Green’s Function of the Linearized Saint–Venant Equations in Laminar and Turbulent Flows

In the present paper, an analytical expression of the Green’s function. of linearized Saint–Venant equations (LSVEs) for shallow water waves is. provided and applied to analyse the propagation of a perturbation superposed. to a uniform flow. Independently of the kinematic character of the base flow,. i.e., subcritical or supercritical uniform flow, the effects of a non-uniform. vertical velocity profile and a non-constant resistance coefficient are. accounted for. The use of the Darcy–Weisbach friction law allows a unified. treatment of both laminar and turbulent conditions. The influence on the. wave evolution of the wall roughness and the fluid viscosity are finally. discussed, showing that in turbulent regime the assumption of constant. friction coefficient may lead to an underestimation of both amplification and. damping factors on the wave fronts, especially at low Reynolds numbers.. This conclusion has to be accounted for, particularly in describing hyper-. concentrated suspensions or other kinds of Newtonian mixtures, for which. the high values of the kinematic viscosity may lead to relatively low. Reynolds numbers.