A deep-water swell has period and amplitude

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Waves, acoustics and compressible flow · Waves, acoustics and compressible flow

Signal Speeds in Fluids, Ch Waves of finite height: Stokes waves, shoaling and breaking

Problem

A deep-water swell has period

T = 6.0\,\mathrm{s}

and amplitude

a = 1.5\,\mathrm{m}

. Its second-order Stokes profile is

\eta = a\cos(kx-\omega t) + \tfrac12 k a^2 \cos\!\big[2(kx-\omega t)\big],

with

k

found from the deep-water dispersion relation

\omega^2 = gk

. Find ((a)) the wave steepness

ka

; ((b)) the height of the crest above the mean water level; ((c)) the depth of the trough below the mean water level.

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