Author(s): Elham Darvishi; John D. Fenton; Salah Kouchakzadeh
Keywords: Control structures; curved flow; flow-structure interactions; hydraulic structure design; one-dimensional models; spillways; transcritical flow
Abstract: A finite-slope Boussinesq equation is developed to model curved transcritical flow over spillways and broad-crested weirs, even with large slopes. At a number of computational points, finite difference approximations for all derivatives in the differential equation are used to give a system of nonlinear algebraic equations which can be solved by standard optimization methods. A number of laboratory experiments were performed with different transcritical flow problems including changes in channel gradients and a trapezoidal weir. The equation and the numerical model were tested using results from those experiments and from those for a steep and sharply-curved weir structure, with good results. They can be used as a computational flume to determine the head-discharge characteristics of proposed structures. A novel feature of the equation and numerical method is that higher derivatives of the bed topography are best ignored, apparently mimicking the effects of flow separation in smoothing it.