Geophysical and Astrophysical Fluid Dynamics

Abstract:

The relative merits of three contrasting empirical orthogonal decomposition methods in common use (namely, Proper Orthogonal Decomposition, Biorthogonal Decomposition and Multivariate Singular Systems Analysis) are considered as applied to baroclinic flow data. The regimes analysed are a steady, drifting wave, a modulated amplitude vacillating wave flow and a neighbouring multi-mode state which exhibits intermittency. The results are used to make a qualitative comparison of the methods in terms of convergence properties, variance capture and eigenfunction structure. The feasibility of using the resulting empirical orthogonal functions to transform partial differential equations to ordinary differential equations by Galerkin projection is mentioned. © 1997 Elsevier Science B.V.

Abstract:

Baroclinic instability is the principal mode of non-axisymmetric flow in the large-scale atmospheric circulation at mid-latitudes, and is responsible for oganising the structure and behaviour of major weather systems. This instability can also be fruitfully studied in the laboratory under controlled conditions. In this paper, we review recent work carried out by the authors and collaborators on various routes to chaotic behaviour in rotating, stratified flows. Results include the discovery of new multi-mode regimes in which small ensembles of baroclinic waves interact in a nonlinear mode competition with the thermally-driven axisymmetric component of the Bow, generating chaotic oscillatory variability on very long timescales. We discuss various attempts to capture this type of behaviour in simple models, and consider the significance of the phenomenon as a paradigm for understanding the nature of long timescale variability in the climates of the Earth and Mars. (C) 1998 Elsevier Science Ltd. All rights reserved.