CONVECTION DRIVEN BY THE NONUNIFORM ABSORPTION OF THERMAL RADIATION AT THE FREE SURFACE OF A STAGNANT POOL

This is a study of the flow driven by the buoyancy effect associated with the non-uniform volumetric absorption of a spatially uniform flux of thermal radiation that impinges on a body of fluid. The nonuniform absorption of radiation is due to the presence of regions of relative turbidity (coloring, suspension of particulates, algae) that alter the optical properties of the fluid. Focusing on the earliest stages of buoyancy-driven flow in the immediate vicinity of a relatively absorptive region, this study shows that the flow acquires a double-counterflow structure and that its effect is to rearrange the fluid so that increasingly warmer layers are positioned closer to the free surface. Analytically, the phenomenon is investigated on the basis of scale analysis and an asymptotic solution that is valid for vanishingly small times or Grashof numbers. Numerical experiments performed in a shallow two-dimensional layer confirm the flow structure and scaling trends anticipated theoretically.