next up previous
Next: Formulas from wave refraction Up: No Title Previous: Tsunami

Wave Refraction: Snell's Law

tex2html_wrap667

tex2html_wrap_inline635

tex2html_wrap_inline637

Snell's Law:

eqnarray103

Total power between wave rays A''A and B''B    (wave height tex2html_wrap_inline639 , group velocity tex2html_wrap_inline641 )

eqnarray113

Total power between wave rays AA' and BB'    (wave height tex2html_wrap_inline643 , group velocity tex2html_wrap_inline645 )

eqnarray121

eqnarray128

In the case 1 is at tex2html_wrap_inline615 then we replace subscript 1 with 0 and put no subscript for 2 (at depth d)

eqnarray138

Then H at depth d is related with tex2html_wrap_inline621 at infinite depth from:

eqnarray153

tex2html_wrap_inline651       tex2html_wrap_inline653

Textbook(SPM) defines as

tex2html_wrap_inline655 = wave height in deep water if the wave is not refracted

eqnarray178

tex2html_wrap_inline657 is given as tex2html_wrap_inline623 on Table C-1 of the 2nd volume of SPM.

Then the refraction coefficient may be defined as:

eqnarray192

eqnarray199

From geometry shown in figure at the beginning of this section.

tex2html_wrap_inline661

(remember 1 tex2html_wrap_inline663 0,   2 tex2html_wrap_inline663 no subscript)

eqnarray211





Soon Woong Chang
Fri Oct 22 11:39:22 CDT 1999