Vortex models of shear laminar and turbulent flows

V. L. Mironov, S. V. Mironov

Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhnii Novgorod

Abstract: We discuss a mathematical model of laminar and turbulent shear flows of liquids and gases in rectangular channels based on a system of differential equations describing the longitudinal motion and rotation of vortex tubes. We show that in the case of a plane steady flow, this system of equations has two-parameter analytical solutions for velocity distributions in the cross-section of the channel, which are in good agreement with known experimental data and the results of numerical simulations. Model approximations of velocity profiles of laminar flows of non-Newtonian liquids and developed turbulent flows of liquids and gases in rectangular channels are discussed as examples.

Keywords: equation of vortex flows, non-Newtonian liquid, turbulence, Reynolds tensor, eddy viscosity

UDC: 517.956

MSC: 35Q35; 76A05; 76F25

DOI: 10.36535/2782-4438-2025-239-32-42

 English version: Journal of Mathematical Sciences (New York), 2025, 292:3, 362–372