Numerical Simulation of the Kolmogorov Flow under Various Boundary Conditions

This paper is devoted to direct numerical simulation (DNS) of the Kolmogorov flow for viscous weakly compressible fluid in the square computational domain. Laminar, chaotic, and vortex flow regimes are formed depending on the problem parameters. The paper examines the influence of boundary conditions on the structure of emerging regimes. As a result of the occurrence of a inverse energy cascade supported by constant energy pumping in the form of a sinusoidal force, one large vortex is formed in the case of no-slip boundary conditions, occupying the entire computational domain. Under periodic boundary conditions, a vortex dipole is formed in the flow. The energy spectra analysis of the obtained flow regimes is carried out. It is shown that in the vortex regime for both types of boundary conditions, the energy spectrum at low wavenumbers corresponds to the inverse energy cascade. The inertial-range spectrum law for laminar, chaotic, and vortex modes is discussed. The average profiles of the vortex velocity for a single vortex and a vortex dipole are constructed. Reasonable agreement between the numerical results and theoretical predictions is observed.