7 = Ae i(kc+ly-wt) Agk u= iko = i(ka+ly-wt) wcosh(KH) - cosh[k(z + H)]e:(kx+1 Agl v = ilo = wcosh(KH) - cosh[k(z + H)]el(ke+ly-wt) AgK wcosh(KH) - sinh[x(z + H)]ei(ka-ly-ut). dz (5.9) d i(kz+ly-at) W= Exercise 37 Show that in the case of deep water waves, the eigensolution in (5.9) is approximately given by 1 7 kg = A ei(kx+ly-wt) lg Kg u : ekz kg V ekz w igkekz while in the case of shallow water waves, we have 7 kg u = A KVIH lg KVGA 1 cosh(kz) cosh(kz) VGH sinh(62), ei(kx+ly-wt). w 7 = Ae i(kc+ly-wt) Agk u= iko = i(ka+ly-wt) wcosh(KH) - cosh[k(z + H)]e:(kx+1 Agl v = ilo = wcosh(KH) - cosh[k(z + H)]el(ke+ly-wt) AgK wcosh(KH) - sinh[x(z + H)]ei(ka-ly-ut). dz (5.9) d i(kz+ly-at) W= Exercise 37 Show that in the case of deep water waves, the eigensolution in (5.9) is approximately given by 1 7 kg = A ei(kx+ly-wt) lg Kg u : ekz kg V ekz w igkekz while in the case of shallow water waves, we have 7 kg u = A KVIH lg KVGA 1 cosh(kz) cosh(kz) VGH sinh(62), ei(kx+ly-wt). w