The Slow Manifold of a Five-Mode Model

Abstract

The slow manifold of an inviscid five-mode model introduced by Lorenz is investigated. When the influence of the gravity modes on the Rossby modes is neglected, the analytical solution given by Lorenz and Krishnamurthy is generalized. When gravity-Rossby coupling is included, direct numerical solutions are computed by solving a nonlinear boundary value problem. In all cases, the slow manifold has gravity mode oscillations that mimic free gravity waves and whose amplitude is proportional to the exponential of the reciprocal of the Rossby number ε.