Tertiary Instability Research Articles

Numerical experiments on stability and transition in plane channel flow

Various secondary and tertiary instabilities in plane channel flow are explored via time-dependent numerical simulations using the incompressible Navier-Stokes equations. Comparisons are made between transitional flows at Reynolds numbers 1500, 5000, and 8000. The lambda vortex, detached shear layer, and inverted vortex regions are identified and the origin of the latter is explained. The laminar breakdown of the Re=1500 flow is computed with high resolution and the nature of its ensuing hairpin eddies is clarified by numerical particle paths. The potential of center-mode rather than wall-mode transitions is proposed and the resulting flow structure is described.

Inviscid evolution of stretched vortex arrays

The nonlinear evolution of an array of pairs of inviscid counter-rotating vortices, subjected to an applied stretching strain field, has been studied numerically using the contour-dynamics method. The array configuration is effectively the Corcos-Lin model of streamwise vortices in the braid region of a nominally two-dimensional mixing layer. For each individual vortex the simulations elucidate the strong interaction between the vortex self-induction, the vorticity amplification of the stretching strain, and the local in-plane strain applied by all other members of the array. When the initial vorticity distribution is modelled by a non-uniform piece-wise-constant vorticity field defined over a nested set of non-intersecting contours, the dynamical evolution reveals fine structure consisting of strong vortex roll-up accompanied by trailing, filament-like spiral vortex sheets, and the presence of tertiary instabilities. It is shown by a particular example that these features are largely absent in an equivalent computation in which array members are modelled by the commonly used uniform-vortex approximation.