Abstract
A new time invariant of the shallow-water model on the f plane for an isolated distribution of vorticity is obtained. The physical interpretation of the new invariant and its relation to past studies is discussed. It corresponds to a global nonlinear geostrophic balance of the localized distribution of vorticity, and defines a manifold in spectral space where the inertial frequency is filtered out exactly for all time. The author argues that if the initial distribution of vorticity is not on this manifold, it is not in balance. Thus, an exact realization of a slow manifold generated by a number of finite constraints is obtained. The new time invariant is obtained with no assumption on the Froude number, the Rossby number, and the amplitude characterizing the distribution of vorticity.
