Tides and waves in the vicinity of Saint Helena

Abstract

Sea-bed pressures taken close to the shore-line at St Helena over 39 days are analysed for information on tides, swell, and medium frequency waves. The tidal records are analysed in conjunction with short records taken by others from Ascension, Trindade and Tristan da Cunha Islands. A nine-year series from Simons Bay, South Africa, is also investigated as a possible reference base. It is found to be partially unsuitable on account of a node in the diurnal tides, previously unsuspected, but this itself is relevant to the diurnal cotidal map. A phenomenal monthly tide at Simons Bay, with sidereal rather than anomalistic monthly periodicity, is also noted. Taking a year’s record from Ascension Island as tidal reference, new constants are evaluated for all four islands, and these are used to deduce cotidal maps fo the open South Atlantic. Two types of maps are considered, one a linear interpolation of the constants, the other derived from a locally forced tide (modified by the Earth tide) and a pair of Poincare waves calculated for a ‘(β-plane ’ approximation, assuming constant depth. Although not entirely realistic, the latter scheme fits the semi-diurnal tide data very closely, but not the diurnal data. Both types of map confirm positive semi-diurnal amphidromes, according with the computations of Pekeris and Accad and of Bogdanov and Magarik, and negative diurnal amphidromes according with Dietrich’s maps. Tidal records made at St Helena in 1761 by Maskelyne and Mason provide a unique opportunity to search for possible instabilities in the ocean tides. By careful comparison of the two sets of data, it is concluded that the semi-diurnal tides are virtually unchanged, but there is a significant change in phase of about 10° at all diurnal frequencies which may point to an instability in the diurnal modes in the Atlantic, as suggested by Garrett & Munk from other considerations. A frequency-time plot of the swell wave spectra shows dispersive ridges as found in the Pacific and elsewhere. These point to storm origins principally in the South Pacific and the North Atlantic Oceans. Large-scale ' rollers ’ were not encountered, but there was some evidence that they have similar origins. Medium frequency waves (1 to 30 mHz) were recorded simultaneously at two points round the St Helena coast. Their spectra and coherence were studied with a view to identifying trapped modes. A theory is evaluated for waves trapped by a circular island with paraboloidal shelf (as approximately at St Helena) in contrast to the vertical wall models studied by Longuet-Higgins and others. Its main feature is that resonance peaks are much flatter than in the vertical wall cases, and do not increase with frequency. Analysis of the data shows features in common with the theory up to about 3 mHz and at some other energy peaks, but at higher frequencies there is evidence for energy leakage due to topographical roughness.

Secular Changes in the Oceanic Tides at Brest, 1711?1936

“…In comparing recent tidal records from the South Atlantic island of Saint Helena with some observations made there by the astronomers Maskelyne and Mason, 208 years previously, the author (Cartwright 1971) detected a secular increase in the phase lead of the diurnal tide, of about 5 deg/century. Both records were of rather short duration, about 40 days, but a rough calculation of probable sampling errors suggested that the observed change might be regarded as 'significant' while the smaller changes observed in the semi-diurnal tides of the same records were 'insignificant'.…”

“…Search for small shifts between this synthesis and the observed extrema is a fairly straightforward procedure. (A similar method was applied by the author (Cartwright 1971) to compare old and new data from St Helena, using a response analysis for Ascension Island as a common link. )…”

“…In the successful application of this method described in Cartwright (1971), the given series was a year's complete sequence of maxima and minima at a place (Ascension) little affected by weather. It was therefore possible to extract meaningful weights for time-lagged variables (in that case the gravitational potentials themselves), which are necessary to describe an admittance which varies with frequency.…”

A survey of recent changes in the main components of the ocean tide

“…Long term changes in the tide at particular locations have been noted a number of times before (e.g. Cartwright 1971Cartwright , 1972Godin, 1995;Pouvreau, 2008). However, it has not been until recently that more comprehensive regional studies have been undertaken, with quite intriguing findings.…”

Adventures in applied mathematics

“…One of the interesting theoretical results is the existence of a South Atlantic amphidrome (21°S, 15°W) whose reality is supported by island observations. Further corroboration has come from Dr. Cartwright's recent tidal expedition [14] A great deal of additional work remains to be done by applied mathematicians before the whole complex of tidal phenomena on the earth is understood. The significance of this problem stems from the fact that it is the simplest dynamical system on a global scale which we can tackle at present and from which we can gain experience which we may hope to apply to the even more exacting task of elucidating the dynamics of our atmosphere.…”