Internal Gravity Waves

Ocean waves move due to gravity: the water at crests is heavier than the air surrounding it and so it falls, overshoots its equilibrium position and then at a trough feels an upward restoring force. The same phenomena occurs below the ocean surface. Cold water lifted upward into warmer surroundings will feel a downward buoyancy force and downwarddisplaced warm water will feel an upward buoyancy force. If this motion is periodic in both space and time, it is referred to as an internal gravity wave. Internal gravity waves are manifest in two qualitatively different forms, which we will refer to here as “interfacial waves” and “internal waves”. (The dynamics of internal waves are broadly discussed in the textbook “Internal Gravity Waves” (Sutherland 2010)). Interfacial waves exist at the interface between dense and less dense fluid such as the thermocline, which refers to the interface between warm and cold water, or an atmospheric inversion, which refers to the interface between warm and cold air. In the ocean and in laboratory experiments, they can also exist at a halocline, which is the interface between fresh and salty water. An example of such a wave is shown in Figure 1a, in which a subsurface disturbance has launched a wave beneath a nearly flat surface. Looking down on the surface, the presence of these waves is evident from fluctuating horizontal flows and, on large scales, changing surface roughness. Large-amplitude interfacial waves at the thermocline in the ocean and launched onto the continental shelf by tides provide enhanced transport of fluid and biology. For this reason, they are of interest to marine biologists, sediment geologists as well as theoretical modellers. The second form of internal gravity wave exists in continuously stratified fluid, which means that the effective density of the fluid gradually decreases with height. These waves again move up and down due to buoyancy, but they are not confined to an interface; they can move vertically as well as horizontally through the fluid. These are shown in Figure 1b in which model hills create a perturbation that launches waves moving upward through the fluid whose density decreases linearly with height as the salinity decreases. Though not of primary importance, internal waves have a non-negligible influence upon weather and climate through the vertical transport of energy and momentum. In the atmosphere, for example, the waves launched by flow over mountains exert drag on the air far above where they break. In the ocean, wave breaking is a source of deep-ocean mixing, which is an important means of vertically redistributing heat. On the mesoscale, breaking