Simulation and study of stratified flows around finite bodies

The flows past a sphere and a square cylinder of diameter $d$ moving horizontally at the velocity $U$ in a linearly density-stratified viscous incompressible fluid are studied. The flows are described by the Navier–Stokes equations in the Boussinesq approximation. Variations in the spatial vortex structure of the flows are analyzed in detail in a wide range of dimensionless parameters (such as the Reynolds number $\mathrm{Re}=Ud/\nu$ and the internal Froude number $\mathrm{Fr}=U/(Nd)$, where $\nu$ is the kinematic viscosity and $N$ is the buoyancy frequency) by applying mathematical simulation (on supercomputers of Joint Supercomputer Center of the Russian Academy of Sciences) and three-dimensional flow visualization. At $0.005 < \mathrm{Fr} < 100$, the classification of flow regimes for the sphere (for $1 < \mathrm{Re} < 500$) and for the cylinder (for $1 < \mathrm{Re} < 200$) is improved. At $\mathrm{Fr} = 0$ (i.e., at $U=0$), the problem of diffusion-induced flow past a sphere leading to the formation of horizontal density layers near the sphere's upper and lower poles is considered. At $\mathrm{Fr} = 0.1$ and $\mathrm{Re} = 50$, the formation of a steady flow past a square cylinder with wavy hanging density layers in the wake is studied in detail.