Validity of the twin-force analogy in Couette flows

This study combines linear stability analysis (LSA) and direct numerical simulations (DNS) to investigate the coupling mechanisms of rotation, stratification and shear in two flow geometries: spanwise rotating stratified plane Couette flow (between two infinite parallel plates) and sheared annular centrifugal Rayleigh–Bénard convection (between two concentric cylinders). First, LSA reveals a universal scaling law with respect to left parenthesis 1 minus eta right parenthesis ( 1 − η ) (1-η ) , where eta η η denotes the radius ratio, for the deviation between annular and planar system results, quantitatively establishing the dynamical connection between annular and planar geometries. Building on this, DNS results indicate that the breakdown of the twin-force analogy in the turbulent regime originates from mode competition: buoyancy tends to drive three-dimensional chaotic plumes via baroclinic effects, whereas the Coriolis force tends to sustain quasi-two-dimensional longitudinal vortices. The Prandtl number determines the dominant mechanism in the near-wall region by regulating the relative thicknesses of the thermal and momentum boundary layers, thereby leading to a systematic dissimilarity between heat and momentum transport. Furthermore, this study provides a new theoretical basis for transport prediction in complex flows from the perspectives of enstrophy and mode competition.