ALBERT

Description: Double high or low tides are usually explained by adding a higher harmonic to the dominating tide. In its simplest form, the criterion for a double tide is that the amplitude ratio between the higher harmonic and the dominating constituent is larger than 1/n2 where n is the ratio of their periods. However, it is not always clear how the higher harmonic becomes large enough to generate the double tide. This is rectified here by identifying three possible ways to enhance the higher harmonic enough to produce a double tide. Using TPXO9, the latest version of the altimetry constrained global tide database, potential locations for all three classes are identified and the existence of double tides are then evaluated using historic long-term tide gauge data from nearby locations. Thirteen locations with double tides were identified this way across the classes, of which seven are discussed further and shown to fit the classification scheme. The search criterion for classes 1 and 2, based on the amplitudes of M2, S2, and M4, work well with TPXO9 and suggests over 400 locations with double tides. The main reason we cannot identify more double tide locations is a lack of TG data, especially in the polar areas. Class 3, which requires an embayment resonant for the higher harmonic initially provided over 8000 potential locations, but only a few of these were in embayments. This class thus requires more manual work to identify the locations. It is concluded that the mechanism behind double tides in most textbooks needs to be revised because they are far more frequent in both space and time than previously thought.

Description: Doodson proposed a minimum criterion to predict the occurrence of double high (or double low) waters when a higher-frequency tidal harmonic is added to the semi-diurnal tide. If the phasing of the harmonic is optimal, the condition for a double high water can be written bn2∕a 〉 1 where b is the amplitude of the higher harmonic, a is the amplitude of the semi-diurnal tide, and n is the ratio of their frequencies. Here we expand this criterion to allow for (i) a phase difference ϕ between the semi-diurnal tide and the harmonic and (ii) the fact that the double high water will disappear in the event that b∕a becomes large enough for the higher harmonic to be the dominant component of the tide. This can happen, for example, at places or times where the semi-diurnal tide is very small. The revised parameter is br2∕a, where r is a number generally less than n, although equal to n when ϕ = 0. The theory predicts that a double high tide will form when this parameter exceeds 1 and then disappear when it exceeds a value of order n2 and the higher harmonic becomes dominant. We test these predictions against observations at Port Ellen in the Inner Hebrides of Scotland. For most of the data set, the largest harmonic of the semi-diurnal tide is the sixth diurnal component, for which n = 3. The principal lunar and solar semi-diurnal tides are about equal at Port Ellen and so the semi-diurnal tide becomes very small twice a month at neap tides (here defined as the smallest fortnightly tidal range). A double high water forms when br2∕a first exceeds a minimum value of about 1.5 as neap tides are approached and then disappears as br2∕a then exceeds a second limiting value of about 10 at neap tides in agreement with the revised criterion.

Description: Doodson proposed a criterion to predict the occurrence of double high (or double low) waters when a higher frequency tidal harmonic is added to the semi-diurnal tide. If the phasing of the harmonic is optimal, the condition for a double high water can be written bn2/a 〉 1 where b is the amplitude of the higher harmonic, a is the amplitude of the semi-diurnal tide and n is the ratio of their frequencies. Here we expand this criterion to allow for (i) a phase difference φ between the semi-diurnal tide and the harmonic and (ii) the fact that the double high water will disappear in the event that b/a becomes large enough for the higher harmonic to be the dominant component of the tide. This can happen, for example, at places or times where the semi-diurnal tide is very small. The revised parameter is br2/a, where r is a number generally less than n, although equal to n when φ = 0. The theory predicts that a double high tide will form when this parameter exceeds 1 and then disappear when it exceeds a value of order n2 and the higher harmonic becomes dominant. We test these predictions against observations at Port Ellen in the Inner Hebrides of Scotland. For most of the data set, the largest harmonic of the semi-diurnal tide is the 6th diurnal component, for which n = 3.The principal lunar and solar semi-diurnal tides are about equal at Port Ellen and so the semi-diurnal tide becomes very small twice a month at neap tides. A double high water forms when br2/a first exceeds a minimum value of about 1.5 as neap tides are approached and then disappears as br2/a then exceeds a second limiting value of about 10 at neap tides in agreement with the revised criterion.