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Long period tide
Long-Period tides are gravitational tides, typically with amplitudes of a few centimeters or less and periods longer than one day, generated by changes in the Earth's orientation relative to the Sun, Moon, and Jupiter. The distance between a reference point on the surface of the Earth relative to these objects can be expressed as an infinite combination of periods and, as the distance changes, so does the tidal forcing. An analysis of the changing distance by Pierre-Simon de Laplace in the 18th century shows that these periods at which gravity varies cluster into three species, the semi-diurnal and diurnal tide constituents which have periods of a day or less, and the long period tidal constituents (see also tide). Long period tidal constituents with relatively strong forcing include the lunar fortnightly (Mf) and monthly (Ms) as well as the solar semiannual (Ssa) and annual (Sa) constituents. In addition to having periods longer than a day-long period tidal forcing is distinguished from that of the first and second species by being zonally symmetric. The long period tides are also distinguished by the way in which the oceans respond. In contrast to the first and second species, the long period tidal forcings occur sufficiently slowly that they do not excite surface gravity waves. This property of exciting surface gravity waves is responsible for the high amplitude semi-diurnal tides in the Bay of Fundy, for example. In contrast, the ocean responds to long period tidal forcing with a combination of an equilibrium tidal response along with a possible excitation of barotropic Rossby wave normal modes
==Formation mechanism==
Gravitational Tides are caused by changes in the relative location of the Earth, sun, and moon, whose orbits are perturbed slightly by Jupiter. Newton's law of universal gravitation states that the gravitational force between a mass at a reference point on the surface of the Earth and another object such as the Moon is inversely proportional to the square of the distance between them. The declination of the Moon relative to the Earth means that as the Moon orbits the Earth during half the lunar cycle the Moon is closer to the Northern Hemisphere and during the other half the Moon is closer to the Southern Hemisphere. This periodic shift in distance gives rise to the lunar fortnightly tidal constituent. The ellipticity of the lunar orbit gives rise to a lunar monthly tidal constituent. Because of the nonlinear dependence of the force on distance additional tidal constituents exist with frequencies which are the sum and differences of these fundamental frequencies. Additional fundamental frequencies are introduced by the motion of the Sun and Jupiter, thus tidal constituents exist at all of these frequencies as well as all of the sums and differences of these frequencies, etc. The mathematical description of the tidal forces is greatly simplified by expressing the forces in terms of gravitational potentials. Because of the fact that the Earth is approximately a sphere and the orbits are approximately circular it also turns out to be very convenient to describe these gravitational potentials in spherical coordinates using spherical harmonic expansions.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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