The diurnal tide in an ocean bounded by two meridians

In a series of papers it has been shown by Goldsbrough how, by the introduction of a certain form of null-function, solutions of the general dynamical equations may be obtained for the tides in an ocean on a rotating globe bounded by two meridians from pole to pole. The method is described in Part I of the series and in that and succeeding papers its application has been made to special cases. In particular in Part Ill the method has been used to consider the lunar semi-diurnal tide M2 in an ocean of uniform depth bounded by two meridians 60° apart. In the present paper solutions have been found in a similar way for the diurnal tide in the same type of ocean. The results obtained show agreement with observations in that the amplitudes of the diurnal tide are considerably smaller than those of the semi-diurnal tide. Also, at points suitable for comparison, there is a close similarity in the values of the ratio of the heights of the two tides obtained theoretically and from observations. The wave represented by the solution is of an unusual type, the range of values of the phase over the whole ocean being exceptionally small. It is shown that the wave obtained is equivalent to the combination of a stationary wave and a progressive wave of much smaller amplitude, and that this type of combination can have only a limited range of phase angles. As a result there are periods during which neither high nor low tide occurs at any point of the ocean. The cotidal lines, when present, move across from one boundary to the other approximating more closely to the meridians as they approach the central meridian which is actually a cotidal line.