assn5 - Sketch frst the curve o C g vs k and observe that...

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1.138J/2.062J/18.376J, WAVE PROPAGATION Fall, 2006 MIT C. C. Mei HW 5: Due Nov 30. Take-home fnal will be handed out on Dec 4 1. Capillary-gravity waves. Consider a ±ree sur±ace with capillarity in water infnite depth. Solve ±or the transient two -dimensional response to a localied initial elevation on the ±ree sur±ace b 1 ζ ( x, 0) = π x 2 + b 2 Deduce by Fourier trans±orm the ±ormal solution. Deduce the asymptotic result ±or ζ ( x, t ) ±or large t but fxed x/t . and describe the physics.
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Unformatted text preview: Sketch frst the curve o C g vs k and observe that or some x/t there are two stationary points. Examine the case where the two stationary points coalece to one where ( k ) = 0 , but ( k ) = 0 . Suggestion : You have to perorm Taylor expansion o the phase unction by keeping the term involving ( k ). 1...
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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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