NONLINEAR EQUILIBRATION OF 2-DIMENSIONAL OPTIMAL PERTURBATIONS IN VISCOUS SHEAR-FLOW

Two-dimensional perturbations configured for maximum energy growth in laminar viscous sheaf flow are shown to develop into quasisteady finit e amplitude structures, provided that the initial perturbation has suf ficient energy and a nearby nonlinear mode exists. For Poiseuille flow , which supports finite amplitude equilibria for Reynolds numbers abov e approximately 2900, an optimal perturbation with initial energy dens ity equal to or greater than 0.1% of the mean flow energy density clos ely approaches the quasiequilibrium state within 10 advective time uni ts. For Couette flow, which has no finite amplitude solution, the opti mal perturbations decay rapidly after reaching maximum amplitude unles s the configuration is sufficiently close to a linear mode with slow e xponential decay rate. While the quasiequilibrium structure for Poiseu ille flow is locally inflectional, it supports only weak instabilities with scales larger than the local region.