Gravity drives the flow within the Stewartson layer in centrifugal convection

Abstract

We conduct three-dimensional numerical simulations on centrifugal convection (CC) in a closed annular container, incorporating gravity and no-slip top and bottom boundaries, to systematically investigate rotation-induced secondary flow. The Stewartson layer, identified by an elongated circulation in mean vertical velocity plots, emerges near the inner and outer cylinders only beyond a critical gravitational forcing. Quantitative analyses confirm that the layer thickness scales as $\delta_{st}\sim Ek^{1/3}$ due to rotational effects, consistent with results from rotating Rayleigh-B\'enard convection, where $Ek$ represents the Ekman number. The internal circulation strength, however, is determined by both gravitational buoyancy and rotational effects. We propose that gravitational buoyancy drives the internal flow, which balances against viscous forces to establish a terminal velocity. Through theoretical analysis, the vertical velocity amplitude follows $W_{st}\sim Ek^{5/3}Ro^{-1}Ra_gPr^{-1}$, showing good agreement with simulation results across a wide parameter range. Here, $Ro^{-1}$ represents the inverse Rossby number, $Ra_g$ the gravitational Rayleigh number, and $Pr$ the Prandtl number. The theoretical predictions match simulations well, demonstrating that the Stewartson layer is gravity-induced and rotationally constrained through geostrophic balance in the CC system. These findings yield fundamental insights into turbulent flow structures and heat transfer mechanisms in the CC system, offering both theoretical advances and practical engineering applications.