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

TL;DR

This paper develops and solves a semi-empirical 3D turbulence model for the far wake behind a body of revolution, using symmetry reductions and numerical methods, with results aligning with experimental data.

Contribution

It introduces non-invariant solutions to a semi-empirical turbulence model using symmetry analysis and numerical solutions, expanding understanding of turbulent wake behavior.

Findings

Solutions match experimental data

Model reduction via similarity transformations

Numerical solutions of ODE system

Abstract

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.