What Is the Tidal Model?

The tidal dynamics theory (dynamic theory of tide) is a tidal theory that studies the tidal waves in the ocean, that is, the long-wave motion caused by the tidal force, according to the principles and methods of fluid dynamics. This theory has been developed around the problem of solving Laplace's tide equation. Newton first recognized that ocean tides should be considered essentially as a hydrodynamic issue. ^[1]

According to the principles and methods of fluid dynamics, study the tidal wave in the ocean, which is a kind of long wave motion caused by the tidal force.

Newton first recognized that ocean tides should be considered essentially as a hydrodynamic issue. After Newton, PS Laplace pioneered the theory of ocean tidal dynamics in 1775. He ignored the nonlinear and friction terms in the fluid motion equation, and obtained the Laplace tide equation expressed in spherical coordinates:

In 1897, SS Huff successfully obtained the solution of the tide equation expressed by a spherical harmonic function. He still assumes that the ground is completely covered by seawater, but at the same time considers forced vibration and free vibration, and considers the mutual attraction of water particles on the tide wave. He concluded that for the equatorial region, when the depth is 8850 meters, the period of the free half-day vibration is 12 hours and 1 minute, which is very close to the period of the half-day tide, which may cause resonance. According to the calculation results of this theory, the amplitude of the main solar half-day tide (S2) is more than 200 times larger than the equilibrium tide. The main Taiyin half-day tide (M2) is about 10 times larger than the equilibrium tide.

In 1913, GR Gotzbluff considered the idealized Arctic Ocean bounded by a latitude circle, and demonstrated that the resonance depth at which it occurs a half-day tide is 160 meters, and the average depth of the actual ocean (including the auxiliary sea) is 1296. Meters, so the possibility of resonance is very small. It is known that the tidal vibration of the Arctic Ocean is mainly maintained by the tidal waves of the Atlantic Ocean.

The ideal ocean tide wave theory bounded by the meridian was mainly completed by J. Plauderman and AT Dusen in the first half of the 20th century. They set a precedent for numerical solutions and calculated oceans at several different depths. It was proved that tidal waves are often affected by factors such as tidal force and geostrophy, and standing waves appear in two directions that are perpendicular to each other. The amplitude at the intersection of the nodal lines is zero (no tide point), and from this point to the surroundings, the amplitude increases. Lines of points with the same amplitude are called iso-amplitude lines; lines of points that reach the climax at the same time are called synchronic time lines. Because the latter rotates around the no-tidal point, this tidal wave is called a rotating tidal wave. It has both the characteristics of forward and standing waves, also known as forward standing waves, and is the main form of tidal wave motion in the ocean.

The advent of large-scale fast electronic computers in the late 1960s facilitated the study of ocean tides. In 1969, CL Pickles et al. Used the modified Laplace tide equation to approximate the profile and depth distribution of the global ocean. Without observing data, they only considered the tidal force and friction of the celestial body to obtain the M2 tide. distributed. In 1972, WE Farrell considered a small range of ocean tides in a columnar space from the sea surface to the ocean floor. The results show that the potential of the ocean tide itself and the potential of the crustal deformation caused by the weight of the ocean tide are the same as those of celestial bodies. The combined potential of gravitational potential and the deformation potential of solid earth caused by it is of the same magnitude. At the same time, MC Hendschott introduced the ground tide effect, calculated the global M2 tide, and pointed out that the tide level change caused by the ground tide effect is approximately equal to one third of the original gravitational tide amplitude. However, the conclusions of different scholars are not consistent.

In 1975, GW Platzman took the Atlantic Ocean and the Indian Ocean as a whole, and took a model close to the actual ocean, and obtained free vibrations with periods of 23, 21, 12.8, and 11.1 hours, which are close to the period of the main tide wave. Can cause resonance. This may be the reason for the semi-day and full-day tides of the Atlantic Ocean and its adjacent seas.

The results of the numerical simulation of the tidal wave above confirm that the basic motion of the oceanic subtidal wave is a rotating tidal wave system, but between several rotating tidal waves, there are regions with slow phase changes and large tidal ranges. Some people call the tide waves here anti-rotating. This phenomenon is particularly pronounced in the central Indian Ocean and the Pacific Ocean.

The tidal wave in the ocean was considered earlier. As for the tidal wave in the sea area or the bay, it can be regarded as a free long wave (Kelvin wave) under the influence of geostrophic movement. For semi-closed bays, the superposition of Kelvin waves and Poincaré waves is often used to meet the boundary conditions of rectangular sea areas in order to solve this wave equation.

For shallow waters, nonlinear effects must be considered. From the energy point of view, the power consumed by ocean tides is about 3.7 × 10 ¹⁹ erg · s ^-1 , which may be one of the reasons for the slow self-transition of the earth. ^[2]