Interfusion, labeling and stream lines in flow of inviscid barotropic fluid

Abstract

It is shown that the Euler system of hydrodynamic equations for inviscid barotropic fluid for density and velocity is not a complete system of dynamic equations for the inviscicd barotropic fluid. It is only a closed subsystem of four dynamic equation. The complete system of dynamic equation consists of seven dynamic equations for seven dependent variables: density, velocity and labeling (Lagrangian coordinates, considered as dependent variables). Solution of the Cauchy problem for the Euler subsystem is unique. Solution of the Cauchy problem for the complete hydrodynamic system, containing seven equations, is unique only for irrotational flows. For vortical flows solution of the Cauchy problem is not unique. The reason of the nonuniqueness is an interfusion, which cannot be taken into account properly in the framework of hydrodynamics. There are some arguments in favour of connection between interfusion and turbulence.