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The Parameter Dependence of Eddy Heat Flux in a Homogeneous Quasigeostrophic Two-Layer Model on a β Plane with Quadratic Friction

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  • 1 Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, New Jersey
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Abstract

This study investigates the parameter dependence of eddy heat flux in a homogeneous quasigeostrophic two-layer model on a β plane with imposed environmental vertical wind shear and quadratic frictional drag. We examine the extent to which the results can be explained by a recently proposed diffusivity theory for passive tracers in two-dimensional turbulence. To account for the differences between two-layer and two-dimensional models, we modify the two-dimensional theory according to our two-layer f-plane analyses reported in an earlier study. Specifically, we replace the classic Kolmogorovian spectral slope, −5/3, assumed to predict eddy kinetic energy spectrum in the former with a larger slope, −7/3, suggested by a heuristic argument and fit to the model results in the latter. It is found that the modified theory provides a reasonable estimate within the regime where both β˜=βkd2U1 and the strength of the frictional drag, c˜D=cDkd1, are much smaller than unity (here, cD is the nondimensional drag coefficient divided by the depth of the layer, kd is the wavenumber of deformation radius, and U is the imposed background vertical wind shear). For values of β˜ and c˜D that are closer to one, the theory works only if the full spectrum shape of the eddy kinetic energy is given. Despite the qualitative, fitting nature of this approach and its failure to explain the full parameter range, we believe its documentation here remains useful as a reference for the future attempt in pursuing a better theory.

Current affiliation: Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Chiung-Yin Chang, cyinchang@uchicago.edu

Abstract

This study investigates the parameter dependence of eddy heat flux in a homogeneous quasigeostrophic two-layer model on a β plane with imposed environmental vertical wind shear and quadratic frictional drag. We examine the extent to which the results can be explained by a recently proposed diffusivity theory for passive tracers in two-dimensional turbulence. To account for the differences between two-layer and two-dimensional models, we modify the two-dimensional theory according to our two-layer f-plane analyses reported in an earlier study. Specifically, we replace the classic Kolmogorovian spectral slope, −5/3, assumed to predict eddy kinetic energy spectrum in the former with a larger slope, −7/3, suggested by a heuristic argument and fit to the model results in the latter. It is found that the modified theory provides a reasonable estimate within the regime where both β˜=βkd2U1 and the strength of the frictional drag, c˜D=cDkd1, are much smaller than unity (here, cD is the nondimensional drag coefficient divided by the depth of the layer, kd is the wavenumber of deformation radius, and U is the imposed background vertical wind shear). For values of β˜ and c˜D that are closer to one, the theory works only if the full spectrum shape of the eddy kinetic energy is given. Despite the qualitative, fitting nature of this approach and its failure to explain the full parameter range, we believe its documentation here remains useful as a reference for the future attempt in pursuing a better theory.

Current affiliation: Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Chiung-Yin Chang, cyinchang@uchicago.edu
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