Abstract:
Dam-break flows are well known to be with non-hydrostatic pressure distribution in a vertical plane. However, all most all the mathematical models for dam-break flows use SaintVenant equations which assume hydrostatic pressure in the vertical; direction. In this report, an attempt has been made to study dam-break flows taking the effect of non-hydrostatic pressure distribution into account. For this purpose, the governing equations used in the present mathematical model are Boussinesq equations. Comparing with the Saint-Venant equations, these equations have three extra terms in the momentum equation. Due to the presence of a third order term in the equations, the numerical procedure adopted is third order accurate. The mathematical model is validated against previous experimental results. The model is applied to study the effect of non-hydrostatic pressure distribution on the free surface profile and the height and propagation of dam-break flood wave for various depth ratios (ratio of initial depths, downstream and upstream of the dam). The effect due to bed roughness and bed slope is also studied. The results show that inclusion of extra terms introduce oscillations that are actually taking place in the free surface. These oscillations are significant only for depth ratios greater than 0.4. The maximum deviation of the water level is of the order of 7%. The effect of non-hydrostatic pressure distribution exists only for a short time after the breaking of the dam. This time period depends on the depth ratio. However this may prevail for a considerable distance down stream of the dam. Out of the three extra terms used in the governing equations, first term (consisting of time derivative) is unimportant.
