Abstract

Boundary layer theory is used to show that, at large Reynolds numbers, the three-dimensional Navier–Stokes equations can be rewritten in a form with diffusion velocity that was previously known for the cases of two-dimensional and axisymmetric flows. Relying on this hypothesis, a closed system of equations that is a development of a similar model for the indicated special cases is derived to describe fluid flows in the Lagrangian approach. Simultaneously, a number of mathematical issues are investigated. The existence of an integral representation for the velocity field with integrals with respect to Lagrangian coordinates is proved by analyzing the equations of motion of selected Lagrangian particles and applying the theory of ordinary differential equations with parameters. An equation describing the vorticity flux from the body surface is derived.

中文翻译：

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大雷诺数的三维粘性流的拉格朗日描述

摘要

边界层理论用于表明，在较大的雷诺数下，三维Navier-Stokes方程可以用先前在二维和轴对称流动情况下已知的扩散速度来重写。根据该假设，得出了一个封闭的方程系统，该系统是针对所示特殊情况的类似模型的发展，用于描述拉格朗日方法中的流体流动。同时，研究了许多数学问题。通过分析选定的拉格朗日粒子的运动方程并应用常微分方程理论和参数，证明了速度场具有相对于拉格朗日坐标的积分表示形式。