reviewed by: John Luick

Tides are long waves, either progressing or standing. The dominant period usually is 12 hours 25 minutes, which is 1/2 of a lunar day. Tides are generated by the gravitational potential of the moon and the sun. Their propagation and amplitude are influenced by friction, the rotation of the earth (Coriolis force), and resonances determined by the shapes and depths of the ocean basins and marginal seas.

The most obvious expression of tides is the rise and fall in sea level. Equally important is a regular change in current speed and direction; tidal currents are among the strongest in the world ocean.

Description of tides

The result of alternate spring and neap tides is a half monthly inequality in tidal heights and currents. Its period is 14.77 days, which is half the synodic month. (Synodic: related to the same phases of a planet or its satellites. A synodic period or synodic month is thus the time that elapses between two successive identical phases. In tidal theory synodic always refers to the moon, so a synodic month is the time that elapses between successive identical phases of the moon, for example between successive new moons.) There are other inequalities with similar and longer periods.

The Tide-Generating Forces

As the earth revolves around the gravitational centre of the sun/earth system, the orientation of the earth´s axis in space remains the same. This is called revolution without rotation (see the animation for further explanation).

The tide generating force is the sum of gravitational and centrifugal forces. In revolution without rotation the centrifugal force is the same for every point on the earth´s surface, but the gravitational force varies (Figure 11.1). It follows that the tide generating force varies in intensity and direction over the earth's surface. Its vertical component is negligibly small against gravity; its effect on the ocean can be disregarded. Its horizontal component produces the tidal currents, which result in sea level variations (Figure 11.2).

The gravitational force exerted by a celestial body (moon, sun or star) is proportional to its mass but inversely proportional to the square of the distance. The Sun's mass is equivalent to some 332,000 Earth masses, while the mass of the Moon corresponds to only 1.2 percent of the mass of the Earth. The mean distance Sun -Earth is 149.5 million km, the mean distance Earth - Moon only 384,000 km. If the gravitational force of the Sun and Moon are compared, it is found that the Sun's enormous mass easily makes up for its larger distance to Earth, to the extent that the gravitational force of the Sun felt on Earth is about 178 times that of the Moon. As a result the Earth's orbit around the Sun is not seriously distorted by the Moon's movement around the Earth.

However, as is evident from Figure Figure 11.1, tides are not produced by the absolute pull of gravity exerted by the Sun and the Moon but by the differences in the gravitional fields produced by the two bodies across the Earth's surface. Because the Moon is so much closer to the Earth than the Sun, its gravitational force field varies much more strongly over the surface of the Earth than the gravitational force field of the Sun. Quantitative analysis shows that the differences of the gravitational forces across the Earth's surface are proportional to the cube of the distances Sun - Earth and Earth - Moon. As a result the Sun's tide-generating force is only about 46% of that from the Moon. Other celestial bodies do not exert a significant tidal force.

Main tidal periods

The tides can be represented as the sum of harmonic oscillations with these periods, plus harmonic oscillations of all the other combination periods (such as inequalities). Each oscillation, known as a tidal constituent, has its amplitude, period and phase, which can be extracted from observations by harmonic analysis. Hundreds of such oscillations have been identified, but in most situations and for predictions over a year or so it is sufficient to include only M2 , S2 , K1 and O1. Practical predictions produced on computers for official tide tables use significantly more terms than these four; for example, the Australian National Tidal Facility uses 115 terms to produce the official Australian Tide Tables.

Tidal Classification

The form factor F is used to classify tides. It is defined as

F = ( K1 + O1 ) / ( M2 + S2 )

where the symbols of the constituents indicate their respective amplitudes. Four categories are distinguished :

value of Fcategory
0 - 0.25semidiurnal
0.25 - 1.5mixed, mainly semidiurnal
1.5 - 3mixed, mainly diurnal
> 3diurnal

Figure 11.3 shows examples.

Shape of the Tidal Wave

The scales of variations in the forcing field are of global dimensions. Only the largest water bodies can accommodate directly forced tides. On a non-rotating earth the tides would be standing waves; they would have the form of seiches, ie a back and forth movement of water across lines of no vertical movement (nodes). On a rotating earth the tidal wave is transformed into movement around points of no vertical movement known as amphidromic points.

The animation compares seiche movement with tidal movement around an amphidromic point. Note that on a rotating earth the tides take the shape of propagating waves: The wave propagates around the amphidromic point in clockwise or anti-clockwise fashion.

Details of the shape of the tidal wave depend on the configuration of ocean basins and are difficult to evaluate. Computer models can give a description of the wave on an oceanic scale (Figure 11.4). Their results have to be verified against observations of tidal range and times of occurrence of high and low water. Distortions of the wave on the continental shelf caused by shallow water make it difficult to assess results for the open ocean. In deep water the tidal range rarely exceeds 0.5 m.

Co-oscillation tides

Tides in marginal seas and bays cannot be directly forced; they are co-oscillation tides generated by tidal movement at the connection with the ocean basins. Depending on the size of the sea or bay they take the shape of a seiche or rotate around one or more amphidromic points.

If the tidal forcing is in resonance with a seiche period for the sea or bay, the tidal range is amplified and can be enormous. This produces the largest tidal ranges in the world ocean (14 m in the Bay of Fundy on the Canadian east coast; 10 m at St. Malo in France, 8 m on the North West Shelf of Australia and at the extreme north of the Gulf of California in Mexico; all are mainly semidiurnal tides). Tidal range is then largest at the inner end of the bay, in accordance with the dynamics of seiches in open basins. Modest amplification is exerienced in Spencer Gulf of South Australia where the tidal range at spring tide is 3 m at the inner end, while it is less than 1 m at the entrance to the Gulf.

Figure 11.5 shows an example of a co-oscillation tide in a large bay. The tide is forced from the open end by the oceanic tide, which has an maximum tidal range (at spring tide) of about 1 m. Because of the width of the basin the Coriolis force is able to shape the wave, producing amphidromic points around which the wave propagates. Amplification is particularly large along the British coast and in the English Channel.

© 1996 - 2005 M. Tomczak. Last updated 3/3/2005
Acknowledgements to Herman C. Peters of the Dutch North Sea Directorate for suggesting improvements to the text.

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