| <div class="definition"><div class="short_definition">(''Also called'' gravitational wave.) A [[wave disturbance]] in which [[buoyancy]] (<br/>''or'' [[reduced gravity]]) acts as the restoring force on parcels displaced from [[hydrostatic equilibrium]].</div><br/> <div class="paragraph">There is a direct oscillatory conversion between [[potential]] and [[kinetic energy]] in the [[wave motion]]. Pure gravity waves are stable for fluid systems that have [[static stability]]. This static stability may be 1) concentrated in an [[interface]] or 2) continuously distributed along the axis of [[gravity]]. The following remarks apply to the two types, respectively. 1) A [[wave]] generated at an [[interface]] is similar to a [[surface wave]], having maximum amplitude at the interface. A plane gravity wave is characteristically composed of a pair of waves, the two moving in opposite directions with equal speed relative to the fluid itself. In the case where the upper fluid has zero [[density]], the interface is a [[free surface]] and the two gravity waves move with speeds <div class="display-formula"><blockquote>[[File:ams2001glos-Ge44.gif|link=|center|ams2001glos-Ge44]]</blockquote></div> where ''U'' is the current speed of fluid, ''g'' the [[acceleration of gravity]], ''L'' the [[wavelength]], and ''H'' the depth of the fluid. For [[deep-water waves]] (or Stokesian waves or short waves), ''H'' >> ''L'' and the [[wave speed]] reduces to <div class="display-formula"><blockquote>[[File:ams2001glos-Ge45.gif|link=|center|ams2001glos-Ge45]]</blockquote></div> For [[shallow-water waves]] (or Lagrangian waves or long waves), ''H'' << ''L'', and <div class="display-formula"><blockquote>[[File:ams2001glos-Ge46.gif|link=|center|ams2001glos-Ge46]]</blockquote></div> All waves of consequence on the ocean surface or interfaces are gravity waves, for the [[surface tension]] of the water becomes negligible at wavelengths of greater than a few centimeters (<br/>''see'' [[capillary wave]]). 2) Heterogeneous fluids, such as the [[atmosphere]], have static stability arising from a [[stratification]] in which the [[environmental lapse rate]] is less than the [[process lapse rate]]. The atmosphere can support short internal gravity waves and long external gravity waves. The short waves (of the order of 10 km) have been associated, for example, with [[lee waves]] and [[billow waves]]. Such waves have vertical accelerations that cannot be neglected in the vertical equation of [[perturbation motion]]. The long gravity waves, moving relative to the atmosphere with speed ±(''gH'')<sup>½</sup>, where ''H'' is the height of the corresponding [[homogeneous atmosphere]], have small vertical accelerations and are therefore consistent with the [[quasi-hydrostatic approximation]]. In neither type of gravity wave, however, is the [[horizontal divergence]] negligible. For meteorological purposes in which neither type is desired as a solution, for example, [[numerical forecasting]], they may be eliminated by some restriction on the magnitude of the horizontal divergence. The above discussion is based upon the [[method of small perturbations]]. In certain special cases of water waves, for example, the [[Gerstner wave]] or the [[solitary wave]], a theory of finite-amplitude disturbances exists. <br/>''See'' [[shear-gravity wave]].</div><br/> </div><div class="reference">Gill, A. E. 1982. Atmosphere–Ocean Dynamics. Academic Press, . 95–188. </div><br/>
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