A. V. Schmidt | Searcharxiv

arXiv2010

Non-invariant solutions of the three-dimensional semi-empirical model of the far turbulent wake

A semi-empirical three-dimensional model of turbulence in the approximation of the far turbulent wake behind a body of revolution in a passive stratified medium is considered. The sought quantities are the kinetic turbulent energy, kinetic energy dissipation rate, averaged density defect and density fluctuation variance. The full group of transformations admitted by this model is found. The model is reduced to the system of the ordinary differential equations due to similarity presentations obtained and B-determining equations method. System of ordinary differential equations satisfying natural boundary conditions was solved numerically. The solutions obtained agree with experimental data.

physics.flu-dyn↗

arXiv2003

Linear determining equations, differential constraints and invariant solutions

A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical determining equations used in the search for admissible Lie operators. As applications of this approach non-linear heat equations and Gibbons-Tsarev's equation are discussed. We introduce the notion of an invariant solution under an involutive distribution and give sufficient conditions for existence of such a solution.

math-ph↗