The Semidiurnal Tide of the Atlantic Ocean

A number of the theoretical considerations which have been set forth have been applied, particularly by Defant, towards explaining the tides of the Atlantic Ocean. Defant (1932) has dealt with both the semidiurnal and the diurnal tides, but in the following we shall consider mainly the semidiurnal tide.

The Atlantic Ocean and its continuation, the Norwegian Sea and the Polar Sea, can be considered as a long bay which is closed in the north, whereas in the south it is in open communication with the Antarctic Ocean. On the basis of this concept the tides of the Atlantic Ocean can be considered as composed of two parts, a cooscillating tide which is maintained by the tide of the Antarctic Ocean, and a free tide which is maintained by the direct effect of the tide-producing forces. Neglecting the rotation of the earth and the effect of friction, both the cooscillating and the free tide can be computed by means of the method of numerical integration which was presented on p. 539, taking into account that the energy of the part of the tide wave which enters the Norwegian Sea and the Polar Sea is completely dissipated on the shallow shelves of these areas and that for this reason no reflected wave returns from these areas (p. 577). Part of the entire tide wave will be reflected, however, and the resultant picture will have some similarity to that which was discussed when dealing with the effect of friction on the tide (p. 574).

The numerical computations involved are somewhat lengthy but have been carried through by Defant. The result, in agreement with the conclusions presented on p. 575, is that the semidiurnal tide of the Atlantic Ocean can be considered as composed of two standing oscillations having a phase difference of one quarter period or three lunar hours. The computation renders only the variation in amplitude and phase along the middle section of the Atlantic Ocean and, in order to obtain absolute values, it is necessary to introduce observed values from two localities. As such observations Defant selected the tidal data from the Azores in the North Atlantic Ocean and from Tristan da Cunha in the South Atlantic.

A check on the theory is obtained by comparing observed values of the amplitude and the phase of the semidiurnal tide at other islands of the Atlantic Ocean with the computed values, and a further check is possible by comparing theoretical phase angles along the central part of the Atlantic Ocean with those which can be derived from Sterneck's chart of cotidal lines for the diurnal tide. This chart, which is reproduced in fig. 150, is based not only upon data from islands but upon all available data on the coasts. The full-drawn lines in fig. 151 show Defant's computed values of the amplitude and phase of the semidiurnal tide along a line which approximately follows the center of the Atlantic Ocean.

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The crosses indicate the amplitude or phase at the island stations, the names of which are shown in the figure, and the dashed line in fig. 151B indicates the change in phase according to Sterneck's map. The agreement between observations and computations is remarkably good, all of the crosses falling nearly on the computed curves. The discrepancy in the northern part of the North Atlantic Ocean between the computed phase and the phase as derived from Sterneck's map can be accounted for by the fact that the location of the amphidromic point to the south of Greenland is admittedly uncertain. The agreement speaks strongly in favor of Defant's concepts, and further evidence for the validity of his computations is obtained by an examination of the tidal currents as

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derived mainly on the Meteor Expedition. Figure 151C shows the computed phase of the maximum tidal current which corresponds to the theoretical amplitude and phase of the tide, and in the same figure are entered as dots the observed phases of the tidal current at 16 anchor stations. All the observed values fall remarkably close to the computed curve, and this result is of great importance because it represents an entirely independent check on the correctness of the fundamental assumptions concerning the character of the tide.

Certain discrepancies are revealed, however, if one compares the observed amplitudes of the tidal currents with the theoretical. Defant points out that the computed and observed velocities show similar variations with latitude if one subtracts from the observed velocities a latitude effect which can be ascribed to the earth's rotation. The latter was neglected when making the computation and must therefore be eliminated from the observed values. The correction which should be applied is due to the fact that on the rotating earth the velocity of the tidal current is

if v₀ represents the corresponding velocity, neglecting the earth's rotation, and where s = (T sin ϕ)/12. (p. 571). In order to make a comparison between the computed and the observed values, the latter should be reduced by multiplication with .

After having done this, Defant finds that the character of the variation of the velocities agrees with the computed velocities, but the observed velocities are between two and three times greater than the computed. The computations give velocities of about 3 cm/sec, whereas the reduced observations give velocities of about 8 cm/sec. Defant suggests that this discrepancy arises because the direction of the tidal currents is not uniform through an entire cross section, as postulated by the theory, but another possible explanation is suggested on p. 595. Whether or not these explanations are accepted, the evidence in favor of Defant's theory is so great that his explanation of the semidiurnal tides of the Atlantic Ocean has to be given weight.

Concerning the character of the tidal currents it should be observed, furthermore, that the current measurements plainly show the effect of the earth's rotation. At all anchor stations the average semidiurnal current between the surface and the greatest depth of observation showed rotating currents, the direction of rotation being cum sole in 55 of 60 cases, including as cum sole four cases in which the current was practically alternating. The ratio between the major and minor axes of the current ellipses was on an average close to the theoretical value s = (T sin ϕ)/12 (p. 571). Thus, in mean latitude 36°18′, the observed ratio between the

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axes was 0.57 against computed 0.61, and in latitude 8°57′, the observed ratio was 0.19 against computed 0.16. These results clearly demonstrate the effect of the rotation of the earth, which was also brought out by the general increase of velocities when departing from the Equator.

Defant also computed the difference between the time of the maximum tidal current at the different anchor stations and the time of high water. He finds that in general high water occurs about one and a half hours before the maximum tidal current towards the north, and points out that this time difference should be zero if one had to deal with a progressive wave, and three hours if one had to deal with a standing wave. The fact that the time difference lies between these two values also shows that the semidiurnal tide of the Atlantic Ocean has neither the character of a progressive wave nor that of a standing wave, but is intermediate and can be regarded as brought about by superposition of several standing waves. It may especially be observed that in the South Atlantic Ocean the wave has nearly the character of a progressive wave, whereas in the North Atlantic Ocean the characteristics of a standing wave are more conspicuous.

The diurnal tide of the Atlantic Ocean is less well-known and Defant confines himself to a more summary treatment, the results of which indicate, however, that similar concepts are applicable in that case as well. It should be particularly pointed out that in the case of the diurnal wave the ratio between the axes of the current ellipses does not increase as rapidly as required by the simple theory on p. 571. According to this theory the current ellipse should degenerate in 30°N to a circle with infinite radius, and beyond 30°N diurnal waves of the simple character considered should no longer be possible. The observations show that the ratio between the axes of the diurnal current ellipses increases very slowly with increasing latitude, indicating that in relation to the diurnal wave the Atlantic Ocean cannot be considered as a wide ocean but as a bay or canal of moderate width. This conclusion may have bearing on future studies of the diurnal tides.

Similar treatment of the tides of other oceans has not yet been attempted and will encounter much greater difficulties. This is particularly true when considering the Pacific Ocean, which is so large that there the free tides must be of much greater importance.