Dependence of the Highly Truncated Spectral Vorticity Equation on Initial Conditions

Abstract

The analytic solutions in time to the highly truncated (low-order) spectral vorticity equation, involving the nonlinear interaction of one planetary wave with an arbitrary zonal flow, have been investigated for a wide variety of initial conditions which span the range of atmospheric observations. These conditions include both a characteristic mean wintertime zonal jet, a simulated double jet, all planetary waves from wavenumbers 1?12, and various wave configurations for wavenumber 3. The results show wide variability in solutions from configurations which are almost independent in time to those which describe highly elliptic oscillations. There is no systematic dependence of nonlinearity on total energy amplitude of the system nor do small initial perturbations necessarily imply quasi-linearity. The solutions described for this simple model exemplify the extreme complexity of large-scale atmospheric turbulence.