Localized edge states in plane Couette flow

Yohann Duguet, Philipp Schlatter, and Dan S. Henningson

The dynamics at the threshold of transition in plane Couette flow is investigated numerically in a large spatial domain for a certain type of localized initial perturbation, for Re between 350 and 1000. The corresponding edge state is an unsteady spotlike structure, localized in both streamwise and spanwise directions, which neither grows nor decays in size. It is shown that the localized nature of the edge state is numerically robust, and is not influenced by the size of the computational domain. The edge trajectory appears to transiently visit localized steady states. This suggests that basic spatiotemporally intermittent features of transition to turbulence, such as the growth of a turbulent spot, can be described as a dynamical system.

Phys. Fluids 21, 111701 (2009)

Stability of relative equilibria of three vortices

Hassan Aref

Three point vortices on the unbounded plane have relative equilibria wherein the vortices either form an equilateral triangle or are collinear. While the stability analysis of the equilateral triangle configurations is straightforward, that of the collinear relative equilibria is considerably more involved.This paper gives analysis based on explicit formulas for the three eigenvalues determining the stability, including a new formula for the angular velocity of rotation of a collinear relative equilibrium.

Phys. Fluids 21, 094101 (2009)