Abstract
We investigate a mechanism for producing double-lows and double-highs in the semi-diurnal tide by selective amplification of higher harmonics in a resonant gulf. A double low water is observed at Providence, RI, near the head of Narragansett Bay on days when there is a flattening of the low water tidal curve at Newport, at the mouth of the bay. The flattening is caused by an unusually large quarter-diurnal component to the tide at Newport. The quarter diurnal component has the right phase (a maximum close to the time of the minimum in the semi-diurnal tide) to produce a prolonged flattening of the tidal curve around low water. The natural period of Narragansett Bay (for quarter-wavelength resonance) is close to 4 h and the quarter diurnal tide is amplified, relative to the semi-diurnal tide, within the bay. The selective amplification of the higher harmonic further prolongs the flattening effect at Providence and, occasionally, is sufficient to create a double low water at the head of the bay from quarter and semi-diurnal tides alone. More often, though, a sixth-diurnal harmonic produced within the bay, added to the flattened low water at Providence, creates the double low water. This mechanism of selective amplification of tidal harmonics could be relevant to double tides elsewhere.
Highlights
Double-high and double-low waters in the semi-diurnal tide are an unusual feature of sea level observations
Our aim in this paper is to investigate the extent to which this selective amplification of a tidal harmonic, or harmonics, leads to the formation of the double low water seen at Providence
The common explanation offered is that a double tide is created by the addition of higher harmonics to the main tide
Summary
Double-high and double-low waters in the semi-diurnal tide are an unusual feature of sea level observations. If b/a is 0.25 at the mouth of the bay, the selective amplification of the harmonic will increase this ratio to 0.4 at the head and a flattened low tide at Newport should become a double low water at Providence, given that the phase is correct. The ratio of D4 to D2 amplitudes at Newport varies with the spring-neap cycle and is greatest at times of smaller tidal range This is somewhat surprising (higher harmonics produced by shallow-water effects tend to increase in amplitude more quickly than that of the semi-diurnal tide). In the remaining 60 cases, the relative amplification of the quarter diurnal tide in the gulf serves only to flatten the tidal curve at low water at Providence and a higher frequency oscillation acts to create a double low water. The fact that the natural period of the bay is close to 4 h means that any small disturbance will produce an oscillation with this period
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