A weather buoy in deep water well offshore reports a swell of period and height

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 weather buoy in deep water well offshore reports a swell of period

T = 11.0\,\mathrm{s}

and height

H_0 = 3.0\,\mathrm{m}

, travelling straight towards a straight, gently sloping beach. ((a)) Shoal the swell with

K_{\rm s}=\sqrt{v_{\rm g0}/v_{\rm g}(h)}

and find, by bisection on

h

, the depth

h_{\rm b}

at which its shoaled height reaches McCowan's breaking ratio,

K_{\rm s}(h)H_0 = 0.78h

. Give

h_{\rm b}

and the breaking height

H_{\rm b}

. ((b)) Compare

h_{\rm b}

with the estimate

H_0/0.78

, and say why that estimate comes out too shallow.

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