Modeling Mesoscale Circulations by Coupled Nonlinear Systems

Purdue University, West Lafayette IN

Investigators

Abstract

Low-order models (LOMs) have played an important role in understanding of basic mechanisms of atmospheric dynamics through a focus on key elements and retaining only minimal number of degrees of freedom. LOMs are low-order systems of nonlinear ordinary differential equations derived from basic equations of atmospheric dynamics, commonly by the Galerkin method. Despite a number of highly attractive features, the method does not prevent a LOM from violations of fundamental conservation properties of the original equations, which often results in unphysical behavior. In previous studies, the investigators have developed a modular approach to constructing physically sound LOMs of atmospheric circulations, in which classical mechanical systems, the Volterra gyrostats (the simplest one being the celebrated Lorenz model of two dimensional Rayleigh-Benard convection), serve as elementary building blocks. Systems of coupled gyrostats avoid unphysical behavior by always conserving energy in the inviscid, unforced limit. At the same time, because the conservative part of most models in atmospheric dynamics (e.g., the primitive, shallow water and quasi-geostrophic equations) is Hamiltonian, maintaining the Hamiltonian structure in a LOM is viewed as an effective way to retain in it the fundamental conservation properties of the original system. As demonstrated in the Principal Investigators' preliminary studies, the gyrostatic approach is particularly promising in this endeavor. Under this project, an attempt will be made to develop useful Hamiltonian LOMs for important fluid dynamical systems, beginning with Rayleigh-Benard convection that provides the principal mechanism for mesoscale shallow convection. Relatively simple gyrostatic (particularly Hamiltonian) LOMs inherently possessing fundamental conservation properties of the fluid dynamical equations will provide a new effective tool to further a scientific understanding of essential mechanisms and their interaction in atmospheric dynamics. From the Broader Impacts perspective, eventually this research could lend new insights into issues of atmospheric predictability and, hence, limits to forecasting.