Perturbation approach for a flow over a trapezoidal obstacle

In this paper, we tackle the two-dimensional and irrotational flow of inviscid and incompressible fluid over a trapezoidal obstacle. The free surface of the flow which is governed by the Bernoulli condition is determined as a part of solution of the problem. This condition renders difficult an analytical solution of the problem. Hence, our work's objective is utilize the Hilbert transformation and the perturbation technique to provide an approximate solution to this problem for large Weber numbers and various configurations of the obstacle. The obtained results demonstrate that the used method is easily applicable, and provides approximate solutions to these kinds of problems.