Evolution of locally unstable shear flow near a wall or a coast

Publisher Website
Google Scholar
Abstract
An important phase of turbulence production in the flow past a wall occurs with the intermittent inflexional instability of the streamwise current. But according to a linearized inviscid calculation this instability (Kelvin-Helmholtz) can be reduced or eliminated by the presence of a (slippery) wall. Attention is therefore directed to the temporal evolution of a finite-amplitude patch of inflected fluid, i.e. one that is localized in the downstream direction. The model has piecewise uniform vorticity, and the contour-dynamical method is used. Numerical integrations show that sufficiently wide initial patches will eject slow fluid near the wall until it comes into close contact with the free stream, whereupon the ejection is deflected around a large eddy which is surrounded by a stable shear flow. The parametric regime in which this kind of finite instability occurs is sketched, and the Reynolds stress is computed. The initial condition assumed in this calculation depends on the prior existence and intensification of a local spanwise circulation, and this process is briefly discussed using a separate two-dimensional calculation. This shows that widely separated vorticity isopleths tend to completely merge, implying that such fronts in a real fluid may only be viscously limited. The analogous process of potential vorticity frontogenesis may be important in oceanic coastal currents.