Vortex–Wave Interactions/Self‐Sustained Processes in High Prandtl Number Natural Convection in A Vertical Channel with Moving Sidewalls

Natural convection takes place when a temperature difference is maintained across a vertical channel filled with fluid. The horizontal temperature gradient drives a unidirectional flow in the vertical direction. This flow is augmented by sidewalls moving in equal and opposite directions. There is much interest in the generic turbulent structures that can occur both in shear flows and convection and here we give the basic structure associated with wavefields interacting with streamwise vortex structures. The high Grashof number limit is considered and it is shown how a self‐sustained process can occur with vortices interacting with a wave system in a manner similar to that discussed by Hall and Smith [1], hereafter referred to as HS1 and Hall and Sherwin [2], hereafter referred to as HS2. The waves occur as neutral modes of small amplitude riding on top of large amplitude vortices aligned with the direction of gravity. The waves then drive the vortex structure through nonlinear effects thus closing the self‐sustained process. The simplified interaction equations for the process differ significantly from the corresponding equations in Couette or Blasius flow and we derive the initial form of their solution. The results apply to natural convection without the motion of the sidewalls and indeed to Couette flow when there is no heating. Our analysis explains the origin of subharmonic self‐sustained processes which are known to occur in Couette flow.