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doi:10.5194/os-2017-12
© Author(s) 2017. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
07 Apr 2017
Review status
This discussion paper is under review for the journal Ocean Science (OS).
The double high tide at Port Ellen: Doodson's criterion revisited
Hannah A. M. Byrne, J. A. Mattias Green, and David G. Bowers Bangor University, School of Ocean Sciences, Menai Bridge, Anglesey, LL59 5AB, UK
Abstract. 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.

Citation: Byrne, H. A. M., Green, J. A. M., and Bowers, D. G.: The double high tide at Port Ellen: Doodson's criterion revisited, Ocean Sci. Discuss., doi:10.5194/os-2017-12, in review, 2017.
Hannah A. M. Byrne et al.
Hannah A. M. Byrne et al.
Hannah A. M. Byrne et al.

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Short summary
Some places experience double high tides, where the tide starts to ebb for a short while, only to briefly flood again before finally receding. The result is a very long high tide with weak currents, and is important for navigational purposes. The existing theory for when and where double high tides occur does not always capture them, and it can only be applied to double highs occurring on a twice-daily tide. Here, the criteria has been generalised to capture all double high or low tides.
Some places experience double high tides, where the tide starts to ebb for a short while, only...
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