(C) A small-amplitude wave is progressing in the positive x-direction on the surface ofwater of constant density p and depth h, so that the equation of the surface is z = n(x, t) wherez is measured vertically upwards from the undisturbed surface (z = 0).=e sin(kx - wt) with € < 1, the pressure in the fluid can beYou are given that for n(x, t)writtenP= Papgz + po,where Pa is the constant atmospheric pressure and is given by= eg sin(kx - wt) cosh[k(z + h)]/cosh(kh).Here k and w are related through the dispersion relationc = gk tanh kh.Consider the form of this flow in the shallow water limit, kh → 0.1. What is the dispersion relation in this limit?2. What is the wave speed?3. Show that to leading order in kh the horizontal component of velocity is the same at alldepths.4. Show that to leading order in kh the vertical component of velocity varies linearly withdepth, satisfying the kinematic boundary conditions on y = 0 and y = :-h.

Answered: Image /qna-images/answer/280ad92c-2c88-4dc1-9429-a85b3411229c.jpg

Answered: (C) A small-amplitude wave is…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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