A subpolar shelf sea at latitude has a uniform depth

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 subpolar shelf sea at latitude 63∘N63^\circ\mathrm{N} has a uniform depth h=120 mh = 120\,\mathrm{m}. Its seasonal pycnocline has buoyancy frequency N=4.0×10−3 s−1N = 4.0\times10^{-3}\,\mathrm{s^{-1}}. The semi-diurnal tidal frequency is ωtide=1.405×10−4 s−1\omega_{\rm tide} = 1.405\times10^{-4}\,\mathrm{s^{-1}} (period 12.42 h12.42\,\mathrm{h}). Take Ω=7.292×10−5 rad s−1\Omega = 7.292\times10^{-5}\,\mathrm{rad\,s^{-1}} and g=9.81 m s−2g = 9.81\,\mathrm{m\,s^{-2}}. Separately, a storm surge sets up a step of height Δ=0.6 m\Delta = 0.6\,\mathrm{m} in the sea surface across the same 120 m120\,\mathrm{m}-deep sea, which is at rest. Model the sea with the linear shallow-water equations on a plane of constant ff, and treat it as unbounded along the step. ((a)) Find the Coriolis parameter ff at 63∘N63^\circ\mathrm{N}. ((b)) State the band of angular frequencies, and of periods, that free inertia-gravity waves occupy in the pycnocline. ((c)) Decide whether a free semi-diurnal internal tide can propagate at 63∘N63^\circ\mathrm{N}, and check the decision against the critical latitude of 74.5∘74.5^\circ at which ff reaches the semi-diurnal frequency. ((d)) For the storm-surge step, find the half-width of the front the step adjusts to and the peak geostrophic current in the final state. ((e)) State what fraction of the potential energy released by the step's collapse is radiated away as Poincare waves, and what fraction remains as kinetic energy of the geostrophic front.

Browse the problem library