Velocity distribution and wake-law in gradually decelerating flows

Abstract

An attempt was made to explain deviations of measured Reynolds-shear stresses from the linear distribution and measured velocity ū from the log-law in decelerating flows. Starting from the Reynolds equations, this investigation shows that the momentum flux ρū driven by a nonzero wall-normal velocity plays an important role for these deviations. The term ρū , similar to the Reynolds stress, should not be neglected in the momentum equation, therefore. Theoretical and experimental studies evidence the existence of an upward velocity component in decelerating flows. It was confirmed that the classical log-law is applicable if and only if the wall-normal velocity is zero, and the wake-function is caused by an up-flow. The relation between the wake-strength and the wall-normal velocity was also established. The model developed produces reasonable agreement with measured velocity profiles available in the literature.

Keywords:

• Log-law
• non-uniform flow
• Reynolds-shear stress
• velocity distribution
• wake-law
• wall-normal velocity