Bistability and hysteresis of maximum-entropy states in decaying two-dimensional turbulence

作者：Loxley P N^*; Nadiga B T

来源：Physics of Fluids, 2013, 25(1): 015113.

DOI：10.1063/1.4774348

We propose a theory that qualitatively predicts the stability and equilibrium structure of long-lived, quasi-steady flow states in decaying two-dimensional turbulence. This theory combines a maximum entropy principal with a nonlinear parameterization of the vorticity-stream-function dependency of such long-lived states. In particular, this theory predicts unidirectional-flow states that are bistable, exhibit hysteresis, and undergo large abrupt changes in flow topology; and a vortex-pair state that undergoes continuous changes in flow topology. These qualitative predictions are confirmed in numerical simulations of the two-dimensional Navier-Stokes equation. We discuss limitations of the theory, and why a reduced quantitative theory of long-lived flow states is difficult to obtain. We also provide a partial theoretical justification for why certain sets of initial conditions go to certain long-lived flow states.

• 出版日期2013-1