Here are your short notes on Stationary wave theory

The stationary wave theory was advanced by R.A. Harris in 1904, which was based on an unobjectionable foundation of the harmonic constants.

Harris, in contrast to Whewell, considered the tides as pure standing waves, and tried to find oscillating areas in the World Ocean, the reed period of which was in resonance with the period of the tide-generating force.

The stationary wave theory aimed at solving the complexities and anomalies found in tides on the basis of observations and measurements. The progressive wave theory, in the opinion of Harris was purely theoretical, far from the realities, for the assumption of the progressive wave was made in a channel of infinite length.

Harris thought of another type of wave which according to him was very important to tidal analysis. This is the stationary wave or standing oscillation. Modern work considers the tides regional or even local phenomena instead of a world phenomenon.

Whereas the progressive wave was not possible on the earth, except the narrow belt of continuous water around the Antarctica, the stationary wave could easily develop in a basin of finite dimension. This idea can be easily illustrated.

If a rectangular basin, partly filled with water, is tilted and then set down horizontally again, the water within it will move to and fro with an oscillatory motion, but will not leave the basin; hence the term standing oscillation is used.

If one of the basins is slightly raised, the water in the basin will start oscillating as a result of which the water is high at one end and low at the other. But there would be no change in the water level in the middle of the basin.

In fact, there is one line about which there is oscillation of water. This line is called the nodal line. This is known as the unimodal system. On the other hand, in the bimodal system, the water oscillates along two lines.

In this case, such a rocking is produced that water is high in the middle of the basin at the same time that it is low at both ends. The period of oscillation is determined by the formula T = 2L√gh, where L is the length of the tank, represents the depth of the water, and g the acceleration of gravity.

This shows that each basin has its natural period of oscillation which depends on its length and the depth of water only. If this natural period of oscillation coincides with the period of the tide-generating force, the response of the basin to the appropriate tidal period will be quick, and a state of resonance will be set up.

The underlying idea of the stationary wave theory is that in each and every ocean there are periods of oscillation which correspond to the periods of the tide-producing forces.

Thus, the stationary waves are best developed in those areas of the oceans which correspond exactly or approximately to the period of the tide-generating forces. It should be borne in mind that as the width of the basin does not matter, so the width of the oceanic oscillating areas is of little significance.

The stationary wave theory explains a number of tidal anomalies by considering the position of a particular place in relation to the nodal line of an oscillating system. If a place is near the nodal line the amplitude of the tide should be small.

On the contrary, if the place is farther away from the nodal line, the tide is bound to be large. According to Marnier, "there is considerable evidence in favour of this new theory of the making of the ocean tide.

The most valuable contribution of Harris to the problem of tides is that he postulated regional oscillating areas as the origin of the dominant tides of the various oceans and discarding the concept of tide as a single world phenomenon."