Loxley, Peter

Nadiga, B T

2013

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.

Physics of Fluids, 25(1), p. 1-17

1089-7666

1070-6631

https://hdl.handle.net/1959.11/20320

American Institute of Physics

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

Journal Article

Publication