Underwater sunlight maxima in the Menai Strait

Abstract

In a tidal sea, the time variation of underwater daylight depends on the rise and fall of the tide as well as the motion of the sun across the sky. If conditions are right, more than one maximum in underwater daylight can occur in a single day. In this paper we apply a simple analytical solution for the number of maxima and their timing to observations in the Menai Strait in Europe. The number of maxima depends on the value of the parameter γ = kRω2q2 where k is the diffuse attenuation coefficient, R is the tidal range, ω the angular frequency of the tide and q is a factor proportional to the day length. If the value of γ is greater than a critical value, and the day is long enough, then a double maximum in underwater sunlight is formed. The maxima lie between noon and low water, and their time relative to noon is given by tL = γ/(γ+4) where tL is the time of low water relative to noon. The critical value of γ varies from 4 to about 18, depending on the time of high water. The necessary length of day to produce the double maximum depends on the time of low water relative to noon, the required condition being |tL|<3q/2+6q/γ, where tL is the time of low water in hours relative to noon. The observations reported here are in agreement with these predictions. In the high tidal ranges of the Menai Strait, γ exceeds the critical value for about half the spring–neap cycles in summer, and the daily pattern of illumination switches from a double peaked to a single peaked curve. Maxima occur as early as 6 am and as late as 7 pm. Over this complete range, the times of the observed maxima are close to those predicted, the rms difference between times of observed and predicted maxima is about 45 min and the mean difference is less than 10 min. We conclude that the analytical theory presented here is a useful practical tool for predicting maxima in underwater sunlight in a tidal sea.