Free-surface flows under an inclined sluice gate

Abstract

In this thesis we consider the problem of free-surface flows under a gate that is inclined at an angle [gamma]. The fluid is treated as inviscid and incompressible. The flow is assumed to be steady two-dimensional and irrotational. The effect of surface tension is neglected. Dynamic boundary condition is applied on both upstream and downstream free surfaces subject to gravitational force. The problem is solved numerically by using boundary integral equation technique. After the discretization, we obtain a system of nonlinear algebraic equations which can be solved by the Newton's method. When the upstream free surface separates at a stagnation point, numerical results for inclined gate are presented for various values of [gamma]. These solutions exist for certain values of gate inclination, in particular, [chi][is less than][chi][is less than or equal to][pi]2 . Here [chi] is the lower bound for gate inclination depending on the gate length and the corresponding Froude number. As the gate length decreases, nonlinear effect on the upstream waves becomes more pronounced in that the waves tend to develop narrow crests and broad troughs. Difficulties arise in the numerical computation as we attempt to calculate solutions for [gamma] | [chi]. This is because the free surface near upstream separation can no longer satisfy the prescribed stagnation point behavior. We also investigate the problem of flows past an inclined gate with smooth attachment. It is found that there are solutions for which the flows have been continuously tangent at both ends of the gate at which separation occurs.