A straight channel with parallel coasts at and

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Waves in two and three dimensions, dispersion and wave packets

Signal Speeds in Fluids, Ch Waves in a rotating fluid: inertial, Poincare and Kelvin waves

Problem

A straight channel with parallel coasts at

y=0

and

y=W

, with

W=50\,\mathrm{km}

, has uniform depth

h=40\,\mathrm m

and lies at latitude

51^\circ\mathrm N

. A Kelvin wave,

\eta=\eta_0e^{-y/L_{\rm R}}\cos(kx-\omega t)

trapped against the coast at

y=0

, enters the channel from the open ocean and propagates in the

+x

direction. ((a)) Sketch the co-tidal pattern: draw the lines of simultaneous high tide across the channel, state their shape and spacing, and mark which coast carries the larger tidal range. ((b)) State which coast is on the wave's right for this Northern Hemisphere channel, and compute the ratio of tidal range between the two coasts.

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