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The Quarterly Journal of Mechanics and Applied Mathematics 1976 29(1):89-100; doi:10.1093/qjmam/29.1.89
© 1976 by Oxford University Press
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UNSTEADY WAVE MOTIONS ON A SLOPING BEACH WITH APPLICATION TO UNDER-WATER EXPLOSIONS

KRIPA SINDHU CHAUDHURI

( Department of Mathematics, Jadavpur University Calcutta 32, India )

A general solution of the two-dimensional problem of Cauchy–Poisson waves over beaches sloping at an angle {lambda} = {pi}/2q is obtained for all positive integral values of q. The wave integral is exactly evaluated in a closed form in several cases. The asymptotic value of the wave integral due to an instantaneous impulse Q {delta}(x – a) is obtained for large values of gt2/4|x±a |and is illustrated graphically. The theory is next applied to study the effect of an under-water explosive line source parallel to the shore line. Certain peculiarities of the motion are illustrated graphically.


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