Turbulence-induced melting of a nonequilibrium vortex crystal in a forced thin fluid film

TL;DR

This paper uses numerical simulations to explore how a vortex crystal in a thin fluid film transitions from ordered to turbulent states as the Reynolds number increases, revealing a sequence of nonequilibrium phase transitions.

Contribution

It introduces a detailed analysis of turbulence-induced melting in a vortex crystal using fluid dynamics measures, nonlinear dynamics tools, and phase transition concepts.

Findings

Sequence of nonequilibrium phase transitions observed

Initial ordered vortex lattice becomes turbulent with increasing Reynolds number

Order parameters and spatial correlations characterize different phases

Abstract

To develop an understanding of recent experiments on the turbulence-induced melting of a periodic array of vortices in a thin fluid film, we perform a direct numerical simulation of the two-dimensional Navier-Stokes equations forced such that, at low Reynolds numbers, the steady state of the film is a square lattice of vortices. We find that, as we increase the Reynolds number, this lattice undergoes a series of nonequilibrium phase transitions, first to a crystal with a different reciprocal lattice and then to a sequence of crystals that oscillate in time. Initially the temporal oscillations are periodic; this periodic behaviour becomes more and more complicated, with increasing Reynolds number, until the film enters a spatially disordered nonequilibrium statistical steady that is turbulent. We study this sequence of transitions by using fluid-dynamics measures, such as the Okubo-Weiss parameter that distinguishes between vortical and extensional regions in the flow, ideas from nonlinear dynamics, e.g., \Poincare maps, and theoretical methods that have been developed to study the melting of an equilibrium crystal or the freezing of a liquid and which lead to a natural set of order parameters for the crystalline phases and spatial autocorrelation functions that characterise short- and long-range order in the turbulent and crystalline phases, respectively.