SIMILARITIES IN THE STRUCTURE OF SWIRLING AND BUOYANCY-DRIVEN FLOWS

We look at two classes of contained flow: swirling flow and buoyancy-d riven flow. We note that the strong links between these arise from the way in which vorticity is generated and propagated within each. We ta ke advantage of this shared behaviour to investigate the structure of steady-state solutions of the governing equations. First, we look at f lows with a small but finite viscosity. Here we find that, Batchelor r egions apart, the steady state for each type of flow must consist of a quiescent stratified core, bounded by high-speed wall jets. (In the c ase of swirling flow, this is a radial stratification of angular momen tum.) We then give a general, if approximate, method for finding these steady-state flow fields. This employs a momentum-integral technique for handling the boundary layers. The resulting predictions compare fa vourably with numerical experiments. Finally, we address the problem o f inviscid steady states, where there is a well-known class of steady solutions, but where the question of the stability of these solutions remains unresolved. Starting with swirling flow, we use an energy mini mization technique to show that stable solutions of arbitrary net azim uthal vorticity do indeed exist. However, the analogy with buoyancy-dr iven flow suggests that these solutions are all of a degenerate, strat ified form. If this is so, then the energy minimization technique, whi ch conserves vortical invariants, may mimic the stratification of temp erature or angular momentum in a turbulent flow.