Turbulence and emergent large scales in "horizontal convection"

There has been argument about whether convection driven by heating and cooling at the same level with zero net buoyancy flux can be vigorous and turbulent, with potential implications for the role of surface buoyancy fluxes in global ocean circulation. Direct Numerical Simulations (DNS) and laboratory experiments show that differential heating/cooling in one direction at the base of a box and on the scale of the box (the Rossby, 1965, problem) leads to a sequence of flow transitions at large Rayleigh numbers and a turbulent boundary layer regime. However, the flow in this case is highly constrained. Here we report convection above a horizontal plate having an array of many warm and cold patches, thus relaxing the constraints. DNS of the thermal equilibrium state, in which there must be no net heat flux through the boundary, shows a full spectrum of scales throughout the bulk of the fluid with an inertial turbulence sub-range. We also find the emergence of domain-scale structures in a deep domain, which are motions much larger than the scale of the forcing. Laboratory experiments with an array of imposed inputs of freshwater and saline solution through a permeable horizontal base are consistent with the DNS and show the same regime transition from a stable array of turbulent plumes to domain scale turbulence. The results show similarities with Rayleigh-B\'enard convection at $Ra>>10^{10}$, in which buoyancy flux is dominated by long-lived, large-scales of turbulence,. The large scales undergo shear instability leading to turbulence production throughout the bulk of the flow as the dominant mechanism for viscous dissipation. Thus horizontal convection (without the constraint of side walls) and RBC share the emergence of large scales for the most effective for transport of buoyancy.

In collaboration with Madeleine Rosevear and Bishakhdatta Gayen, Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia.