Year: 2025
Type: article
Abstract: This study presents a new exact solution describing the non-uniform distribution of velocity and pressure fields in an isothermal steady shear flow of a viscous incompressible fluid. The obtained exact solutions remain valid when kinematic viscosity is replaced with turbulent viscosity in the Navier-Stokes equations. We demonstrate that within the class of functions linear in some coordinates, any joint non-uniform solution for the velocity field must have a specific structure characterized by constant spatial accelerations. Specifically, either only two particular accelerations vanish, or all four spatial accelerations equal zero (corresponding to the homogeneous velocity field in the Ekman solution). No other joint solutions exist within this specified class. We analyze in detail the case with two non-zero spatial accelerations and provide the complete exact solution. To elucidate the fundamental properties of this solution, we investigate the corresponding boundary value problem and present comprehensive illustrative material.
DOI: 10.14498/vsgtu2179
Institutions: Ural Federal University, Institute of Engineering Science
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Russian Science Foundation
Award: G1582316008
OpenAlex ID: W4414750156