A wave buoy in the North Sea

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

Fluids and Continuum Physics, Ch Surface gravity and capillary waves

Problem

A wave buoy in the North Sea, in water

60\ \mathrm{m}

deep, reports a swell of period

7.5\ \mathrm{s}

and amplitude

0.90\ \mathrm{m}

(that is, a crest-to-trough height of

1.8\ \mathrm{m}

). Model the swell as a single small-amplitude sinusoidal deep-water gravity wave on inviscid, incompressible water of density

1000\ \mathrm{kg\,m^{-3}}

, ignore surface tension, and take

g = 9.8\ \mathrm{m\,s^{-2}}

. The wave energy per unit surface area is

\mathcal{E} = \tfrac12\rho g a^{2}

and it travels at the group velocity. ((a)) Estimate the wave energy per unit area of sea surface. ((b)) Estimate the energy flux per metre of crest, in kilowatts per metre. ((c)) A row of wave-energy devices

250\ \mathrm{m}

long faces the swell and converts

30

per cent of the incident flux to electricity. Estimate its mean electrical output while this sea state lasts.

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