THE LINEAR THEORY OF THERMAL CONVECTION IN HORIZONTAL PLANE COUETTE FLOW,
Abstract
An examination is made of the effects of horizontal shear on thermal convection with a simple model in which an incompressible fluid is contained in an infinite channel. The initial steady state assumed is one of constant horizontal shear in the mean flow and constant (unstable) temperature gradient. Small disturbances are then introduced and the linearized perturbation equations solved. In the inviscid, non-conducting case it was found that for the largest scale modes the pressure forces cause the momentum transport to be up the gradient at short wave-lengths but at long wave-lengths (except for the lowest mode) inertia effects dominate the flow, giving down-gradient transport. It was also found that with rotation about a vertical axis the Reynolds stress is non-zero even in the absence of shear. Thus, a mean flow should develop even if there were none initially. In the general case with shear and rotation it was found that for convective 'cells' whose wave-lengths along the channel are comparable with the channel width, the disturbances with growth rates small compared to the angular rotation rate transport momentum up the gradient. It is suggested that the interaction of giant, long-lived convection cells with the solar rotation might give an equatorward momentum transport that would support a differential rotation. In the real fluid case (without rotation) it was found that the preferred modes of convection are cells which resemble transverse rolls in the absence of shear, and longitudinally elongated cells when shear is present. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1969
- Accession Number
- AD0698350
Entities
People
- Robert P. Davies-jones
Organizations
- University of Colorado Boulder