Two Dimensional Waves Generated By a Surface Pressure Disturbance Over a Sloping
Two Dimensional Waves Generated By a Surface Pressure Disturbance Over a Sloping
M C Shen
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1) that c v; z ^ = -^^2?i/^ ^ 'K^^^ S2-, (0dC P In the follovring, v/e show that / is bounder at infinity. We deform the contour P to a contour D as shov/n in Fig. ?, and 2 w Z -. 2 Vf z - Re XI e ^ S2o(^n^ 7^[ ( C-4^)g. ( OJ, _ p n ^^ ^n ^ ^ *= - ^n 28 2 iw z -Re ie ^ 6^, (-i)[(4 + l)sAO]. _ . We can easily see that as z — > . 2 T-W z ^ _> _ Re ie S g (_!)[( t^ + i)g (C)]. _ . . In order to find a complete steady-state solution of (2. 1) v/e must consider the steady-state solutions of the homo...geneous equations obtained from (2. 1) viith, ^ . It has been fo\md in [?] that the only solution of ^xx ^yy -\i^'^ + g(t) = 0, ^n = ° ' v;hich is boun. Ed at infinity and meets the recuirement that &^iO ^ ^ ^ as i, — > 00 takes the form C v/'^z = - Re 2^ r e S ^ ^s, _{JdC, v;here A is a real constant. As z — > oo, . 2 __ _ iv; z ^ — > - Re iAe ^ [((, -:- i)Gii{s)]^^ .^ • 29 Therefore, the corn lete solution of our . Roblem will be 2 w z I- (5. 7) 5= -Re| sin wt / e^ i S. ( i, )[s^, ( 'J + a.
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