Shear layer stability in a two-dimensional disk.

摘要

The dynamics of rotating fluids provide a rich aggregate of periodic, quasi-periodic, and irregular behavior. Many investigations of two-dimensional (2D) flows containing fluid velocity inflections present the Kelvin-Helmholtz (KH) instability. In this investigation we study the saturation of the KH instability for a forced circular shear layer in a differentially rotating split-disk.; Complex vortex interactions are reasonably well understood through experimentation but modeling them requires highly accurate numerical schemes. To explore these flows our investigations employ an efficiently parallelized, highly accurate pseudospectral scheme for the solution of the incompressible Navier-Stokes equations in a disk geometry, Torres & Coutsias [32]. Beyond the initial KH instability, secondary transitions in the flow yield symmetry breaking bifurcations resulting in periodic and irregular states. Simulations are provided for the intermediate states between the n = 4 and n = 3 vortex braids. Oscillating states not previously seen in numerical studies are reported. Unlike the jump transitions between braids of different order, the oscillating states were found to be supercritical bifurcations and thus, not hysteretic. Period doubling bifurcations are observed during some spin-up studies in which intermediate symmetry breaking bifurcations are bypassed.; Accurate spectral simulation offers the means for systematic exploration of the dynamics associated with rotating fluids. Herein we construct such a scheme and present bifurcation analysis for secondary transitions.