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Internal waves (marked with arrows) caused by the Strait of Gibraltar

Internal waves are gravity waves that oscillate within, rather than on the surface of, a fluid medium. They arise from perturbations to hydrostatic equilibrium, where balance is maintained between the force of gravity and the buoyant restoring force. A simple example is a wave propagating on the interface between two fluids of different densities, such as oil and water. Internal waves typically have much lower frequencies and higher amplitudes than surface gravity waves because the density differences (and therefore the restoring forces) within a fluid are usually much smaller than the density of the fluid itself. Internal wave motions are ubiquitous in both the ocean and atmosphere. Nonlinear solitary internal waves are called solitons.

The atmosphere and ocean are continuously stratified: potential density generally increases steadily downward. Internal waves in a continuously stratified medium may propagate vertically as well as horizontally. The dispersion relation for such waves is curious: For a freely-propagating internal wave packet, the direction of propagation of energy (group velocity) is perpendicular to the direction of propagation of wave crests and troughs (phase velocity). An internal wave may also become confined to a finite region of altitude or depth, as a result of varying stratification or wind. Here, the wave is said to be ducted or trapped, and a vertically standing wave may form, where the vertical component of group velocity approaches zero. A ducted internal wave mode may propagate horizontally, with parallel group and phase velocity vectors, analogous to propagation within a waveguide.

At large scales, internal waves are influenced both by the rotation of the Earth as well as by the stratification of the medium. The frequencies of these geophysical wave motions vary from a lower limit of the Coriolis frequency (inertial motions) up to the Brunt-Väisälä, or buoyancy frequency (buoyancy oscillations). Above the Brunt-Väisälä frequency may exist evanescent internal wave motions, for example those resulting from partial reflection. Internal waves at tidal frequencies are produced by tidal flow over topography/bathymetry, and are known as internal tides. Similarly, Atmospheric tides arise from, for example, non-uniform solar heating associated with diurnal motion.

• Discussion and videos of internal waves made by an oscillating cylinder.