Numerical Investigation of a Viscous Two-Dimensional Fluid Flow in a Closed Cell

A two-dimensional flow of a viscous fluid in a cell of finite size is studied numerically. The flow arises as a result of an inverse cascade supported by a constant pumping. Several distinct states are observed. One of them is dominated by a large eddy with a well-defined average velocity profile. In the second state, strong chaotic large-scale fluctuations predominate. A laminar flow is observed in the third state. The nature of the resulting state depends on the fluid kinematic viscosity coefficient, the magnitude of the external pumping force wave vector, and the value of the bottom friction factor. When the values of the kinematic viscosity and wave vector are fixed, a small value of the bottom friction factor leads to the appearance of the first state. As the coefficient of the bottom friction factor increases, there occurs a transition from a flow with one large vortex to a laminar flow through a series of states with several unstable vortices, which we call chaotic motion. The paper presents the results of numerical simulation of a weakly compressible viscous fluid flow in a closed cell with no-slip boundary conditions on the walls. Pumping is carried out by a static force periodic in space in two directions. The simulation is carried out for various values of the bottom friction factor.