Helicity and Thermal Convection with Shear

Abstract

The relations between nonlinear energy transport and helicity of the flow are studied through simulations of thermal convection with mean shear. Parallel-plate convection with a rotating mean shear, a linear undirectional shear, a parabolic undirectional shear, and without background flow is simulated by performing direct numerical simulations with periodic boundary conditions in the horizontal directions and a no-slip condition in the vertical. The results indicate that the normalized three-dimensional nonlinear energy transfer among scales is inversely correlated with the squared relative helicity of the flow.The buoyancy-forced convective elements in parallel-plate convection with a curved mean shear are more likely to be helical than are those with other types of mean shear. The disturbance helicity budgets are then analyzed to study the sources of eddy helicity. The budgets show that the transfer of helicity from the mean flow and the enhancement by buoyancy are both dominant sources.