TIDAL PHENOMENA
+ hurricane water elevation profiles
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tides and tidal phenomena are studied because :
safe coastal navigation requires
knowledge of tide stage and flow
Dispersion and aggregation of
shore-line materials are affected by
tides
flooding can be enhanced or
reduced by tide ranges and phases
large tide ranges can be used to
run generators and supply power
tide stages and flow can significantly affect nearshore and estuary
biological, chemical, and geological
distributions.
These four cranes, each valued at $ 1.25 million, entered San Francisco Bay on
June 14, 2002 arriving from Shanghai, China. Their purpose is to raise 40’ long
containers from cargo ships. They had to pass under the Oakland Bridge to reach
their destination. The tidal range on that day was 4.1 feet and the bridge had a
vertical motion of 6 inches. Detailed knowledge of the tidal cycle was necessary for
the piloting that brought the vessel under the bridge as the cranes cleared the
bottom of the bridge by six feet.
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Types of Observed Tides
Diurnal Tides
fluctuations are largely due to the
changes in the Moon’s declination
(angle from the celestial equator)
Semidiurnal Tides
fluctuations are due to the relative
positions of the Sun and Moon
Mixed Semidiurnal Tides
the most commonly seen waveform
reflecting local basin geometry and
the moon’s declination
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patterns in observed tidal elevations
There are three types of tides recognized for classification by their patterns of water elevation :
diurnal tides are those exhibiting one high and one low elevation each 24 hours
semi-diurnal have two equal high and low elevations each 24 hours
mixed tides have two unequal high and low elevations each 24 hours.
At any geographic position on a coastline, the types of tide vary among the three above.
However, the Equilibrium Theory indicates that only one type of tide will occurs at a given
latitude. Actually it is found that the types of tides are not limited to certain latitudes. This is a
major reason the Dynamic Theory is used to predict tides. The Ttheory takes into account the
effects of a basin’s shape and bottom topography in the prediction of a tide wave’s propagation
and form. Remember that the partition of a shallow water wave’s energy can shift between
kinetic and potential and this respectively reflects changes in the waves speed and elevation.
These shifts affect the result of superposition of types of waves with one another at a given
location and in this manner the Dynamic Theory can reproduce a wide variety in elevations
irrespective of latitude.
Diurnal tides are fundamentally composed of lunar, solar and the lunar-solar partial tides. Each
of these partials contributes a particular type of gravitational influence and in this case the
factor that is the dominant one is the moon’s declination, that is, the angle of the moon’s
position relative to the celestial equator. Diurnal tides have relatively small ranges of
elevation and are rare around the globe being found in the Gulf of Mexico, Australia and
Antarctica.
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Semi-diurnal tides are strongly influenced by the relative positions of the moon and
sun relative to the center of the earth. They are common along Atlantic and Indian
ocean coastlines. Their elevations are normally 2 to 4 meters and can reach 6
meters [Bay of Fundy]. Mixed tides are those that occur due to the declination of the
moon and nearby local effects such as the configuration of the shoreline and the
depths of local bottom topography. These tides are found along Pacific coasts and
are influenced by the superposition of waves associated with a large number of
amphidromic systems. Mixed tides can have relatively high elevations, 2 to 6 meters.
coastal currents associated with tides
There are horizontal water movements, currents, that accompany the rise and fall of
tide elevations in the shallow depths along coastlines. Fundamentally, the periodicities of the currents are the same as the rise and fall of the elevations, diurnal and
semidiurnal . In general, count on this : when tide elevation is changing most rapidly,
flow is strongest. However, time differences between the vertical rise and fall of
elevations and turning points in the horizontal flow of tidal currents can arise in
particular geographic locations. The cause of these differences often are the constrictions in estuary or bay entrances or perhaps seaward flow of river waters through
entrances or the influence of local winds. Whatever and whenever differences occur,
in the filling or, especially, the draining of semi-enclosed bodies of water, they can be
analyzed while referring to temporal phasing between elevation and flow events.
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There are two tide patterns observed in the Gulf of Mexico, diurnal and mixed.
Tides along the Texas coastline are diurnal. The western coast of Florida and
Yucatan Peninsula tides are mixed.
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about astronomical tides
Tides are what we call the regular rise and fall of sea level during the 24 hours of a day. They have
very long wavelengths, thousands of kilometers due to their generation by the sweeping of the
attraction of the moon over the ocean, and periods of 12.4 or 24.8 hours due to the repetition of the
generation impetus [see two bulges]. The ratio of depth to wavelength [~0.05] always marks them as
shallow water waves and we reckon their speed by the square root of the product of the acceleration
of gravity and depth. In 4000 meters of water they propagate at approximately 200 meters per
second and for shorthand we say that tides propagate energy at speeds proportional to water depths.
The elevation by which a tide’s vertical excursion is assessed is known as the tide datum and this is
not always the same sea level. Country-to-country, the choice of the datum varies : it often refers to
the mean of observed low tides or it can even be the lowest tide level ever recorded at a given
location. Tides affect navigation, therefore commerce, and for this reason their prediction has long
been the subject of observation, analysis, and modeling.
Tide waves are produced by the physical combination of the gravitational force of attraction by the
moon and sun with the centrifugal force associated with the rotation of the earth about center of mass
of the earth and moon taken together. Both forces deform the sea water mass and the results are
bulges on the ocean surface. The superposition of these bulges are the complete tidal elevation,
both above and below a datum, around the globe.
The initial model of the tides was possible after the effect of gravitational attraction was understood
and therefore Isaac Newton was the physicist that developed the equilibrium theory of tides. There
were several assumptions made by Newton to simplify his model : the globe was completely covered
with water; the water depth was deep enough so there was no interaction with the bottom; the forces
producing the tide are everywhere in balance. The model indicates there are two bulges : one
located directly under the moon and one opposite the moon, on the other side of the globe
.
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This graphic illustrates how the equilibrium forces are balanced over the
globe;
the centrifugal force [thin white vector]
within earth and moon system balances
the forces of gravitational attraction [blue
vector] between earth and moon;
To
moon
the
resultant
of
centrifugal
and
gravitational forces is known as the tideproducing force [thick white vector];
there is a force known as the tractive
force; it is a component of the tideproducing force along the sea surface :
the tractive force is the one that makes
the water move.
Tide-producing force
Gravitational force due to Moon
Centrifugal force
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the tractive forces that raise the two bulges of Newton’s Equilibrium tide model
Note that half-way around the globe from a
point directly under the moon the tractive
effort, the force on the water along the
surface, goes to zero. It reverses toward a
point on the globe directly opposite the one
under the moon. In each half, the maximum
tractive effort occurs half-way from the zero
to each of the points [see the maximum
length of the red vectors].
The tractive
effort directly under the moon and
opposite is also zero. These are the
forces acting along the surface of
Newton’s model that are responsible for
and hold the bulges of the equilibrium
tide in relation to each other and the
moon.
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Superposition of the two bulges that
combine to form the tidal envelope on a
globe.
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equilibrium theory results
When reasoning with the results of his theory, Newton considered that the globe was rotating
beneath the bulges; at a given geographic location high tides were present when the region was
under a bulge and there was a low tide when the same region was as far away as possible from a
bulge. So Newton’s theory can explain why there are spring and neap tides.
Spring tides are tides that have larger than average ranges. They are generated when the Earth,
moon and sun are aligned along a line through their centers, a juxtaposition occurring twice a
month at new moon and full moon. At this time, the high tides are at their highest and low tides at
their lowest. These highs and lows come about because the superposition of the gravitational
attractions of sun and moon yields maximum reinforcement of the bulges. Neap tides occur when
there is the greatest mis-alignment of the earth, sun and moon; that is when the line between earth
and moon centers is at right angles to the line between the earth and sun centers; that is minimum
superposition of the gravitational fields. A far as astronomical appearances, Spring tides happen at
new and full lunar phases; neap tides when the moon is in first- and third-quarter phases .
Newton’s theory was a significant step in tide understanding. Yet there are tide characteristics that
it can not explain : it can not yield the times when given stages of the tide will happen or explain
why there are diurnal, semi-diurnal or mixed tide patterns. For that information, one must turn to
another tide theory.
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dynamic theory of tides
The physicist Pierre-Simon Laplace was impressed with Newton’s theory and its results. He
realized that a more complete prediction would require a model that is more realistic, and
therefore more complex. His theory would include additional physical features that would also
be expressed mathematically. Like all appropriate theoretical developments, this new theory
had to include Newton’s forces : gravity and the physical effect of the earth’s rotation. The
Laplace contributions are called partial tides and four of them, lunar daily, solar daily, lunar and
solar semi-dailys, are mechanisms that provide for the accurate prediction of approximately
three-quarters of the observed tides. At present, nearly 400 of these “partial tides” have been
identified.
The dynamic theory assumes that the tides are enclosed in an ocean basin. The tide circles
around the basin, counterclockwise in a northern hemisphere, under influence of the basin
boundary’s shape and the bottom topography depth. The wave takes the form of a standing
wave rotating about a central node where the tidal range is zero. The edges of the basin are
the antinodes. A rotary standing tide wave circles the basin once every twelve hours and
illustrations usually show the progress of the wave every hour. The amphidromic pattern has
three aspects : the central nodes are called amphidromic points; the lines radiating outward
from the amphidromic point to the basin boundaries are known as cotidal lines along which
agiven phase of the waves occur at the same time. There are lines that encircle the
amphidromic point known as corange lines, lines that connect points that have equal
tidal ranges.
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The DYNAMIC theory of astronomical tides considers the motion
of the waves over ocean basins under the influence of bottom
topography, earth’s rotation, and blocking effects of continents on
propagation.
A physical tide model represents a wave that rotates counterclockwise in the northern hemisphere around a basin, once a day
in a diurnal case, and twice for semi-diurnal tides.
In a time sequence, a high tide at the western edge of a basin creates a pressure
gradient sloping down and away to the east. A geostophic analysis of this gradient
yields a current that moves water toward the equator. At the equator, waters gather
(from both sides), a pressure gradient sloping downward to the north supports the
notion of geostrophic flow eastward and so on, until the basin has been boxed.
This semi-circular motion naturally defines an inner location around which the wave
turns and at which there is no tide elevation or motion; it is known as an
amphidromic point. Normally there is one per geographic basin as shown to the left.
From each of these points, lines that define the position of any phase of the wave
emanate in a wavy fashion that indicates the influence of the bottom topography on
wave propagation speed. The numbers run from 0 to 12 (0) and indicate an elapsed
time of one hour. Why are some of these lines that indicate, say a wave crest
position, closer to one another than others ?
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Open ocean tides are regulated by the rotation of the tide waves in an amphidromic sytsem.
In the system, the waves rotate about a central amphidromic point, a location at which there
is no discernable tidal response. A simple model of this system is composed of a shallow
water standing wave that rotates counterclockwise in a constant depth northern hemisphere
ocean about a circular, enclosed basin. The wave’s amplitude excursion, positive elevation
and negative, are maximum at opposite basin edges and zero at the amphidromic point. A
complete rotation around the basin is accomplished every twelve hours.
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… world wide distribution of amphidromes and co-tidal lines … note the amphidromic point off the
west coast of the United States and, in particular, the hour 8 cotidal line north of Seattle …
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Tides can produce remarkable phenomena through combinations of reflections from
continental land masses and changes of propagation direction and speed brought
about by refraction due to changes in bottom topography. The large range of tidal
elevation in Canada’s Bay of Funday is a well known example. Even more striking
phenomena can occur when a tide wave approaches a large island adjacent to a
continental land mass. As a tide wave propagates slower in shallow waters between
the island and coast it continues to propagate with a faster speed in deeper waters
offshore of the island. What can occur is the wave meeting itself along the inner
portion of an island with a difference in phase and therefore tidal elevation.
Locations wherein it meets itself wrapping around the island can give rise to events
that were beyond explanation prior to a comprehensive understanding of the ocean’s
response to the forces of tidal dynamics. A famous phenomenon takes place off the
western coast of Greece between the mainland and the island of Euboea at the city
of Halkis. The combination of tidal phase differences and the action of wind systems
over the inner waters can produce a varying number of reversal in flow past Halkis.
There can be as many as five or six changes in flow direction.
On the western Canadian coast, there is a similar event that gives the appearance of
a seam in the waters of Dixon Entrance at the northern confluence of inshore and
offshore waters between the Queen Charlotte Islands, Prince of Wales Island and the
coast of British Columbia. The next slide shows the meeting of the two phases of
the tide.
an offshore tidal phenomena
A tide wave from the Pacific rotates counter-clockwise around an amphidrome centered in the Pacific Ocean near 35 degrees
north and 145 degree west longitude. It sweeps along the west coast of the North American continent, enters Queen Charlotte
Sound and propagates northward through Hecate Strait toward Dixon Entrance at a slower speed [due to shallower depths on
the continental shelf] than its movement at sea along the western side of the Queen Charlotte Islands into the Entrance.
Within the Entrance the two parts of the wave, now out of phase, meet and due to different elevations, produce a discontinuity
in the water level herein observed at Rose Spit. Wind waves, running on either side of the discontinuity, break against one
another.
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here is some additional information on
Huricanes beyond the text …. specifically
about Texas events …..
… two Hurricanes that struck Texas …
Carla
SEP 1961
Celia
AUG 1970
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When should one expect a hurricane in the Gulf of Mexico ?
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hurricanes that have made landfall in the northwestern gulf coast region
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Hurricane Celia made land fall at Aransas Pass and Port Aransas in August,
1970. This storm was unique in the fact that, although not the biggest to strike
this coastal area, it brought wind gusts that were greater than most hurricane
sustained winds. Celia had sustained winds of 130 mph with gusts of over 180
mph. The structural damages inflicted, in today’s dollars, exceeded 190 billion
dollars yet there were only 9 deaths and 490 injuries.
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Hurricane Celia : note the low pressure center and low wind values as the wind
direction switches during passage of the system
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One way of analyzing the intensity and water damage from a hurricane is to plot
high water values versus coastline. Note the highest value at Aransas Pass as the
system center passed inland slightly south of this bay entrance.
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Carla made landfall between Port O’Connor and Port Isabel in September of 1961; it
was one of the strongest systems to strike Texas in half a century. Sustained winds
of more than 150 mph over the shelf marked it as a category 5 storm on the SaffirSimpson intensity scale; winds were lower, 120 mph at landfall. Forty-three deaths
were attributed to this storm.
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Another way to assess possible damage is to plot water level excursion at a
specific location of interest. At Galveston, the high waters were more than 2
meters above the background water level.
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GUESS FROM WHENCE THIS STUFF CAME
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