Analysis of specific kinetic energy for the Birikh–Ostroumov shear diffusion flow

Abstract

The article presents a new exact solution for stratified steady-state shear diffusion flows of a viscous fluid in an infinite horizontal layer with impenetrable boundaries. The announced exact solution belongs to the Ostroumov–Birikh family. Two components of the velocity vector depend on the vertical (transverse) coordinate. The concentration field and the pressure field are described by linear forms relative to horizontal (longitudinal) coordinates, with coefficients depending on the third coordinate. The components of the velocity field and the shear stress field are analyzed in detail, and the behavior of the specific kinetic energy is studied. It is shown that this exact solution is capable of describing the stratification of the shear stress field and the nonmonotonic behavior of flow velocity. The relation of flow velocities and shear stresses to the distribution of specific kinetic energy is revealed.