Reinterpreting the Large Scale Horizontal Kinetic Energy Spectrum in the Troposphere

Abstract:

The aim of this study is to develop the necessary understanding of kinetic energy (KE) spectrum as a function of horizontal wavenumber and the different dynamical processes whose interactions provide important contributions to the kinetic energy cycle. It is well-known in the literature that the horizontal kinetic energy spectrum exhibits a -3 slope in the large scales (synoptic scales). Under the framework of two-dimensional turbulence (non-divergent motions) the existence of such a power law is explained by the presence of upscale energy cascade and downscale enstrophy cascade on either side of the KE injection range. For the application of 2D turbulence theory which considers the fluid to be barotropic, the pressure gradient term is generally considered irrelevant. Our results indicate a significant contribution of pressure gradient term at large scales which is an indicator for the presence of baroclinicity, which poses the question of whether the KE spectrum at large scales can really be interpreted using 2D turbulence. In this regard the formulation of the transformed primitive equations (Gassmann(2014,2019)), where only the terms having an active contribution to the evolution of KE and Ertel's potential energy (EPV) are remaining, is used to illustrate how the non-linear spectral fluxes contribute to the spectral budget of kinetic and available potential energy (APE) at different height levels. Results indicate a strong forward cascade of active non-linear spectral flux at large scales in the mid-troposphere where the flow is in geostrophic balance and that the assumption of 2D turbulence may be potentially flawed.