Oscillations of shear flow along a slotted plate: small- and large-scale structures

Abstract

Shear flow along a slotted plate can give rise to highly coherent, small-scale oscillations within each slot; the dimensionless frequency is an order of magnitude lower than the frequency of the classical Kelvin–Helmholtz instability. Within a given slot, the unsteady development of a swirl pattern, as well as the flow into and out of the slot, is compatible with the evolution of a large-scale structure, which shows increased agglomeration of vorticity along the surface of the plate. Moreover, the streamwise phase shift of the unsteady flow rates through the slots is in accord with the phase shift of the velocity fluctuation of the downstream propagating disturbance along either side of the plate. This phase shift is associated with development of the large-scale structure, and corresponds to a dimensionless frequency that scales on the plate length, as verified by experiments over ranges of length and inflow velocity. The value of this dimensionless frequency is close to that in the absence of the slotted plate i.e. the Kelvin–Helmholtz instability of the free shear layer.