Tides and other oscillations

Forced like clockwork by the moon and the sun, the tides are the most predictable oceanic motions. The gravitational pull of the moon (and to a lesser extent of the sun) creates "bulges" of water on opposite sides of the earth. A point on the earth passes through these bulges twice a day, resulting in semi-diurnal (half daily) components to the tide. Because the moon and the sun do not generally lie over the equator, one of the bulges is larger than the other, leading to diurnal (daily) components to the tides.

A modulation of the tidal range results from the relative position of the moon and the sun: when the moon is new or full, the moon and the sun act together to produce larger "spring" tides; when the moon is in its first or last quarter, smaller "neap" tides occur. The cycle of spring to neap tides and back is half the 27-day period of the moon's revolution around the earth, and is known as the fortnightly cycle. The combination of diurnal, semi-diurnal and fortnightly cycles dominates variations in sea level throughout the islands, as illustrated by tidal curves for Honolulu and Hilo (see below).

Plate 12
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Plate 12. A typical time series of sea level at Honolulu (bottom) and Hilo (top) harbors, for two fortnights in May 1990. Source: Sea Level Center, University of Hawaii/ NOAA.
Units: centimeters.

On scales of oceanic basins, tides exist as very long waves propagating in patterns determined by their period and the geometry of the basin. The image below shows the response of the North Pacific to the tidal period of 23 h 56 min, the largest diurnal component.

Plate 13
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Plate 13. Co-tidal lines for the diurnal K1 tide (23 h 56 min). Tidal range, in centimeters, indicated by shading, and lines of equal tidal delay (or phase, in hour), contoured. Source: TOPEX project, Jet Propulsion Laboratory, NASA.

Poster 13b

Poster 13b. Co-tidal lines for the semi-diurnal M2 tide. Tidal range, in centimeters, indicated by shading, and lines of equal tidal delay (or phase, in hour), contoured. Source: TOPEX project, Jet Propulsion Laboratory, NASA.

Lines along which high tide occurs at the same time (called phase lines), converge to a point west of Hawai'i where the tidal range is zero (called amphidrome). Phase lines rotate counter-clockwise around this amphidrome, so that the offshore diurnal tide reaches the Hawai'i island first, then sweeps across Maui, O'ahu and finally Kauai.

Local bathymetry affects the ranges and phases of the tides along the shore, as the tidal waves wrap around the islands. For example, high tide at Haleiwa on the north shore of O'ahu occurs over an hour before high tide at Honolulu Harbor. The ranges and phases of the semi-diurnal component of 12 h 25 min period (called M2), and of the diurnal component of 23 h 56 min period (called K1) at several coastal sea level stations are given in the table below:

Harbor	M2 range	M2 phase *	K1 range	K1 phase *
Hilo	43.6 cm (17.2")	-1h 2m	34.8 cm (13.7")	+0h 18m
Kawaihae	39.4 cm (15.5")	-0h 11m	32.6 cm (12.8")	-0h 34m
Honolulu	33.0 cm (13.0")	0	31.4 cm (12.4")	0
Kaneohe	31.0 cm (12.2")	-1h 28m	37.0 cm (14.6")	+1h 19m
Kahului	33.0 cm (13.0")	-1h 40m	35.4 cm (13.9")	+0h 15m
Nawiliwili	29.8 cm (11.7")	-0h 28m	31.6 cm (12.4")	+0h 6m
Port Allen	29.8 cm (11.7")	-0h 36m	31.8 cm (12.5")	-0h 31m
* phase given in hours and minutes before (-) or after (+) Honolulu harbor

Tidal currents result from tidal variations of sea level, and near shore are often stronger than the large scale circulation. Current meter records collected off O'ahu, Maui and Hawai'i show that semi-diurnal and diurnal tidal currents tend to be aligned with the shoreline. Due to high variability of tidal currents around the islands, however, this statistical picture may not correspond to the flow at a particular time: tidal currents cannot be predicted as precisely as sea level. Strong swirls often result from tidal currents flowing around points and headlands, and present hazards to divers.

Plate 9a

Plate 9. Measured tidal current ranges, at semi-diurnal (in red) and diurnal (in blue) periods. The major axes of the ellipses indicate the most probable orientation and strength of tidal currents; however because the phase of currents vary during the tidal cycle, it is not possible to predict how many hours after high water at Honolulu will currents be in the directions shown. Period: 1960 to 1995. Sources: University of Hawaii, Hawaii Institute of Geophysics; National Ocean Data Center, NOAA; Science Applications Internal Corporation. Units: cm/s.

Variations of sea level and currents at periods of 1.5 to 3 days are also observed around the Hawaiian islands. Although they manifest themselves as oscillations, just like tides, they are not forced by gravitation, but by time-varying winds and possibly swells. They displace the sea surface by only a few centimeters, but the depth of isotherms by tens of meters. Such oscillations, usually occurring during the winter, may be associated with currents up to 50 cm/s (1 knot), and horizontal water displacements of 8 km (5 miles).

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