On simple models for simulation of nonlinear processes in convection and turbulence

The mechanism of nonlinear interaction in hydrodynamics is studied with dynamical systems having finite degrees of freedom. The equations are assumed to have the same integrals of motion and main features as those peculiar to hydrodynamical equations. The simplest system of this kind is a triplet (a system described by three parameters). Its equations of motion coincide with the Euler equations in the theory of the gyroscope. The forced motion of a triplet is treated theoretically. A real hydrodynamical system controlled by the equations of motion of a triplet was devised and verified in the laboratory.

The simplest theoretical model of baroclinic motion which provides a basis for studies of of forced heat convection in an ellipsoidal cavity was also constructed. Under certain conditions, the addition of rotation causes a regime of motion analogous to the Rossby regime in a rotating annulus.

More complicated models constructed from a large number of interacting triplets can simulate the cascade process of energy transformation in developed turbulence.