The semi-diurnal internal tide,

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

Signal Speeds in Fluids, Ch Internal gravity waves in a stratified fluid

Problem

The semi-diurnal internal tide, ω=1.405×10−4 rad s−1\omega = 1.405\times10^{-4}\,\mathrm{rad\,s^{-1}}, is generated over a ridge in an ocean of depth h=4000 mh = 4000\,\mathrm m with uniform N=3×10−3 s−1N = 3\times10^{-3}\,\mathrm{s^{-1}}. Treat the ocean as non-rotating, with a rigid lid and a flat floor. A beam leaves the floor as a plane wave whose vertical wavenumber is that of mode 1, m=π/hm = \pi/h. ((a)) Find the horizontal wavenumber kk of this wave and its horizontal wavelength. ((b)) Find the horizontal and vertical components of its group velocity, in magnitude, and the time its energy takes to climb from the floor to the surface. How far does that energy travel horizontally during the climb? ((c)) Compare the horizontal component of the group velocity with the mode-1 speed c1c_1, and the horizontal distance covered in one climb and one descent with the mode-1 wavelength at this frequency. What does the comparison say about how a vertical mode is built?

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