SYMMETRY OF THE COUPLING MATRIX BETWEEN FORCES AND FLOWS IN STRATIFIED TURBULENT FLOW IN A CHANNEL WITH AN ARBITRARILY SHAPED CROSS SECTION

Abstract

In this work, the stratified turbulent flow of several fluids in a channel of arbitrary shape was considered. It was assumed that the hydrostatic problem of finding free boundaries between different fluids has been solved, the regions in which individual fluids move are known, and the turbulent viscosity is known, but it is not constant in the cross section. The motion of the media arose under the actions of the applied pressure gradient and volumetric gravitational forces. Due to the conjugacy of the joint flow of N liquids, the density of the applied forces in the kth flow (<i>F_k</i>) can affect the flow rate of the ith liquid: <i>Q_i</i> &#61; &Sigma;_j&#61;1^N <i>L_ik F_k</i>. The results obtained prove in the most general form that the matrix of the coupling coefficients between the forces and flows is symmetric: <i>L_ik &#61; L_ki</i>. This resembles the symmetry in Onzager's matrix of phenomenological coefficients in nonequilibrium thermodynamics; however, the reasons for these symmetries are different.