Improved low-order model for shear flow driven by Rayleigh-Bénard convection

An analysis of the low-order model for two-dimensional fluid flow with shear proposed by Drake et al. [Phys. Fluids B 4, 488 (1992)] is undertaken. Their two-term model for the shear is an extension of the model put forth by Howard and Krisnamurti [J. Fluid Mech. 170, 385 (1986)], and is shown to be an improved model in the sense that it respects certain conditions for vorticity conservation arising directly from the Boussinesq equations. In so doing, it provides a more realistic model of the physics involved. An important consequence of the improved model is the appearance of cutoff values for the shear instability that are dependent upon the aspect ratio of the interacting Rayleigh-Taylor cell. Numerical results are presented as confirmation of this prediction.