The effect of asymmetric large-scale dissipation on energy and potential enstrophy injection in two-layer quasi-geostrophic turbulence

2010/11/13 by Eleftherios Gkioulekas, Gkioulekas, Eleftherios
Earth and Planetary Sciences · Engineering · Environmental Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Climate variability and models #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Oceanographic and Atmospheric Processes #nlin.CD

paper · pdf · doi:10.48550/arxiv.1011.3163

29 pages; resubmitted to J. Fluid Mech

openalex publication_date 2010/11/13 · arxiv created 2011/12/27 · arxiv updated 2015/03/17 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In the Nastrom-Gage spectrum of atmospheric turbulence we observe a k^-3 energy spectrum that transitions into a k^-5/3 spectrum, with increasing wavenumber k. The transition occurs near a transition wavenumber k_t, located near the Rossby deformation wavenumber k_R. The Tung-Orlando theory interprets this spectrum as a double downscale cascade of potential enstrophy and energy, from large scales to small scales, in which the downscale potential enstrophy cascade coexists with the downscale energy cascade over the same length-scale range. We show that, in a temperature forced two-layer quasi-geostrophic model, the rates with which potential enstrophy and energy are injected place the transition wavenumber k_t near k_R. We also show that if the potential energy dominates the kinetic energy in the forcing range, then the Ekman term suppresses the upscale cascading potential enstrophy more than it suppresses the upscale cascading energy, a behavior contrary to what occurs in two-dimensional turbulence. As a result, the ratio \gn/\gee of injected potential enstrophy over injected energy, in the downscale direction, decreases, thereby tending to decrease the transition wavenumber k_t further. Using a random Gaussian forcing model, we reach the same conclusion, under the modeling assumption that the asymmetric Ekman term predominantly suppresses the bottom layer forcing, thereby disregarding a possible entanglement between the Ekman term and the nonlinear interlayer interaction. Based on these results, we argue that the Tung-Orlando theory can account for the approximate coincidence between k_t and k_R. We also identify certain open questions that require further investigation via numerical simulations.

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