On the differences between 2D and QG turbulence

Abstract

Due to their mathematical tractability,two-dimensional (2D) fluid equations are often used by mathematiciansas a model for quasi-geostrophic (QG) turbulence in the atmosphere,using Charney's 1971 paper as justification. Superficially, 2D and QGturbulence both satisfy the twin conservation of energy and enstrophyand thus are unlike 3D flows, which do not conserve enstrophy. Yet QGturbulence differs from 2D turbulence in fundamental ways, which arenot generally known. Here we discuss ingredients missing in 2Dturbulence formulations of large-scale atmospheric turbulence. Weargue that there is no proof that energy cannot cascade downscale inQG turbulence. Indeed, observational evidence supports a downscaleflux of both energy and enstrophy in the mesoscales.It is suggested that the observed atmospheric energy spectrum isexplainable if there is a downscale energy cascade of QG turbulence, butis inconsistent with 2D turbulence theories, which require an upscaleenergy flux. A simple solved example isused to illustrate some of the ideas discussed.