Wind waves of period and amplitude cross a bay whose uniform depth is

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

Fluids and Continuum Physics, Ch Surface gravity and capillary waves

Problem

Wind waves of period T=3.0 sT = 3.0\ \mathrm{s} and amplitude a=0.25 ma = 0.25\ \mathrm{m} cross a bay whose uniform depth is 15 m15\ \mathrm{m}. The water is inviscid and incompressible with irrotational flow, surface tension is neglected, linear theory applies, and g=9.8 m s−2g = 9.8\ \mathrm{m\ s^{-2}}. ((a)) Find the wavelength, assuming the deep-water limit (and confirm it afterwards). ((b)) Find the phase speed. ((c)) Find the group velocity. ((d)) Using the linearised kinematic condition ∂η/∂t=∂ϕ/∂z\partial\eta/\partial t = \partial\phi/\partial z at z=0z = 0, find the largest magnitude of the vertical fluid velocity at the mean surface level.

Browse the problem library