OUR RESTLESS TIDES
A BRIEF EXPLANATION OF THE BASIC ASTRONOMICAL
FACTORS WHICH PRODUCE TIDES AND TIDAL CURRENTS
Chapter 5
Factors Influencing the Local Heights and Times of Arrival of the Tides
It is noteworthy in Fig. 6 that any one cycle of the tides is characterized
by a definite time regularity as well as the recurrence of the cyclical pattern.
However, continuing observations at coastal stations will reveal - in addition
to the previously explained variations in the heights of successive tides of
the same phase - noticeable differences in their successive time of occurrence.
The aspects of regularity in the tidal curves are introduced by harmonic
motions of the earth and moon. The variations noted both in observed heights
of the tides and in their times of occurrence are the result of many factors,
some of which have been discussed in the preceding section. Other influences
will now be considered.
The earth rotates on its axis (from one meridian transit of the "mean"
sun until the next) in 24 hours. But as the earth rotates beneath the envelope
of tidal forces produced by the moon, another astronomical factor causes the
time between two successive upper transits of the moon across the local meridian
of the place (a period known as the lunar or "tidal" day) to exceed
the 24 hours of the earth's rotation period - the mean solar day.
The moon revolves in its orbit around the earth with an angular velocity of
approximately 12.2o per day, in the same direction in which the
earth is rotating on its axis with an angular velocity of 360o per
day. In each day, therefore, a point on the rotating earth must complete a
rotation of 360o plus 12.2o, or 372.2o, in
order to "catch up" with the moon. Since 15o is equal to
one hour of time, this extra amount of rotation equal to 12.2o
each day would require a period of time equal to 12.2o/15o
x 60 min/hr., or 48.8 minutes - if the moon revolved in a circular orbit, and
its speed of revolution did not vary. On the average it requires about 50
minutes longer each day for a sublunar point on the rotating earth to regain
this position directly along the major axis of the moon's tidal force envelope,
where the tide-raising influence is a maximum. In consequence, the recurrence
of a tide of the same phase and similar rise (see middle diagram of Fig. 6)
would take place at an interval of 24 hours 50 minutes after the preceding
occurrence, if this single astronomical factor known as lunar retardation were
considered. This period of 24 hours 50 minutes has been established as the
tidal day.
A second astronomical factor influencing the time of arrival of tides of a
given phase at any location results from the interaction between the tidal force
envelopes of the moon and sun. Between new moon and first-quarter phase, and
between full moon and third-quarter phase, this phenomenon can cause a
displacement of force components and an acceleration in tidal arrival times
(known as priming the tides) resulting in the occurrence of high tides before
the moon itself reaches the local meridian of the place. Between first-quarter
phase and full moon, and between third-quarter phase and new moon, an opposite
displacement of force components and a delaying action (known as lagging of the
tides) can occur, as the result of which the arrival of high tides may take
place several hours after the moon has reached the meridian.
These are the two principle astronomical causes for variation in the times
of arrival of the tides. In addition to these astronomically induced
variations, the tides are subject to other accelerating or retarding influences
of hydraulic, hydrodynamic, hydrographic, and topographic origin - and may
further be modified by meteorological conditions.
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The first factor of consequence in this regard arises from the fact that the
crests and troughs of the large-scale gravity-type traveling wave system
comprising the tides strive to sweep continuously around the earth, following
the position of the moon (and sun).
In the open ocean, the actual rise (see middle diagram, Fig. 6) of the
tidally induced wave crest is only one to a few feet. It is only when the tidal
crests and troughs move into shallow water, against land masses, and into
confining channels, that noticeable variations in the height of sea level can be
detected.
Possessing the physical properties of a fluid, the ocean waters follow all
of the hydraulic laws of fluids. This means that since the ocean waters possess
a definite, although small internal viscosity, this property prevents their
absolute free flow, and somewhat retards the overall movement of the tides.
Secondly, the ocean waters follow the principle of traveling waves in a
fluid. As the depth of the water shallows, the speed of forward movement of a
traveling wave is retarded, as deducted from dynamic considerations. In
shoaling situations, therefore, the advance of tidal waters is slowed.
Thirdly, a certain relatively small amount of friction exists between the
water and the ocean floor over which it moves - again slightly slowing the
movement of the tides, particularly as they move inshore. Further internal
friction (or viscosity) exists between tidally induced currents and contiguous
current in the oceans - especially where they are flowing in opposite
directions.
The presence of land masses imposes a barrier to progress of the tidal
waters. Where continents interpose, tidal movements are confined to separate,
nearly closed oceanic basins and the sweeps of the tides around the world is not
continuous.
Topography on the ocean floor can also provide a restraint to the forward
movement of tidal waters - or create sources of local-basin response to the
tides. Restrictions to the advance of tidal waters imposed both by shoaling
depths and the sidewalls of the channel as these waters enter confined bays,
estuaries, and harbors can further considerably alter the speed of their onshore
passage.
In such particularly confined bodies of water, so-called "resonance
effects" between the free-period of oscillation of the traveling, tidally
induced wave and that of the confining basin may cause a surging rise of the
water in a phenomenon basically similar to the action of water caused to "slosh"
over the sides of a wash basin by repeatedly tilting the basin and matching
wave crests reflected from the opposite side of the basin.
All of the above, and other less important influences, can combine to
create a considerable variety in the observed range and phase sequence of the
tides - as well as variations in the times of their arrival at any location.
Of a more local and sporadic nature, important meteorological contributions
to the tides know as "storm surges", caused by a continuous strong
flow of winds either onshore or offshore, may superimpose their effects upon
those of tidal action to cause either heightened or diminished tides,
respectively. High-pressure atmospheric systems may also depress the tides, and
deep low-pressure systems may cause them to increase in height.
Go to Chapter 6 of "Our Restless Tides"
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Revised: February, 1998