Each observation below is something the linear wave does not predict

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

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

Problem

Each observation below is something the linear wave does not predict. For each, decide whether Stokes drift, amplitude dispersion or breaking explains it, and support the choice with the number asked for. All three are in deep water. ((a)) On a windless day a surface drifter sits in a steady swell of period

8.0\,\mathrm{s}

and amplitude

1.0\,\mathrm{m}

. A current meter moored nearby, averaging over many periods at a fixed point below the troughs, records no mean current, yet the drifter moves about

4\,\mathrm{km}

a day in the direction the swell travels. Find the surface drift speed your mechanism predicts. ((b)) In a wave flume

1.5\,\mathrm{m}

deep, a train of waves

2.0\,\mathrm{m}

long and

0.16\,\mathrm{m}

high is timed between two gauges

10.0\,\mathrm{m}

apart. Individual crests take

5.5\,\mathrm{s}

to pass from one gauge to the other. Find the crossing time your mechanism predicts. ((c)) Far from land, over water

4000\,\mathrm{m}

deep, waves measured at

39.0\,\mathrm{m}

from crest to crest grow to about

5.5\,\mathrm{m}

high and their crests spill into whitecaps. Find the greatest height your mechanism allows at this wavelength.

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