The present work investigates the effect of the flow profile induced by an inlet condition on the roll-wave evolution in turbulent clear-water flows. The study employs theoretical and numerical analyses. Firstly, the influence of the inlet condition on the spatial evolution of a single perturbation in a hypercritical flow is examined through the expansion near a wavefront analysis. The results show that an accelerated unperturbed profile reduces the disturbance spatial growth. A decelerated profile causes an increase. The effect of the flow profile on the spatial evolution of rollwave trains is then numerically investigated solving the Saint Venant equations with a second-order Runge-Kutta Total Variation Diminishing (TVD) Finite Volume scheme. The numerical simulations comply with the analytical results for the initial and transition phases of the roll-wave development. The unperturbed profile influences even the roll-waves statistical characteristics in the final stage, with a more evident effect in case of accelerated profiles. The influence of the flow profile should be therefore accounted for in the formulation of predictive criteria for roll-waves appearance based on the estimation of the disturbance spatial growth rate.
The paper addresses the prediction of roll-waves occurrence in mud-flows. The spatial growth of a point-wise disturbance is analytically described, based on the linearized flow model of a Herschel and Bulkley fluid, in the neighborhood of an initial uniform base condition. The theoretical achievements allow to generalize to mud-flows the minimum channel criterion commonly used for the prediction of roll-waves in clear-water. The applicability of the criterion is discussed through the comparison with literature laboratory data concerning unstable flows without rollwaves.
By an analysis of the Brock’s model tests (Brock, 1969) conditions for forming of roll-waves are determined together with experimental equations of their parameters in relation to the channel inflow wave (Kunštátský, Maleňák, Pejchal, 1967; Kybast, 2002), aeration of flow (Douma, 1943; Haindl, Lískovec, 1973), channel slope and roughness along the whole range of the water flows. Calculations of lower and upper flow roll-waves discharge, depths, velocities, time periods, wave distances and volumes are presented. and Rozborem Brockových modelových zkoušek (Brock, 1969) jsou určeny podmínky tvoření translačních vln a experimentální rovnice jejich parametrů v souvislosti s rázovou vlnou napouštění koryta (Kunštátský, Maleňák, Pejchal, 1967; Kybast, 2002), s provzdušněním proudu (Douma, 1943; Haindl, Lískovec, 1973), sklonem koryta a s jeho drsností v celém rozsahu tohoto proudění vody. Předložen je výpočet dolního proudu a horního proudu s translačními vlnami, jejich průtoků, hloubek a výšek, rychlostí, časových period, vzdáleností a objemů vln.