Steady-state solutions of the Navier–Stokes equation

Recieved: 09/25/2023

Accepted: 03/25/2024

Published: 06/26/2024

Keywords: Taylor vortices, tornado, gas cloud, Coriolis force, galaxy

To cite this article

Baev A.V. Steady-state solutions of the Navier–Stokes equation. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2024. N 3, p.25-38 https://doi.org/10.55959/MSU/0137-0782-15-2024-47-3-25-38.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Baev A.V. (Lomonosov Moscow State University (MSU))

Abstract

The concept of steady-state solutions of the Navier–Stokes equation is defined. Such solutions expand the concept of stationary, exponentially decrease in time, have a constant spatial velocity field and constant pressure in the absence of external fields. The method of their construction is considered, and the problem of Taylor vortices is solved. A mathematical model of a tornado is proposed. Within the framework of this model, a steady-state solution is obtained as an eigenfunction of the problem in the form of a vortex. Based on the Navier–Stokes equation, a model of the formation of the structure of a gas cloud is proposed. It is shown that due to the Coriolis force, spiral arms arise from flows of gas moving outward. It is proved that the number of arms m is even, and their structure does not depend on the angular velocity of rotation. A formula is obtained for the spiral twist angle depending on the cloud parameters for the case of m=2.