Coherent Structures in Two-Dimensional Turbulent Jets

Abstract

We study coherent structures evolving from a linear jet in a channel on the basis of a statistical equilibrium theory. Using a new, highly efficient numerical algorithm for the solution of the statistical equilibrium equations, we explore the whole three- dimensional parameter space of initial conditions thereby generalizing our previous results. In the limit of very small jet width, the linear analysis predicts a final vorticity distribution which is x-independent for aspect ratios $L < \sqrt {4/3}$ and which is spatially periodic for $L > \sqrt {4/3}$ with an antisymmetric shape spreading over the whole domain. Extrapolating to the”dilute limit” in a large range of initial conditions we numerically get periodic equilibrium states lacking parity invariance. These states can not be obtained within the sinh-Poisson-equation of Montgomery & Joyce [1], derived under the assumption that positive and negative vorticity play a symmetric role.