Plane vortex motion of a continuous medium: description of air rotation in cyclones and anticyclones

The article deals with the plane vortex motion of a continuous medium, which is described by the equations of motion obtained from the minimum action. It is shown that in the stationary case, the angular velocity of rotation of the continuous medium increases with decreasing pressure and decreases with increasing pressure. This is in good agreement with the description of air movement in cyclones and anticyclones. The article shows that within the framework of Euler hydrodynamics it is impossible to describe anticyclones. A critique of Euler’s hydrodynamic equations is presented. It is proposed to replace the Euler hydrodynamic equations with the equations of motion obtained from the action minimum. It is shown that this problem is related to the solution of the problem of the Clay Mathematics Institute—description of turbulence in a continuous medium.