Efficient Nonlinear Low-Order Models in Atmospheric Dynamics

Abstract:

Following the pioneering work of Kolmogorov, Lorenz, and Obukhov, low-order models (LOMs) have been widely employed in studies of atmospheric and climate dynamics for reducing hydrodynamic equations to a small number of modes in order to understand the interplay of principal mechanisms. However, arbitrary truncations in the Galerkin method commonly used to derive LOMs can lead to systems that lack fundamental physical properties, such as energy conservation in the dissipationless limit. The presentation will address this problem by constructing efficient LOMs as coupled 3-mode nonlinear dynamical systems known in mechanics as Volterra gyrostats. Such systems guarantee energy conservation in the dissipationless limit, and their modular nature allows the creation of new LOMs through the addition or removal of gyrostats in existing models (resulting in, for example, Hamiltonian LOMs). In fact, all physically sound models that have appeared in recent publications can be written as coupled gyrostats. These and new LOMs developed by the authors will be discussed in the talk, suggesting that coupled gyrostats may offer a general framework for developing efficient LOMs for atmospheric dynamics.