NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-15-71-2008 Gyrostatic extensions of the Howard-Krishnamurti model of thermal convection with shear Tong C. 1 Gluhovsky A. 2 Biometrics Research RY33-300, Merck Research Laboratories, P.O.Box 2000, Rahway, NJ, 07065, USA Department of Earth and Atmospheric Sciences and Department of Statistics, Purdue University, 550 Stadium Mall Drive, West Lafayette, IN, 47907-2051, USA 06 02 2008 15 1 71 79 Copyright: © 2008 C. Tong 2008 This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Generic License. To view a copy of this licence, visit https://creativecommons.org/licenses/by-nc-sa/2.5/ This article is available from https://npg.copernicus.org/articles/15/71/2008/npg-15-71-2008.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/15/71/2008/npg-15-71-2008.pdf

The Howard & Krishnamurti (1986) low-order model (LOM) of Rayleigh-Bénard convection with spontaneous vertical shear can be extended to incorporate various additional physical effects, such as externally forced vertical shear and magnetic field. Designing such extended LOMs so that their mathematical structure is isomorphic to those of systems of coupled gyrostats, with damping and forcing, allows for a modular approach while respecting conservation laws. Energy conservation (in the limit of no damping and forcing) prevents solutions that diverge to infinity, which are present in the original Howard & Krishnamurti LOM. The first LOM developed here (as a candidate model of transverse rolls) involves adding a new Couette mode to represent externally forced vertical shear. The second LOM is a modification of the Lantz (1995) model for magnetoconvection with shear. The modification eliminates an invariant manifold in the original model that leads to potentially unphysical behavior, namely solutions that diverge to infinity, in violation of energy conservation. This paper reports the first extension of the coupled gyrostats modeling framework to incorporate externally forced vertical shear and magnetoconvection with shear. Its aim is to demonstrate better model building techniques that avoid pathologies present in earlier models; consequently we do not focus here on analysis of dynamics or model validation.

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