Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must change (continuously or discontinuously) with depth/height due to changes, for example, in temperature and/or salinity. If the density changes over a small vertical distance (as in the case of the thermocline in lakes and oceans or an atmospheric inversion), the waves propagate horizontally like surface waves, but do so at slower speeds as determined by the density difference of the fluid below and above the interface. If the density changes continuously, the waves can propagate vertically as well as horizontally through the fluid. Internal waves, also called internal gravity waves, go by many other names depending upon the fluid stratification, generation mechanism, amplitude, and influence of external forces. If propagating horizontally along an interface where the density rapidly decreases with height, they are specifically called interfacial (internal) waves. If the interfacial waves are large amplitude they are called internal solitary waves or internal solitons. If moving vertically through the atmosphere where substantial changes in air density influences their dynamics, they are called anelastic (internal) waves. If generated by flow over topography, they are called Lee waves or mountain waves. If the mountain waves break aloft, they can result in strong warm winds at the ground known as Chinook winds (in North America) or Foehn winds (in Europe). If generated in the ocean by tidal flow over submarine ridges or the continental shelf, they are called internal tides. If they evolve slowly compared to the Earth's rotational frequency so that their dynamics are influenced by the Coriolis effect, they are called inertia gravity waves or, simply, inertial waves. Internal waves are usually distinguished from Rossby waves, which are influenced by the change of Coriolis frequency with latitude.
Visualization of internal waves An internal wave can readily be observed in the kitchen by slowly tilting back and forth a bottle of salad dressing - the waves exist at the interface between oil and vinegar. Atmospheric internal waves can be visualized by wave clouds: at the wave crests air rises and cools in the relatively lower pressure, which can result in water vapor condensation if the relative humidity is close to 100%. Clouds that reveal internal waves launched by flow over hills are called lenticular clouds because of their lens-like appearance. Less dramatically, a train of internal waves can be visualized by rippled cloud patterns described as herringbone sky or mackerel sky. The outflow of cold air from a thunderstorm can launch large amplitude internal solitary waves at an atmospheric inversion. In northern Australia, these result in Morning Glory clouds, used by some daredevils to glide along like a surfer riding an ocean wave. Satellites over Australia and elsewhere reveal these waves can span many hundreds of kilometers. Undulations of the oceanic thermocline can be visualized by satellite because the waves increase the surface roughness where the horizontal flow converges, and this increases the scattering of sunlight (as in the image at the top of this page showing of waves generated by tidal flow through the Strait of Gibraltar).
Buoyancy, reduced gravity and buoyancy frequency According to Archimedes' principle, the weight of an immersed object is reduced by the weight of fluid it displaces. This holds for a fluid parcel of density ρ {\displaystyle \rho } surrounded by an ambient fluid of density ρ 0 {\displaystyle \rho _{0}} . Its weight per unit volume is g ( ρ − ρ 0 ) {\displaystyle g(\rho -\rho _{0})} , in which g {\displaystyle g} is the acceleration of gravity. Dividing by a characteristic density, ρ 00 {\displaystyle \rho _{00}} , gives the definition of the reduced gravity:
g ′ ≡ g ρ − ρ 0 ρ 00 {\displaystyle g^{\prime }\equiv g{\frac {\rho -\rho _{0}}{\rho _{00}}}}
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