On Complete Filtering of Gravity Modes Through Nonlinear Initialization

Abstract

A procedure is outlined which adjusts the initial conditions for any prediction model of a planetary fluid such that no motions of the fluid will evolve with high-frequency, gravity-type time scales despite the model's nonlinearity. Any model which can be characterized by a reasonably small Rossby number may be balanced by the method. The technique requires the determination of the normal modes of the linear part of the equations to be integrated—finite difference or spectral—and proceeds by an expansion technique to build up higher order, nonlinear adjustments to the initial state. Abstract A procedure is outlined which adjusts the initial conditions for any prediction model of a planetary fluid such that no motions of the fluid will evolve with high-frequency, gravity-type time scales despite the model's nonlinearity. Any model which can be characterized by a reasonably small Rossby number may be balanced by the method. The technique requires the determination of the normal modes of the linear part of the equations to be integrated—finite difference or spectral—and proceeds by an expansion technique to build up higher order, nonlinear adjustments to the initial state.