A storm generates deep-water swell of wavelength and height (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 storm generates deep-water swell of wavelength λ=156 m\lambda = 156\,\mathrm{m} and height H=8.0 mH = 8.0\,\mathrm{m} (amplitude a=H/2a = H/2). Using the amplitude-dispersion result quoted for steep waves, vp=g/k (1+12k2a2)v_{\rm p} = \sqrt{g/k}\,(1 + \tfrac12 k^2a^2), which compares waves of the same wavelength, ((a)) estimate the wave steepness kaka; ((b)) estimate the fractional increase in phase speed above the linear value, and the increase in m s−1\mathrm{m\,s^{-1}}.

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