Subcritical Laminar-Turbulent Transition as Nonequilibrium Phase Transition in Two-Dimensional Kolmogorov Flow

We have confirmed numerically that a subcritical laminar-turbulent transition that belongs to the directed percolation (DP) universality class occurs in a purely two-dimensional (2D) simple Navier-Stokes (NS) flow without any walls. The flow is called a (extended) Kolmogorov flow that is governed by the 2D NS equation in a doubly periodic domain with a linear drag and finite unit flow rate in the direction in which the Galilean invariance is broken. We examine the mechanism of the DP class transition while focusing on the role of the additional control parameters: the drag coefficient and unit flow rate. The drag selectively weakens the coherent active structures of the system size. The unit flow rate interferes with the growth of weak disturbances, and the laminar and turbulent states are thus bistable. 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 factors physically correspond to the additional parameters in general flows.