Long-period tides

An analysis of the changing distance of the Earth relative to Sun, Moon, and Jupiter by Pierre-Simon de Laplace in the 18th century showed that the periods at which gravity varies cluster into three species: the semi-diurnal and the diurnal tide constituents, which have periods of a day or less, and the long-period tidal constituents.

[clarification needed] The long period tides are also distinguished by the way in which the oceans respond: forcings occur sufficiently slowly that they do not excite surface gravity waves.

In contrast, the ocean responds to long period tidal forcing with a combination of an equilibrium tide along with a possible excitation of barotropic Rossby wave normal modes [1] Gravitational Tides are caused by changes in the relative location of the Earth, Sun, and Moon, whose orbits are perturbed slightly by Jupiter.

Similar calculations for the lunar monthly tide show that this lower frequency constituent is closer to equilibrium than the fortnightly.

Several authors in the 1960s and 1970s had suggested that the tidal forcing might generate resonant barotropic Rossby Wave modes, however these modes are extremely sensitive to ocean dissipation and in any event are only weakly excited by the long period tidal forcing (Carton,J.A.,1983: The variation with frequency of the long-period tides.

[3] More recently Egbert and Ray presented numerical modeling results suggesting that the nonequilibrium tidal elevation of the lunar fortnightly is more closely connected to the exchange of mass between the ocean basins.

[1] One additional tidal constituent results from the centrifugal forces due, in turn, to the so-called polar motion of the Earth.

[7] The equilibrium amplitude of the pole tide is about 5 mm at it maximum at 45 degrees N. and S. latitudes; it is most clearly observed in satellite altimetry maps of sea surface height.

[9] The long-period tides are very useful for geophysicists, who use them to calculate the elastic Love number and to understand low frequency and large-scale oceanic motions.