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Abstract The influence of gravity waves generated by surface stress and by topography on the atmospheric kinetic energy (KE) spectrum is examined using idealized simulations of a cyclone growing in baroclinically unstable shear flow. Even in the absence of topography, surface stress greatly enhances the generation of gravity waves in the vicinity of the cold front, and vertical energy fluxes associated with these waves produce a pronounced shallowing of the KE spectrum at mesoscale wavelengths relative to the corresponding free-slip case. The impact of a single isolated ridge is, however, much more pronounced than that of surface stress. When the mountain waves are well developed, they produce a wavenumber to the −5/3 spectrum in the lower stratosphere over a broad range of mesoscale wavelengths. In the midtroposphere, a smaller range of wavelengths also exhibits a −5/3 spectrum. When the mountain is 500 m high, the waves do not break, and their KE is entirely associated with the divergent component of the velocity field, which is almost constant with height. When the mountain is 2 km high, wave breaking creates potential vorticity, and the rotational component of the KE spectrum is also strongly energized by the waves. Analysis of the spectral KE budgets shows that the actual spectrum is the result of continually shifting balances of direct forcing from vertical energy flux divergence, conservative advective transport, and buoyancy flux. Nevertheless, there is one interesting example where the −5/3-sloped lower-stratospheric energy spectrum appears to be associated with a gravity-wave-induced upscale inertial cascade.
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Inertia-gravity waves and geostrophic turbulence
Inertia-gravity waves in the atmosphere and ocean are transported and refracted by geostrophic turbulent currents. Provided that the wave group velocity is much greater than the speed of geostrophic turbulent currents, kinetic theory can be used to obtain a comprehensive statistical description of the resulting interaction (Savva et al. , J. Fluid Mech. , vol. 916, 2021, A6). The leading-order process is scattering of wave energy along a surface of constant frequency, $$\omega$$ , in wavenumber space. The constant- $$\omega$$ surface corresponding to the linear dispersion relation of inertia-gravity waves is a cone extending to arbitrarily high wavenumbers. Thus, wave scattering by geostrophic turbulence results in a cascade of wave energy to high wavenumbers on the surface of the constant- $$\omega$$ cone. Solution of the kinetic equations shows establishment of a wave kinetic energy spectrum $$\sim k_h^{-2}$$ , where $$k_h$$ is the horizontal wavenumber.
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- Award ID(s):
- 2048583
- PAR ID:
- 10411607
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 920
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2021.334
