Turcotte, Donald L., and Gerald Schubert. Geodynam-ics. 2nd ed. Cambridge: Cambridge University Press, 2002.

Vanicek, Petr, and Nikolaos T. Christou. Geoid and Its Geophysical Interpretations. New York: CRC Press, 1994.

gravity wave The term gravity wave can be used in two different contexts. The first is in fluid dynamics in reference to waves generated in a fluid medium or at the interface between two fluids, such as air and water. The second context is in astrophysics and general relativity theory.

In fluid dynamics gravity waves form when a unit of fluid at an interface between two different fluids moves to a region with a different density. When this happens gravity attempts to restore the unit of fluid to equilibrium, forming an oscillating wave. Ocean waves generated by the wind are examples of one type of gravity wave known as surface gravity waves. When gravity waves form at boundaries between fluids in the ocean or atmosphere, they are known as internal gravity waves.

The transfer of energy from wind to the ocean surface causes the formation of surface gravity waves on the sea surface by two different mechanisms. If the surface of the ocean is initially flat and a turbulent wind blows across this surface, the fluctuation in the wind imposes fluctuating stresses on the ocean surface, oriented parallel and perpendicular to the surface. These stresses act as a forcing mechanism that may find a matching frequency and wave number for a mode of vibration of the sea surface, then the surface will begin to vibrate as a gravity wave. As more energy is added by the wind, a resonance grows, and the waves grow in amplitude. A resonance is the tendency of a system to oscillate at a maximum amplitude at specific frequencies, known as the resonance frequencies for that system. once the sea-air surface has this initial roughness, a second process helps the waves grow. In this phase the waves interact with the turbulent flow of the overlying air, with energy transferred to the new waves in a critical boundary layer that forms at a specific height where the wave speed equals the mean turbulent flow. This mechanism continues until the wind stops, or the distance (fetch) it can act on ends (where land is encountered), and the waves continue to grow until either of those points is met.

Gravity waves in the atmosphere transfer momentum from the troposphere (lower 6-7 miles [9.7-11 km] of the atmosphere) to the mesosphere (31-53 [50-85 km] miles above the surface], and often form in response to the movement of frontal systems and to the passage of air over mountain peaks. Low-altitude gravity waves may resemble undulating clouds and do not significantly change the velocity of the moving air mass. Gravity waves at higher altitudes at the boundary with low-density air become higher in amplitude and break, however, transferring significant energy and momentum to the mean flow of air in the mesosphere. They are thus extremely important in controlling the dynamics of the middle atmosphere.

Gravity waves are also prominent in Albert Einstein's theory of relativity, which forms the foundation of modern ideas about gravity. In this usage gravity waves can be thought of as gravitational radiation that results from a change in the strength of a gravitational field. In relativity theory any mass that accelerates through space will produce a small distortion in the space through which it is traveling, causing a change in the gravitational field, or a gravity wave, that should be emitted at the speed of light. However, the gravitational force is so small compared with the electromagnetic force that the distortions produced by gravity waves are expected to be less that the diameter of an atomic nucleus for masses the size of galaxies, and no one has yet detected a gravity wave in this relativistic sense. But, active research programs are attempting to detect gravity waves from interactions of massive objects such as merging binary star systems, black holes swallowing stars, and other galactic collisions. In one example scientists have observed the collapse of a binary star system to produce a shrinking orbit with energy loss from the system consistent with energy being carried away from the system by gravity waves as predicted by Einstein's relativity theory, but the waves themselves have not been detected.