TY - JOUR

T1 - Mixing layer and turbulent jet flow in a Hele–Shaw cell

AU - Chesnokov, Alexander

AU - Liapidevskii, Valery

PY - 2020/10/1

Y1 - 2020/10/1

N2 - A plane turbulent mixing in a shear flow of an ideal homogeneous fluid confined between two relatively close rigid walls is considered. The character of the flow is determined by interaction of vortices arising at the non-linear stage of the Kelvin–Helmholtz instability development and by turbulent friction. In the framework of the shallow water theory and a three-layer representation of the flow, one-dimensional models of a mixing layer are proposed. The obtained equations allow one to determine averaged boundaries of the region of intense fluid mixing. Stationary solutions of the governing equations are constructed and analysed. Using the averaged flow characteristics obtained by one-dimensional equations, a hyperbolic system for determining the velocity profile and Reynolds shear stress across the mixing layer is derived. Comparison with the experimental results of the evolution of turbulent jet flows in a Hele–Shaw cell shows that the proposed models provide a fairly accurate description of the average boundaries of the region of intense mixing, as well as the velocity profile and Reynolds shear stress across the mixing layer.

AB - A plane turbulent mixing in a shear flow of an ideal homogeneous fluid confined between two relatively close rigid walls is considered. The character of the flow is determined by interaction of vortices arising at the non-linear stage of the Kelvin–Helmholtz instability development and by turbulent friction. In the framework of the shallow water theory and a three-layer representation of the flow, one-dimensional models of a mixing layer are proposed. The obtained equations allow one to determine averaged boundaries of the region of intense fluid mixing. Stationary solutions of the governing equations are constructed and analysed. Using the averaged flow characteristics obtained by one-dimensional equations, a hyperbolic system for determining the velocity profile and Reynolds shear stress across the mixing layer is derived. Comparison with the experimental results of the evolution of turbulent jet flows in a Hele–Shaw cell shows that the proposed models provide a fairly accurate description of the average boundaries of the region of intense mixing, as well as the velocity profile and Reynolds shear stress across the mixing layer.

KW - Hele–Shaw cell

KW - Jet flow

KW - Mixing layer

KW - Shallow water equations

KW - Hele-Shaw cell

KW - FRICTION

KW - EVOLUTION

KW - DISPERSION

KW - STABILITY

KW - MODEL

KW - SHALLOW

UR - http://www.scopus.com/inward/record.url?scp=85086581721&partnerID=8YFLogxK

U2 - 10.1016/j.ijnonlinmec.2020.103534

DO - 10.1016/j.ijnonlinmec.2020.103534

M3 - Article

AN - SCOPUS:85086581721

VL - 125

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

M1 - 103534

ER -