(a) An internal wave beam is generated by an oscillating source in a lower ocean…
PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Waves, acoustics and compressible flow · Waves, acoustics and compressible flow
Signal Speeds in Fluids, Ch Internal gravity waves in a stratified fluid
Problem
(a) An internal wave beam is generated by an oscillating source in a lower ocean layer where the buoyancy frequency is N2=1.5×10−2rads−1, at forcing frequency ω=6.0×10−3rads−1. The beam then crosses a horizontal boundary into an upper layer where N1=8.0×10−3rads−1. As with the refraction of a wave crossing a boundary between two regions of a layered medium, the frequency of the disturbance must be the same on both sides of the boundary, since the boundary condition must be satisfied at every instant. Find the beam's angle to the vertical in each layer. (b) In a nearby fjord, a fresh surface layer of depth h1=5.0m overlies much deeper, denser water, with reduced gravity g′=0.15ms−2 across the interface. The fresh layer flows out over a sill at a steady surface current U=0.30ms−1. Find the long-wave interfacial speed and the Froude number of the outflow with respect to it, defined as in open-channel flow by Fr=U/c, and state whether the flow is subcritical or supercritical.