric flows with directional wind shear over an axisymmetric isolated mountain. These simulations, which use the WRF-ARWmodel, differ in degree of flow non-linearity and shear intensity, quantified through the dimensionless mountain height and the Richardson number of the incoming flow, respectively. The aim is to diagnose wave breaking based on large-scale flow variables. 
The simulation results have been used to produce a regime diagram giving a description of the wave breaking behaviour in Richardson number–dimensionless mountain height parameter space. By selecting flow overturning occurrence as a discriminating factor, it was possible to split the regime diagram into sub-regions with and without wave
breaking. 
When mountain waves break, the associated convective instability leads to turbulence generation (which is one of the known forms of Clear Air Turbulence, also known as CAT). Thus, regions within the simulation domain where wave breaking and the development of CAT are expected have been identified. The extent of these regions increases with terrain elevation and background wind shear intensity. 
Analysis of the model output, supported by theoretical arguments, suggest the existence of a link between wave breaking and the relative orientations of the incoming wind vector and the horizontal velocity perturbation vector. More specifically, in a wave breaking event, due to the effect of critical levels, the background wind vector and the wave-number vector of the dominant mountain waves are perpendicular. It is shown that, at least for the wind profile employed in the present study, this corresponds to a situation where the background wind vector and the velocity perturbation vector are also approximately perpendicular.

/pdf/turbulence-generation-by-mountain-wave-breaking-in-flows-2pi7fx5cdi.pdf

Turbulence generation by mountain wave breaking in flows with directional wind shear

Mountain wave breaking, and the resulting potential for the generation of turbulence in the atmosphere, is investigated using numerical simulations of idealized, nearly hydrostatic atmospheric flows with directional wind shear over an axisymmetric isolated mountain. These simulations, which use the WRF-ARWmodel, differ in degree of flow non-linearity and shear intensity, quantified through the dimensionless mountain height and the Richardson number of the incoming flow, respectively. The aim is to diagnose wave breaking based on large-scale flow variables. 
The simulation results have been used to produce a regime diagram giving a description of the wave breaking behaviour in Richardson number–dimensionless mountain height parameter space. By selecting flow overturning occurrence as a discriminating factor, it was possible to split the regime diagram into sub-regions with and without wave 
breaking. 
When mountain waves break, the associated convective instability leads to turbulence generation (which is one of the known forms of Clear Air Turbulence, also known as CAT). Thus, regions within the simulation domain where wave breaking and the development of CAT are expected have been identified. The extent of these regions increases with terrain elevation and background wind shear intensity. 
Analysis of the model output, supported by theoretical arguments, suggest the existence of a link between wave breaking and the relative orientations of the incoming wind vector and the horizontal velocity perturbation vector. More specifically, in a wave breaking event, due to the effect of critical levels, the background wind vector and the wave-number vector of the dominant mountain waves are perpendicular. It is shown that, at least for the wind profile employed in the present study, this corresponds to a situation where the background wind vector and the velocity perturbation vector are also approximately perpendicular.

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the R i → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers ( R i ). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to R i = 0.5 , while not so satisfactory, but still showing a large improvement relative to the R i → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the R i ⪆ O ( 1 ) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

/pdf/the-gravity-wave-momentum-flux-in-hydrostatic-flow-with-873qdhfu6n.pdf

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


One source of uncertainty associated with vertical wind shear (VWS) on tropical cyclone (TC) intensity evolution arises when the VWS becomes sufficiently strong such that the TC vortex is unable to overcome the inhibiting effects of VWS (the critical shear regime), resulting in a transition from vortex realignment and eventual reintensification to persistent vortex misalignment and failure of reintensification. To uncover the initiation mechanism of the behavioral transition, this study examines the dynamical evolution of the vortex tilt and precession through a set of CM1 ensemble simulations in moderate shear (7.5 m s−1) that includes the behavioral transition by systematically enhancing the TC vorticity amplitude aloft (vortex resiliency) at a restart point. In this critical shear regime, all experiments exhibit a common precession hiatus behavior, during which the tilt magnitude increases and later leads to divergent outcomes in intensity and tilt evolutions. Volume-averaged horizontal vorticity budget reveals an anomalous differential vorticity flux that emerges in the downtilt-left quadrant during the hiatus period. This differential vorticity flux generates horizontal vorticity that points toward the downtilt-right direction, simultaneously increasing the vortex tilt and slowing down the precession rate. This downtilt-left differential vorticity flux is due to midlevel vortex stretching at the rainband terminus region, where there is a transition from convective to stratiform precipitation. Meanwhile, the downdraft associated with stratiform precipitation also causes vorticity compression at the low levels. These results indicate that the stratiform rainband region is important for increasing the vortex tilt and pausing the precession.

Chau Lam Yu

Papers

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

Tropical Cyclone Tilt and Precession in Moderate Shear: Precession Hiatus in a Critical Shear Regime