Water Waves On a Shallow Sloping Beach

Cover Water Waves On a Shallow Sloping Beach
Water Waves On a Shallow Sloping Beach
Kurt Otto Friedrichs
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(z) at a fixed point z. Evidently, only points z = x on the water surface remain in the water region for arbi- trarily small angles i*^ ; therefore, we consider only points z = x. In accordance with the shallow water theory, see Stoker [3, Section 3], the answer" to this question is probably that X (x) and X (x) behave asymptotically like (10) Xi = 2TrJ^(2 \/v^ ), 11 = SttYqCS \f^7^ ), co Z, involving the regular and singular Bessel f\anctions J^ and Y • These Bessel functions die out at infini...ty, o o Therefore the approximate solutions (10) cannot represent the exact solutions far away from shore since the wave motion does not die out but beloaves sinusoidally at large distances from shore. For a slope angle

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