Search

The paper theoretically investigates the stability properties of the dam-break wave of a fluid with power-law rheology. Assuming the long-wave approximation, a depth-averaged flow model is considered. The linear stability analysis of the wave is carried out to individuate the marginal stability conditions. To this aim, the multiple-scale technique is applied with reference to the kinematic wave solution, which formally limits the validity of the theoretical achievements to relatively long time scales. Both shear-thinning and shear-thickening fluids are considered. Similarly to the case with uniform conditions, the analysis indicates that stable conditions can be associated with a marginal value of the Froude number. However, differently from the uniform conditions, the marginal Froude number is shown to be a function not only of the power-law index but also of the streamwise gradient of the base flow velocity and of the disturbance wavelength. The critical Froude number is found to be larger than the corresponding one in uniform conditions. Numerical solutions of the full model confirmed the outcomes of the linear stability analysis for both shear-thinning and shear-thickening fluids. [ABSTRACT FROM AUTHOR]

The article presents a discussion on a study "Divergence Form for Bed Slope Source Term in Shallow Water Equations," by Alessandro Valiani and Lorenzo Begnudelli. According to the authors, the researchers demonstrate an effective way of dealing shallow flows over complex topographies and proposed a novel technique to treat the source term attributable to bed slope in the shallow water equations. This technique is independent of the numerical method used to solve the shallow water equations. Moreover, the researchers emphasize the importance of hydraulic jump over a flat bed.