Small Wave – Vortex Disturbances in Stratified Fluid

The theoretical description of small hydrodynamic perturbations caused by mass, force and thermal sources in some models of stratified fluid is given. The focus is on the model of a uniformly stratified heat-conducting viscous fluid. It is shown that the small perturbations can be conveniently described by several scalar quasipotentials. One quasipotential is defined by solution of the inhomogeneous differential equation of diffusion. Other quasipotentials satisfy the same high order differential equations with different right-hand sides. The linear differential operator of these equations plays a key role in the theory of small perturbations and corresponding Green's function. It is established that Green's function of small perturbations in an incompressible stratified heat-conducting viscous fluid vanishes at negative times, i.e. satisfies the causality condition. Analysis of the integral Fourier expansion of Green's function in frequencies and wave numbers is performed. It is shown that small perturbations are divided into the aperiodically damped perturbations with large wave numbers and the damped internal waves with small wave numbers. The simplifications arising in the case of unit Prandtl's number and in the limit of ideal stratified fluid are found.