Selection of modes in convective low-order models

The development of physically sound low-order models (LOMs) of convective flow is discussed. LOMs are constructed in the form of coupled three-mode systems known in mechanics as Volterra gyrostats. This structure ensures energy conservation, a property of fundamental importance sometimes missing in atmospheric LOMs. In addition, the gyrostatic form makes it possible to reduce an LOM to one with the minimal number of modes that still describes the effect of interest. The approach is illustrated with two important LOMs. One is the modification of the Howard-Krishnamurti model of convection with shear that restores conservation of both energy and total vorticity to the original model. The other is the Charney-DeVore model of a barotropic atmosphere over topography. In each case, the "minimal'' LOM is extracted that possesses conservation properties and demonstrates the effect of interest: tilting of convection cells and vacillation between high-index and low-index regimes, respectively.