The effect of wind shear on the formation of roll waves in flows down an incline

摘要

In this paper we investigate the effect of a prescribed superficial shear stress on the generation and structure of roll waves developing from infinitesimal disturbances on the surface of a fluid layer flowing down an incline.The unsteady equations of motion are depth integrated according to the von Kármán momentum integral method to obtain a nonhomogeneous system of nonlinear hyperbolic conservation laws governing the average flow rate and the thickness of the fluid layer. By conducting a linear stability analysis we obtain an analytical formula for the critical conditions for the onset of instability of a uniform and steady flow in terms of the prescribed surface shear stress. A nonlinear analysis is performed by numerically calculating the nonlinear evolution of a perturbed flow.The calculation is carried out using a TVD finite volume scheme.The source term is handled by implementing the quasi-steady wave propagation algorithm.Conclusions are drawn regarding the effect of the applied surface shear stress parameter and flow conditions on the development and characteristics of the roll waves arising from the instability.In the particular case of zero shear stress applied at the surface,the results are compared with those yielded by an analytical procedure.