Analytical Solution for Transverse Velocity of Turbulent Flow in Channel

Abstract The analytical solution for the streamwise mean velocity of turbulent flow of incompressible fluid in a channel was presented in Fedoseyev (2023) paper. In this work, we present both the stationary and transient solutions for the transverse velocity component. The obtained transient solution is a product of a series of periodic functions in space and time, multiplied by a growing exponential function of time. This analytical solution reveals the instability and imminence of oscillations in the turbulent flow. The obtained solutions are compared with numerical simulation results and experimental data, demonstrating a close agreement or strong similarity.