Surface‐layer description under free‐convection conditions

Large‐eddy simulation is used to study the structure of the boundary layer close to the surface under free‐convection conditions. The magnitude of the surface friction velocity induced by the large convective eddies is determined as a function of the convective velocity scale, w*, and the surface, roughness length, z0. A simple analytic scaling form is obtained from a balance of forces in the wall layer induced by the convective eddies, giving the effective thickness of the layer and the effective surface stress and temperature dependence. The depth of the wall layer varies significantly with surface roughness and is extremely thin for small roughness, e.g. 0.5% of the mixed layer depth for a roughness length of 10−4zi. The analytic forms are consistent with the numerical predictions over the range of roughness length considered. The probability distribution of the instantaneous surface friction velocity (magnitude only) is examined and found to be reasonably close to Gaussian.