Classification of the stratified fluid flows regimes around a square cylinder

Abstract

The 2D density stratified (in vertical direction) viscous fluid flows around a square cylinder with diameter d (moving in horizontal direction with the velocity U) have been simulated on the basis of the Navier-Stokes equations in the Boussinesq approximation. For solving of the Navier-Stokes equations the Splitting on physical factors Method for Incompressible Fluid flows (SMIF) with hybrid explicit finite difference scheme (second-order accuracy in space, minimum scheme viscosity and dispersion, monotonous) has been used. The numerical method SMIF has been successfully applied for solving of the different problems: 2D and 3D separated homogeneous and stratified fluid flows around a sphere and a circular cylinder; the flows with free surface including regimes with broken surface wave; the air, heat and mass transfer in the clean rooms. At the present paper the original refined classification of 2D stratified viscous fluid flow regimes around a square cylinder at Re ≤ 200 has been obtained and the interesting fluid flows with two hanging vortices in the wake and with two wavy hanging sheets of density (connected with two hanging vortices) have been investigated in details at Fr = 0.1, Re = 50, where Re = U·d/ν is the Reynolds number, Fr = U/(N·d) is the internal Froude number, ν is the kinematical viscosity coefficient, N is the buoyancy frequency.