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Numerical modelling of stratified flows in well-drained basins

The work deals with a numerical investigation of stratified incompressible fluid flows. The numerical modelling is based on the NavierStokes equations in the vector potential-vortex variables with the use of the Boussinesq approximation and grids with separated velocities. The numerical algorithms for calculating twoand three-dimensional stratified flows are described. The algorithm for three-dimensional problems is adapted to calculation paralleling. Some calculations are given. 1. POSING THE PROBLEM We consider stratified fluid flows in well-drained basins. The mathematical model is based on the assumptions [3]: the equations of motion for a viscous incompressible fluid are considered in the Boussinesq approximation [15]; the density stratification is considered to be known; the flows are laminar; the free surface is modelled as a rigid surface. The system of Navier-Stokes equations in the Boussinesq approximation which describes the flows of a weakly stratified fluid may be written in two equivalent forms [3,4,11-13]. In the velocity-pressure variables this system is written as