Similarity without diffusion: shear turbulent layer damped by buoyancy

The evolution of a turbulent layer generated by velocity shear between two half-spaces of fluid and suppressed by a stable density difference is studied. Initially the layer expands, then shrinks to a point in finite time. By the end of the expansion stage the turbulent diffusion decays to a small value compared to the shear and buoyancy inputs in the turbulent energy balance. During the shrinking stage the diffusion decays even further by comparison. It is shown that at this stage the profiles of the turbulent energy, velocity and buoyancy become virtually self-similar. The differences between this case and the more usual types of self-similarity, where diffusion plays significant role, are discussed.