Time Schemes for Strongly Nonlinear Damping Equations

Abstract

In atmospheric models that include vertical diffusion and surface fluxes of heat and moisture it is common to observe large amplitude ?fibrillations? associated with these noniinear damping terms. In this paper this phenomenon is studied through the analysis of a simple nonlinear damping equation, ?X/?t = ?(KXP)X + S. It is concluded that the behavior of several time schemes for the strongly nonlinear damping equations currently used can be quite pathological, with either large amplitude oscillations, or even nonoscillatory but incorrect solutions. Also presented are new simple schemes, which are easy to implement and have a much wider range of stability. These schemes are applied in the new National Meteorological Center (NMC) spectral model.