An Interpretation of Atmospheric Low-Order Models

Abstract

Low-order models (LOMs) arising in various popular fluid dynamic and atmospheric problems are shown to be equivalent to coupled three-mode nonlinear systems known in mechanics as Volterra gyrostats. The Volterra equations of the gyrostat differ from the Euler equations of the gyroscope by the presence of linear terms, which, unlike ordinary viscous terms, do not affect the energy or the phase volume conservation. In atmospheric LOMs such linear terms, exerting considerable influence on the dynamics, are caused by various factors peculiar to geophysical fluid dynamics (e.g., stratification, rotation, and topography). The simplest Volterra gyrostat in the forced regime is equivalent to the celebrated Lorenz model. Systems of coupled gyrostats also inherently possess fundamental properties of the hydrodynamic equations. Therefore, gyrostats are proposed as elementary modules for developing LOMs of nonlinear fluid dynamic and atmospheric phenomena.