Green’s function of the linearized Saint-Venant equations in laminar and turbulent flows |
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Authors: | Cristiana Di Cristo Michele Iervolino Andrea Vacca |
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Institution: | 1. Dipartimento di Meccanica, Strutture, Ambiente e Territorio, Università di Cassino, Cassino, Italy 2. Dipartimento di Ingegneria Civile, Seconda Università di Napoli, Aversa, Italy
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Abstract: | 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. |
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