Evaporation and cooling of a lake under unstable atmospheric conditions

The problem involves turbulent diffusion of momentum, sensible heat, and water vapor in the lower atmosphere when a neutral, dry air mass encounters a warm, wet surface. The water surface temperature is specified, and the surface roughness is taken to be constant over land and water. The turbulent fluxes are formulated by a semiempirical turbulence theory with the Businger‐Dyer form of the Monin‐Obukhov similarity functions, a water vapor buoyancy term in the Obukhov stability length, and Blackadar's scaling height in the mixing length. The resulting solution of the equations of conservation shows that the stability discontinuity at the leading edge can greatly affect the mean rate of evaporation and that the vertical vapor flux can greatly contribute to the atmospheric stability. The solution is relatively insensitive to the exact form of the Monin‐Obukhov similarity functions or to the exactness of Reynolds' analogy or von Karman's constant. For large fetches and near‐neutral conditions the solution becomes similar to that obtained in Sutton's problem and with Harbeck's empirical formula.