Bulletin of the Australian Mathematical Society

Table of Contents - Volume 11 - Issue02

Research Article

Waves on a shear flow

K.K. Puria1

a1 Department of Mathematics, University of Maine at Orono, Orono, Maine, USA.

Abstract

The propogation of disturbance when a shear flow with a free surface, in a channel of infinite horizontal extent and finite depth, is disturbed by the application of time-oscillatory pressure, is studied. The initial value problem is solved by using transform techniques and the steady state solution is obtained therefrom in the limit t → ∞. The effect of the initial shear on the development of the wave system is investigated.

(Received May 24 1974)

References

  • [1] Debnath, L. and Rosenblat, S., “The ultimate approach to the steady state in the generation of waves on a running stream”, Quart. J. Mech. Appl. Math. 22 (1969), 221–233. [OpenURL Query Data]  [CrossRef]  [Google Scholar]
  • [2] Jones, D.S., Generalised functions (McGraw-Hill, London, New York, Toronto, Sydney, 1966). [Google Scholar]
  • [3] Lighthill, M.J., Introduction to Fourier analysis and generalized functions (Cambridge University Press, Cambridge, 1958). [Google Scholar]
  • [4] Michell, J.H., “The wave-resistance of a ship”, Philos. Mag. (5) 45 (1898), 106–123. [OpenURL Query Data]  [Google Scholar]
  • [5] Puri, K.K., “Linear theory of water waves on a running stream”, J. Eng. Math. 4 (1970), 283–290. [OpenURL Query Data]  [CrossRef]  [Google Scholar]
  • [6] Stoker, J.J., Water waves: the mathematical theory with applications (Pure and Applied Mathematics, 4. Interscience, New York, London, 1957). [Google Scholar]