Internal Waves in the Ocean

Salinity, temperature, and pressure gradients all cause the density of sea water to vary with depth in the ocean, and the density gradient affects the motion of the waters. A quantity N, having the units radians per second, can be defined using the density gradient, the velocity of sound, and the acceleration of gravity.The simplest motions have the form of horizontally progressive waves of frequency ω, wave number κ, and velocity V. If h is the amplitude of the vertical displacement of the water and z the vertical coordinate, then V2(d2h/dz2) + [N2(z) − ω2]h = 0; this equation is formally identical with Schrodinger's wave equation. The stream function of these waves is φ = Vh(z) sin (κx − ωt), and the variable part of the pressure is − ρ dφ/dz, while the vorticity is R = −N2φ/V2. The wave may be described as a lattice of vortices moving with velocity V. In the ocean N(z) ordinarily has one or two maxima called thermoclines. The analogy with the quantum‐mechanical problems of one and two potential minima ...