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

**J.-M. Vanden-Broeck
**

Department of Mathematics and Center for the Mathematical Sciences

University of Wisconsin-Madison

WI 53706, USA

### Abstract:

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.

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© Copyright 1998, Australian Mathematical Society
*TeXAdel Scientific Publishing*

*26/04/2000*