Energy conserving low-order models for potential vorticity dynamics and convection with shear

Low-dimensional Galerkin models of atmospheric circulations are developed in the form of coupled Volterra gyrostats (a natural generalization of the famous Lorenz model). Restricting low-order models (LOMs) to this form

1) ensures energy conservation, thus preventing unphysical behavior often observed in LOMs based on ad hoc truncations;

2) helps to single out the most effective interactions and to design LOMs of optimum size;

3) allows a modular implementation of the Galerkin technique using gyrostats as elementary building blocks.

The approach is illustrated with two important LOMs. One is the Charney - DeVore (1979) model of a barotropic atmosphere over topography. The other is a gyrostatic modification of the Howard - Krishnamurti (1986) model of convection with shear that restores conservation of energy and of total vorticity to the original model. In each case, the ?minimal? LOM is extracted that possesses fundamental conservation properties and demonstrates the effect of interest: vacillation between high-index and low-index regimes and tilting of convection cells, respectively.