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.

中文翻译：

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连续介质的涡旋运动取决于压力变化

在本文中，我们研究了连续介质的涡旋运动，该涡旋运动由从最小作用原理获得的力来描述。结果表明，在连续介质中，涡旋力分量与速度和压力梯度分量成正比。本文介绍了高低压区域中空气的二维涡旋运动。如果压力减小，则连续介质的旋转角速度增大，而如果压力增大，则角速度减小。通过以漏斗形式的空气的涡旋运动获得提升力。结果表明，涡旋力包含欧拉流体力学方程的涡旋项，其相对因子等于连续介质速度的平方除以声速平方。为了正确描述连续介质的运动，有必要用从运动方程中最小作用力获得的力来代替欧拉获得的力。结论是，涡旋运动和湍流由获得的运动方程式描述，而不是由Navier–Stokes方程式描述。这很可能与2000年国际数学大会上宣布的关于湍流的千年描述问题有关。