Wind-up of a spanwise vortex in deepening transition and stall

A fundamental flow problem of unsteady wind-up of a spanwise vortex is stud ied in this theoretical work on deepening dynamic stall and transition in a boundary layer, internal layer or related unsteady motion. It examines the nonlinear evolution of the spanwise vortex produced when the local wall pr essure develops a maximum or minimum, subsequent to the finite-time break-u p of an interacting layer and the impact of normal pressure gradients. The evolution is controlled by an inner-outer interaction between the effects o f the normal pressure gradient and the momentum jumps across and outside th e vortex, which is situated near the strong inflexion point induced in the mean flow. Although the work concentrates on a particular internal-flow con text, many of the flow properties found are generic and in particular apply for a more general case including external flows. Analysis and associated computations point to two main distinct trends in the vortex response, depe nding to a large extent on a parameter gauging the relative strengths of th e above effects. The response is either an explosive one, provoking enhance d wind-up, growth and pressure in the vortex, or it is implosive, causing t he vortex to shrink and virtually empty itself through unwinding, leaving l ittle local pressure variation. A further discussion includes the after-eff ects of this vortex response and some of the connections with experiments a nd direct computations on deepening stall and transition.