(a) A deep-water swell has wavelength . Using the Stokes-Michell limiting steepness ,…

PHYSICS · Subjective · 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) A deep-water swell has wavelength

\lambda = 220\,\mathrm{m}

. Using the Stokes-Michell limiting steepness

H/\lambda = 0.141

, find the greatest height a steady wave of this length can have. (b) A swell running onto a gently sloping beach is

2.5\,\mathrm{m}

high at the point where it starts to break. Using McCowan's shallow-water breaking ratio

H_{\rm b}/h_{\rm b} \approx 0.78

, estimate the depth

h_{\rm b}

at which it breaks.

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