Abstract
Приведен новый класс точных решений уравнений Навье-Стокса. Эти решения описывают нестационарные трехмерные по скоростям и двумерные по координатам течения вязкой несжимаемой жидкости. Процедура построения точного решения обобщает метод Тркала, предложенный для изучения винтовых течений. Новый класс точных решений позволяет описывать невинтовые течения (вектор скорости образует ненулевой угол с вектором завихренности) и течения жидкости, существующие конечное время.
Highlights
The study of the properties of Navier–Stokes equation solutions and continuity equation solutions is known to be based on different approaches, which can be divided into two big groups: analytical research and numerical integration
Conclusion.The paper has presented a procedure for constructing a new class of exact solutions to the Navier–Stokes equations for a viscous incompressible fluid
The obtaining of the new family of exact solutions is based on the modified Trkal method
Summary
The study of the properties of Navier–Stokes equation solutions and continuity equation solutions is known to be based on different approaches, which can be divided into two big groups: analytical research and numerical integration. Analytical research, in turn, is divided into the study of the general properties of flows (one of the latest results were obtained in [1,2,3]) and the integration of the equations of motion of a viscous incompressible fluid. Yu. A new class of non-helical exact solutions of the Navier–Stokes equations, Vestn.
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