A model for the free-surface flow due to a submerged source in water of infinite depth

We consider a free-surface flow due to a source submerged in a fluid of infinite depth. It is assumed that there is a stagnation point on the free surface just above the source. The free-surface condition is linearized around the rigid-lid solution, and the resulting equations are solved numerically by a series truncation method with a nonuniform distribution of collocation points. Solutions are presented for various values of the Froude number. It is shown that for sufficiently large values of the Froude number, there is a train of waves on the free surface. The wavelength of these waves decreases as the distance from the source increases.