Numerical stability in a model of the layered structure of thermohaline fields

Abstract

The paper presents a set-up and the stability criteria for numerical realization of the model of the vertical structure of thermohaline fields caused by double diffusion effects. The model considers the turbulence accompanying the environment layering process as rotationally isotropic in the sense suggested by the theory of rotationally anisotropic turbulence. It is formulated through the set of three nonlinear differential equations for the environment's temperature, salinity, and turbulence kinetic energy. The numerical realization of the model is based on an implicit difference method and the uniform rectangular time-space grid. The numerical stability criterion of the algorithm for the model's approximated solution is estimated by the maximum values of the solutions of system components.