Stability transition and turbulence in horizontal convection

Abstract:

Horizontal convection (HC) is driven by a horizontal difference in temperature or heat flux at a single horizontal boundary of a fluid. In a thermally equilibrated state net heat flux over the boundary is zero and the circulation involves a horizontal boundary flow, turbulent plume motion at the end wall and weak interior return flow, covering the entire the flow domain. HC may be a simple model of the meridional overturning circulation (also known as global thermohaline circulation) based on a convective flow which is driven by a horizontal surface temperature gradient.

We report three-dimensional convective circulation forced by a temperature gradient along the surface of a rectangular channel, using direct and large eddy simulations over a wide range of Rayleigh numbers, Ra ~ 108 - 1015. A sequence of several stability transitions lead to a change from laminar to fully-developed turbulent flow. At the smallest Ra convection is maintained by a balance of viscous and buoyancy forces inside the thermal boundary layer, whereas at the largest Ra inertia dominates over viscous stresses. This results in an enhancement of the overall heat transfer at Ra > 1010, while both dynamical balances give Nu ~ Ra1/5. Our main focus is to analyse the mechanical energy budget. Below the transition the small scales of motion are driven predominately by thermal convection, whereas Ra > 1013 shear plays a dominant role in sustaining the small-scale turbulence. Horizontal convection under rotation is also examined in our recent study.