assn3 - 1.138J/2.062J/18.376J, WAVE PROPAGATION Fall, 2006...

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Unformatted text preview: 1.138J/2.062J/18.376J, WAVE PROPAGATION Fall, 2006 MIT C. C. Mei Homework set no 3, Due Oct 24,2006 1 Refraction of obliquely incident water wave in a shallow sea Read Section 1.5 Chapter 1. Start from eq (5.11). Consider one dimensional bathymetry: h = h ( x ) varying slowly from h at x to h 1 at x . A simple harmonic waves arrives from x . at an angle. Let ( x, y, t ) = [ ( x, y ) e it ] (H.1.1) Find the governing equation for ( x, y ). Assuming oblique incidence so that the incident wave is given by I ( x, y ) = Ae i x + iy , x (H.1.2) where is strictly a constant. Show first that in the far field to the left k = 2 + 2 = gh (H.1.3) then show that the incident wave number vector k = e x + e y is inclined with respect to the x axis by the angle of incidence where tan = / (H.1.4) When the wave enters the zone of slowly varying depth. Try a solution of the form x = A ( x ) exp i ( x ) dx +...
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This note was uploaded on 12/04/2011 for the course ESD 18.327 taught by Professor Gilbertstrang during the Spring '03 term at MIT.

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assn3 - 1.138J/2.062J/18.376J, WAVE PROPAGATION Fall, 2006...

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