Theoretical Studies of Turbulent Transport Processes at Rough Boundaries with Application to the Interface Between Sea Ice and the Ocean

Abstract:

We study the effects of rough walls on turbulent flows to understand the coupling between the rough underside of Arctic sea ice and the ocean. Of particular relevance is the fact that the climatological thickness of Arctic sea ice is a sensitive function of the turbulent ice/ocean heat flux, which depends sensitively on the roughness of the phase boundary. We tailor the geometry of the upper boundary to manipulate
the boundary layer -- interior flow interaction and study the turbulent transport of heat in two-dimensional Rayleigh-B\'enard convection with numerical simulations using the Lattice Boltzmann method. By fixing the roughness amplitude of the upper boundary and varying the wavelength $\lambda$, we find that the exponent $\beta$ in the Nusselt-Rayleigh scaling relation, $Nu-1 \propto Ra^\beta$, is maximized at $\lambda \equiv \lambda_{\text{max}} \approx (2 \pi)^{-1}$, but decays to the planar value in both the large ($\lambda \gg \lambda_{\text{max}}$) and small ($\lambda \ll \lambda_{\text{max}}$) wavelength limits. The changes in the exponent originate in the nature of the coupling between the boundary layer and the interior flow. We present a simple scaling argument embodying this coupling, which describes the maximal convective heat flux.