Sachdev, PL and Philip, V (1986) Invariance group properties and exact solutions of equations describing time-dependent free surface flows under gravity. In: Quarterly of Applied Mathematics, 43 (4). 465 -482.
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Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.
| Item Type: | Journal Article |
|---|---|
| Publication: | Quarterly of Applied Mathematics |
| Publisher: | American Mathematical Society |
| Additional Information: | Copyright of this article belongs to American Mathematical Society. |
| Keywords: | Computational fluid dynamics;flow equations;free boundaries;gravitational effects;group theory;invariance; partial differential equations;shallow water;time dependence;two dimensional flow. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 09 Feb 2010 08:05 |
| Last Modified: | 09 Feb 2010 08:05 |
| URI: | http://eprints.iisc.ac.in/id/eprint/22814 |
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