Subcritical laminar-turbulence transition with wide domains in simple two-dimensional Navier-Stokes flow without walls

TL;DR

This study numerically confirms a subcritical laminar-turbulence transition in a 2D Navier-Stokes flow without walls, belonging to the directed percolation universality class, influenced by drag and flow rate parameters.

Contribution

It demonstrates the occurrence of DP-class transition in a wall-free 2D flow and analyzes how drag and flow rate control the transition mechanisms.

Findings

Transition belongs to directed percolation universality class.

Drag suppresses coherent structures, influencing the absorbing state.

Flow rate affects the growth of disturbances and transition dynamics.

Abstract

We have confirmed numerically that a subcritical laminar-turbulence transition that belongs to directed percolation (DP) universality class occurs in a purely two-dimensional (2D) simple Navier-Stokes (NS) flow without any walls. The flow is called (extended) Kolmogorov flow which is governed by 2D NS equation in a doubly periodic box with a linear drag and a finite flow rate in the direction in which Galilean invariance is broken. We examine the mechanism of DP class transition focusing on the role of the additional control parameters: the drag coefficient and the flow rate. The drag kills coherent active structures of the system size. The flow rate interferes the growth of weak disturbances. These two effects control two essential and intrinsic elements of an absorbing state phase transition, i.e., the existence of an absorbing state and the locality of active dynamical structures. We also discuss what physically corresponds to the additional parameters in general flow.