Vortex motion of a continuous medium depending on the pressure change

Abstract

Abstract In this paper, we study the vortex motion of a continuous medium, which is described by forces obtained from the principle of least action. It is shown that in a continuous medium the vortex force components are proportional to the velocity and pressure gradient components. This article gives a description of the 2D vortex motion of air in zones of high and low pressure. If the pressure decreases, the angular velocity of rotation of the continuous medium increases, whereas if the pressure increases, the angular velocity fades. The lifting force is obtained due to the vortex movement of air in the form of a funnel. It is shown that the vortex force contains a vortex term of the Euler hydrodynamic equations with a relative factor equal to the velocity of the continuous medium squared divided by the sound velocity squared. To describe the motion of a continuous medium correctly it is necessary to replace the forces obtained by Euler with the forces obtained from the minimum of action in the equations of motion. It is concluded that vortex motions and turbulence are described by the obtained equations of motion, and not by the Navier–Stokes equations. Most likely, this is related to the Problem of the Millennium description of turbulence announced at the International Congress of Mathematics in 2000.