On nonlinear cascades in large-scale atmospheric flow

Abstract

Calculations of nonlinear interaction of available potential energy, kinetic energy, enstrophy, and potential enstrophy have been carried out in the domain of wave numbers. The processes of interest are the interactions among waves, the interactions between a given wave and the zonal average, and interactions due to the beta effect for (potential) enstrophy. Results are presented for a three-month (February through April 1963) period. It is found that available potential energy is cascaded from small to large wave numbers, while kinetic energy is cascaded from intermediate wave numbers to both small and large wave numbers: the greater amounts go to the small wave numbers. Enstrophy and potential enstrophy are cascaded from small to large wave numbers with relatively little accumulation in the middle range (8≤m≤11, where m is the wave number). Verification of the existence of an inertial subrange is inconclusive, although power spectrum analyses of enstrophy and potential enstrophy yield a −1 power law, combined with a −3 slope for the associated kinetic energy spectrum. A value of 2.5×104 m2 sec−1 is obstained for the coefficient of eddy viscosity by means of Leith's formulation, while the value of the cut-off wavelength for the −3 range is approximately 420 km by means of the formulation by Kraichnan.