Simulation and study of stratified flows around finite bodies

Abstract

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 Re = Ud/ν and the internal Froude number Fr = U/(Nd), where ν 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 < Fr < 100, the classification of flow regimes for the sphere (for 1 < Re < 500) and for the cylinder (for 1 < Re < 200) is improved. At Fr = 0 (i.e., at U = 0), the problem of diffusioninduced flow past a sphere leading to the formation of horizontal density layers near the sphere's upper and lower poles is considered. At Fr = 0.1 and Re = 50, the formation of a steady flow past a square cylinder with wavy hanging density layers in the wake is studied in detail.

Asymptotics of the Far Fields of Internal Gravity Waves Excited by a Source of Radial Symmetry

“…pycnic elevation, the velocity components, the density, and the pressure) can be determined; a certain initial spatial distribution of these components can be specified [6][7][8]. Far from the perturbation sources, assuming the adequacy of using the linear wave dynamics model, the far fields of internal gravity waves can be calculated from the asymptotic formulas; in this case, as shown by the calculation results, under the majority of real hydrological conditions of the World Ocean the basic contribution to the far fields is made only by first several wave modes [3,4,[16][17][18].…”

“…Therefore, using model representations to describe various sources, in the far zone the wave field can be described using relatively simple analytical formulas [4][5][6]. In this case the initial and boundary conditions must be determined from the results of direct numerical simulation of the near field with account for the nonlinear hydrodynamic equations or using particularly evaluating (semi-empirical) considerations [6][7][8]. The assumption on excitation of IGW packets by the pulse action [4,5,[9][10][11]] may be considered as a possible model of wave generation.…”

Simulations of stably stratified flow past two spheres at Re = 300

“…Finally, we record that the flow solution for the tandem configuration and distance l/D = 1 is a special case, which displays periodic horizontal oscillations in the far-wake field, as shown in Fig. 14 values of l/D, where steady state is maintained (e.g. configuration θ = 0 • and l/D = 0.5 in the lower panel of Fig.…”

2D Hydrodynamics of a Plate: From Creeping Flow to Transient Vortex Regimes

“…Numerical simulation of stratified flows has manifold challenges related to application of the most appropriate numerical schemes, pressure-velocity coupling algorithms, adaptive mesh approaches, no-reflective boundary conditions at external boundaries, optimization of numerical procedures, high performance computing, etc. Since studies on stratified flows are of a great fundamental and practical interest, the most of these numerical problems have been successfully solved using computational packages or program codes of own development [42][43][44]. In the present study, numerical simulation for the formulated mathematical problem is constructed on the basis of the finite volume method using the computational utility OpenFOAM [45].…”