Excited state fluid mechanics and mathematical principles of separation and transition

TL;DR

This paper introduces a new mathematical framework based on the concept of excited states to accurately describe and predict fluid separation and transition, addressing longstanding challenges in fluid mechanics.

Contribution

It develops an axiomatic approach and a general excited state theorem that clarify the conditions and laws governing fluid separation and transition.

Findings

Derived conditions for fluid separation and transition

Established general laws of excited states in flowfields

Provided a foundation for turbulence mechanism research

Abstract

Transition and separation are difficult but important problems in the field of fluid mechanics. Hitherto, separation and transition problems have not been described accurately in mathematical terms, leading to design errors and prediction problems in fluid machine engineering. The nonlinear uncertainty involved in separation and transition makes it difficult to accurately analyze these phenomena using experimental methods. Thus, new ideas and methods are required for the mathematical prediction of fluid separation and transition. In this article, after an axiomatic treatment of fluid mechanics, the concept of an excited state is derived by generating a fluctuation velocity, and it is revealed that fluid separation and transition are special forms of this excited state. This allows us to clarify the state conditions of fluid separation and transition. Mathematical analysis of the Navier--Stokes equations leads to a general excited state theorem suitable for flowfields. Finally, the conditions of separation and transition are derived, and the corresponding general laws are established. The results presented in this article provide a foundation for future research on the mechanism of turbulence and the solution of engineering problems.