Transient Gravity Wave-Critical Layer Interaction. Part I: Convective Adjustment and the Mean Zonal Acceleration

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  • 1 Physical Dynamics, Inc., Bellevue, WA 98009
  • | 2 Geophysical Institute, University of Alaska, Fairbanks, AK 99701
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Abstract

Numerical simulations of vertically-propagating gravity waves interacting with critical layers are presented. For nearly monochromatic wave events, the wave amplitude behavior and mean zonal acceleration agree substantially with the predictions of the semi-analytic models of Grimshaw in 1975, Dunkerton in 1981–82 and Coy in 1983. A mean zonal wind “shock,” or steep sheer zone, forms at the base of a convectively unstable critical layer in these cases.

Because the semi-analytic model is based on the WKB approximation, the gravity wave, mean-flow interaction proceeds somewhat differently when this approximation is not accurate. For highly transient wave packets containing a broad frequency spectrum, momentum deposition and convective instability occurs over a much broader range of heights than predicted by the semi-analytic model. For nearly monochromatic waves, on the other hand, partial reflection from the internal mean flow shock is observed.

The inviscid gravity wave critical layer is inherently turbulent since overturning rapidly develops in the potential temperature field. Negative local Richardson numbers (Ri) are contemporaneous with the development of the internal shock in the monochromatic wave events, are coincident with Lagrangian zonal perturbation velocities exceeding the intrinsic phase speed, and occur very soon after the appearance of regions with Ri<¼. To account for convective wavebreaking a simple, local turbulence parameterization is advanced, which is not based upon turbulent eddy diffusion. Instead, the total wave plus mean flow profile, when required is frictionally relaxed to a convectively neutral equilibrium which conserves potential temperature and total vorticity, analogous to the familiar “convective adjustment” procedure in general circulation models. Despite being a local adjustment within the wave, this turbulence parameterization seems to confirm the amplitude-limiting effects predicted by Lindzen's global amplitude balance model in the relatively simple case studies presented here.

Abstract

Numerical simulations of vertically-propagating gravity waves interacting with critical layers are presented. For nearly monochromatic wave events, the wave amplitude behavior and mean zonal acceleration agree substantially with the predictions of the semi-analytic models of Grimshaw in 1975, Dunkerton in 1981–82 and Coy in 1983. A mean zonal wind “shock,” or steep sheer zone, forms at the base of a convectively unstable critical layer in these cases.

Because the semi-analytic model is based on the WKB approximation, the gravity wave, mean-flow interaction proceeds somewhat differently when this approximation is not accurate. For highly transient wave packets containing a broad frequency spectrum, momentum deposition and convective instability occurs over a much broader range of heights than predicted by the semi-analytic model. For nearly monochromatic waves, on the other hand, partial reflection from the internal mean flow shock is observed.

The inviscid gravity wave critical layer is inherently turbulent since overturning rapidly develops in the potential temperature field. Negative local Richardson numbers (Ri) are contemporaneous with the development of the internal shock in the monochromatic wave events, are coincident with Lagrangian zonal perturbation velocities exceeding the intrinsic phase speed, and occur very soon after the appearance of regions with Ri<¼. To account for convective wavebreaking a simple, local turbulence parameterization is advanced, which is not based upon turbulent eddy diffusion. Instead, the total wave plus mean flow profile, when required is frictionally relaxed to a convectively neutral equilibrium which conserves potential temperature and total vorticity, analogous to the familiar “convective adjustment” procedure in general circulation models. Despite being a local adjustment within the wave, this turbulence parameterization seems to confirm the amplitude-limiting effects predicted by Lindzen's global amplitude balance model in the relatively simple case studies presented here.

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