An evaluation of gas transfer velocity parameterizations during natural convection using DNS

Journal article, 2016

Direct numerical simulations (DNS) of free surface flows driven by natural convection are used to evaluate different methods of estimating air-water gas exchange at no-wind conditions. These methods estimate the transfer velocity as a function of either the horizontal flow divergence at the surface, the turbulent kinetic energy dissipation beneath the surface, the heat flux through the surface, or the wind speed above the surface. The gas transfer is modeled via a passive scalar. The Schmidt number dependence is studied for Schmidt numbers of 7, 150 and 600. The methods using divergence, dissipation and heat flux estimate the transfer velocity well for a range of varying surface heat flux values, and domain depths. The two evaluated empirical methods using wind (in the limit of no wind) give reasonable estimates of the transfer velocity, depending however on the surface heat flux and surfactant saturation. The transfer velocity is shown to be well represented by the expression, k(s) = A (Bv)(1/4) Sc2(n), where A is a constant, B is the buoyancy flux, m is the kinematic viscosity, Sc is the Schmidt number, and the exponent n depends on the water surface characteristics. The results suggest that A = 0.39 and n approximate to 1/2 and n approximate to 2/3 for slip and no-slip boundary conditions at the surface, respectively. It is further shown that slip and no-slip boundary conditions predict the heat transfer velocity corresponding to the limits of clean and highly surfactant contaminated surfaces, respectively.