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					                                 MAR 110: Lecture 16 Outline – Tides   1

                           MAR 110 LECTURE #16

Tides Are Waves
Tidal wave energy is concentrated at periods of
approximately 12 and 24 hours. (ItO)

Equilibrium Tidal Forcing
The theoretical equilibrium tidal ocean covers the whole
Earth deeply enough so that the shallow water tidal waves
can follow astronomical forcing as the Earth rotates below.
                              MAR 110: Lecture 16 Outline – Tides   2

Gravitational Attraction
A “body force” that draws mass together. (ItO)

Basic Dynamic Balance
The centrifugal “force” of circular motion balances the
gravitational attraction; so that our two “moons” do not
crash into each other. (ItO)
                               MAR 110: Lecture 16 Outline – Tides   3

The Earth-Moon Dynamic
The Earth is so massive that the center of Earth-Moon system
rotation is located within the Earth. (ItO)

Earth-moon System: Tide–Producing Forces
The Moon’s gravitational attraction creates a stationary
oceanic bulge on the side of the Earth facing the Moon.
The centrifugal “force” due to the spinning of the System
produces the oceanic bulge on the side of the Earth facing
away from the Moon (ItO)
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Observed Ocean Tides
Sea level records from different locations reveal tides that are
dominated by the twice-a-day or semidiurnal tide (top) ofr the
once-a-day or diurnal tide (bottom). A mixture of the two
period tides is more common. (LEiO)

Once-a-Day or Diurnal Tide
An Earth observer (the stick figure) standing on the Earth at a very high
latitude observes a high tide once-a-day as indicated in the time chart
below. (??)
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Semi-Diurnal Tide

Equilibrium Tides
An observer on the Earth rotates beneath a stationary
double oceanic sea level bulge. An observer at the
equator observes two high tides of different height each
lunar day, as indicated in the time chart to the right. (ItO,
                                  MAR 110: Lecture 16 Outline – Tides   6

Spring – Neap Tides
About every 14 days the range of the tidal sea levels cycles
through a maximum called spring tides and a minimum
called neap tides – as indicated by the sea level record to the
left. This phenomena occurs because the sun and the moon
each produce separate double oceanic sea level bulges, with
the sun’s being about that of the moon, as illustrated to the
right. During spring tides (a time of full or new moon), the
solar and lunar double bulges add to each other to produce
the largest tidal ranges. During neap tides ( a time of half
moon), the solar and lunar tidal bulges subtract from one
another. In short, the spring neap cycle in tidal range arises
from the constructive and then destructive interference of the
solar and lunar tidal sea levels. (??)

Realistic Ocean Tides
On the real Earth oceans are contained in basins bounded
by the continents; not covered by the ocean. Thus the
astronomical tidal forcing creates a standing tidal wave in
our idealized ocean basin that is meant to model the
Atlantic Ocean. (ItO)
                                MAR 110: Lecture 16 Outline – Tides   7

Rotary Standing Wave in an Enclosed Basin
The tidal waves in our idealized enclosed ocean basins are
the rotary standing waves as illustrated above because of the
effects of Earth rotation. Note how the sea level highs (and
lows) rotate around a node in the center of the idealized
basin – a point of no tide or amphidromic point in what is
called an amphidromic system. (ItO)
                                  MAR 110: Lecture 16 Outline – Tides   8

Cotidal Chart of an Amphidromic System
The tidal action ina an amphidromic system can be neatly
summarized in a cotidal chart, which looks like a wagon-wheel.
Cotidal lines (the spokes) mark the location of high tide at each
lunar hour during the tidal cycle. The corange lines (the circular
wheel rim) mark the locations with the same tidal ranges. (ItO)

The Atlantic Ocean Amphidromic System
The North Atlantic tidal system closely resembles an ideal
amphidromic system with some deviation due to bathymetry.
                                 MAR 110: Lecture 16 Outline – Tides   9

Wave Reflection and Standing Waves
A standing wave does not travel or propagate but merely
oscillates up and down with stationary nodes (with no
vertical movement) and antinodes (with the maximum
possible movement) that oscillates between the crest and
the trough. A standing wave occurs when the wave hits
a barrier such as a seawall exactly at either the wave’s
crest or trough, causing the reflected wave to be a mirror
image of the original. (??)

Standing Waves
Standing waves can also occur in an enclosed basin
such as a bathtub. In such a case, at the center of
the basin there is no vertical movement and the
location of this node does not change while at either
end is the maximum vertical oscillation of the water.
This type of waves is also known as a seiche and
occurs in harbors and in large enclosed bodies of
water such as the Great Lakes. (??, ??)
                                 MAR 110: Lecture 16 Outline – Tides   10

Seiche Period
The wavelength of a standing wave is equal to twice
the length of the basin it is in, which along with the
depth (d) of the water within the basin, determines the
period (T) of the wave. (ItO)

Bay Tides and their Period
Another type of standing wave occurs in an open basin that
has a length (l) one quarter that of the wave in this case,
usually a tide. In this case the node is at the inlet of the
basin with the antinode at the closed end. The most
commonly used example of this type of standing wave is the
Bay of Fundy. (ItO)
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Gulf of Maine/Bay of Fundy Tides
The North Atlantic tidal excursions at the mouth of
the Gulf of Maine (rather than direct astronomical
forcing) drive the large tides in the Gulf of Maine/Bay
of Fundy system, with the largest tidal ranges at the
head of the Bay of Fundy. (ItO)

Bay of Fundy and Tidal Bores
In regions with significant tides such as the Bay of Fundy it is not unusual
for a tidal bore to form which is a wave or wall of water at the leading edge
of the tide wave (right), particularly in rivers or narrow bays and passages.
The tidal bore will continue upstream into the bay or river sometimes for a
hundred miles or more (ex: the Yellow River in China). Since this wave or
wall of water has the mass of the tide behind it, people can use it to push
surfers or even boats upstream for long distances. (??, ItO, LEiO)
MAR 110: Lecture 16 Outline – Tides   12

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