### Numerical solutions of flows under an inclined gate

#### Abstract

Two-dimensional free-surface ows of an inviscid and incompressible fluid under an inclined gate is considered. The ow is assumed to be steady and irrotational. This problem is solved numerically by using boundary integral equation technique. Numerical results for inclined gate are presented for various values of the gate inclination $\gamma$ and the gate lengt L when the upstream free surface separates at a stagnation point. These solutions can be found for certain values of $\gamma$, that is, $\chi_L<\gamma\leq 90^\circ$. Here $\chi_L$ is the lower bound for gate inclination depending on the gate length L and the corresponding downstream Froude number. As the gate length decreases, nonlinear effect on the upstream waves is apparent so that the waves tend to develop narrow crests and broad troughs. When theupstream free-surface separates tangentially from the gate, the so-called smooth attachment, it is found that there exist solutions for larger values of gate inclination. As L increases, the elevation of the crests tends to the maximum level and the waves ultimately reach their limiting conguration characterized by a 120$^\circ$ angle at the crests.

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