Tides

I. Introduction

A. The tides are waves just like the wind-driven waves we have just finished discussing. They have exceedingly large wavelengths, such that even in the deepest ocean they behave as shallow water waves, which means they are refracted by bottom topographic highs. They have very long periods, on the order of hours. They are caused by gravitational and centrifugal forces generated by motions of Earth, moon, and sun.

II. Tide Patterns

A. Differences in water level and timing due to tides are experienced throughout the world. Coastal area that have only one high tide and one low tide every day have what's called a diurnal tide.

B. Regions where two high tides and two low tides occur each day have a semi-diurnal tide.

C. If a semi-diurnal tide has high tides that reach different heights and low tides that drop to different levels, the tide is called a semi-diurnal mixed tide.

D. Tidal patterns can be clearly represented on graphs showing water level on the vertical axis and time of day on the horizontal axis.

E. Tidal observations made over long periods of time are used to calculate the average or mean tidal level (MTL).Averages are also determined for the low- and high- tide levels.

III. Tide Levels

A. The greatest height reached by the water surface each day is called high water.

B. The lowest point to which the surface falls is low water.

C. In a mixed system it is also necessary to differentiate higher high water and lower high water, as well as higher low water and lower low water.

D. As high tide is approached the tide is said to be rising or flooding (flood tide), and as low tide is approached it is said to fall or ebb (ebb tide).

E. Horizontally moving currents are associated with the rise and fall of the tide. In between flood and ebb tide is a time of very little horizontal movement of tidal currents called slack tide.

IV. Equilibrium Tidal Theory

A. Definition - the study of the tides as mathematically ideal wave forms behaving uniformly in response to the laws of physics.

B. Applying this theory to explain tides requires the simplification that Earth is covered with a uniform layer of water uninterrupted by continents. It is the study of the physical relationships between Earth's water covering and the tide-generating bodies, the Sun and Moon.

C. Dynamic tidal analysis or the study of oceans' tides as they occur, modified by continents, the shape of the ocean basins, and Earth's rotation will be discussed later.

D. The effect of sun and moon is most easily explained using Equilibrium Tidal Theory.

E. Study the diagram in your textbook that shows the centrifugal and gravitational forces acting between Earth, moon and sun. Arrows indicate which direction the force in question tends to move Earth's water covering. Centrifugal and gravitational forces move Earth's water in opposite directions.

V. Gravitational forces are familiar because you’ve been told since infancy that gravity holds you on the ground. For objects on Earth's surface, the gravitational pull of Earth is the most influential, but the moon and sun do have an effect. The strengths of the gravitational attractions pulling the Earth, sun, and moon together are proportional to their masses and the distances separating them. These relationships are described by Newton's universal law of gravitation, which tells us that any two bodies attract each other:

G M₁ M₂

F_g = ----------

R²

where M₁ and M₂ are the masses of the two bodies and R is the distance between them. G is the universal gravitational constant.

1. The equation tells us that the more massive the objects, the greater the gravitational force that exists between them.

2. However, the greater the distance between the objects, the

smaller the gravitational force.

3.The moon's pull is important because it is so close and the sun's pull because it is so massive.

a. Earth 81X more massive than moon

b. Sun is 333,000X more massive than Earth

VI. If gravity were the only force at work the moon and Earth would have been pulled together billions of years ago. Also, the Earth/moon system would have collided with the sun. There must be other forces at work to keep this from happening. Those other forces can be thought of as centrifugal forces resulting from several different processes: 1) orbit of the Earth/moon system around the sun, 2) orbit of the moon around Earth, and 3) rotation of Earth around its axis. To envision what is meant by a centrifugal force, think of tying a heavy rock to a rope and swinging the rope around your head. The rope and the strength of your grip are like the gravitational forces because they hold the rock and your body together. On the other hand, the rock does not come crashing down on your head because you are exerting a force to keep it swinging in a circle around your head. That is the centrifugal force.

VII. Physicists and astronomers have calculated the sum of all centrifugal and gravitational forces acting on each portion of Earth's ocean covering at any given time. The sum of the forces is different at different places on Earth's surface. This calculation reveals that Earth's oceans are pulled into two "tidal bulges" protruding out from opposite sides of the planet and generally falling in the plane of the moon's orbit around us. Water particles directly under the moon are strongly attracted by moon's gravity and bulge out toward the moon. At the same time, on the opposite side of Earth, the centrifugal forces acting on the water particles are stronger than the gravitational forces creating a second bulge. These two bulges are separated by two depressions and together they generate the two crests (bulges = two high-tide levels) and two troughs (depressions = two low-tide levels) distributed around the Equator. This first simple model also assumes that the moon always orbits directly around our equator, and that the sun has no influence on Earth's tides. Scientists frequently develop such simplified models at first to help them understand a complicated process. Later as they collect more data and improve their understanding, they increase the complexity, accuracy, and completeness of the model.

A. If the situation portrayed above actually existed, every place on Earth would experience a semi-diurnal tide with two high tides and two low tides following each other every 6 hours. The tides are generated by the rotation of Earth underneath the tidal bulges, which are held in place according to the position of the moon. As a point on Earth's surface enters a water bulge, the tide rises, as it leaves, the tide falls. The positions of the bulges remain practically the same during the course of a 24-hour day. They are held in place by the moon, which moves very little in a 24-hour period.

1. When a spot on Earth's surface starts out directly under a tidal bulge it experiences a high tide. Six hours later this spot has rotated as far as it can go away from a tidal bulge and experiences a low tide. Six hours after that the spot is under the opposite tidal bulge and experiences the second high tide. Following another six hours the second low tide occurs. Finally, after a total of 24 hours the reference location is back under the first tidal bulge experiencing the first high tide of the next day.

2. There are tidal bulges in the solid earth as well, but these are not as great as those in the more fluid water so humans don't notice them.

B. The Tidal Day

1. As the Earth rotates around its axis the moon is also moving in the same direction in its orbit around the Earth. It takes the moon about a month to complete a single orbit around Earth. Because the moon has moved along its orbit during a 24-hour solar day a point on Earth that is initially directly under the moon will not be directly under the moon again at the end of 24 hours. Instead Earth must rotate for another 50 minutes to bring it back in line with the moon. Therefore, the tidal day (or lunar day) is 24 hours and 50 minutes long. This explains why the morning high tide at a NC beach arrives about one hour later each day. The same applies to the other tides experienced each day.

VIII. The Sun Tide

A. The tidal influence of the sun is similar, but smaller than that of the moon, because the sun is so far away. The sun tide amounts to about 46% of that created by the moon.

IX. Spring Tides and Neap Tides

A. Because the moon rotates around the Earth, the relative positions of the Earth, sun and moon vary through a cycle lasting 29 1/2 days. Therefore, the moon's tidal bulges are not always in line with the sun's tidal bulges.

1. When the moon is new or full, the moon's tidal bulges line up with the sun's tidal bulges and the resultant bulges are the largest of the month. In other words, the tidal waves of the sun and moon interfere constructively. At these times of the month Earth experiences the highest high tides and the lowest low tides and, therefore, the greatest tidal range. (The tidal range is the difference in elevation of the sea surface at high tide and at low tide.) This is the Spring Tide.

2. When the moon is in its first or third quarter, however, the tidal bulges of the moon and sun are at right angles to one another and, therefore, partially cancel each other. That is, the tidal waves generated by the moon and sun interfere destructively and tides are the smallest of the month. At these times of the month, Earth experiences the lowest high tides and the highest low tides and, therefore, the smallest tidal range. This is the Neap Tide.

3. So periods of spring and neap tides alternate at about 1-week intervals as the moon orbits around the Earth.

B. Study the diagram in your textbook and practice drawing pictures showing the tides and the positions of the sun, moon and Earth at the time of new, first quarter, full, and third quarter moon.

X. For any given geographic locality the magnitude and pattern of high and low tides depends on the very complex interactions of a number of factors.

A. The effects of the relative positions of sun, moon, and Earth were just discussed and the effect of the Earth's rotation during a 24 hour period has also been discussed. However, there are other factors that affect a person's "tidal experience".

B. Latitude - The Earth's axis of rotation is tilted with respect to the moon's orbit. That is, most of the time the moon does not orbit around Earth in the plane of our Equator. Therefore, as the moon orbits the Earth, it spends half the month above the equator and half the month below the equator. (Study the diagram in your textbook.) One of the moon's tidal bulges occurs in the Northern Hemisphere and the other occurs in the Southern Hemisphere. The center of the tidal bulges may lie at a latitude as high as 28.5^o. Therefore, at mid- to high- latitudes a point on Earth's surface passes through only one crest (or high) and one trough (or low) during a tidal day. This pattern produces a diurnal tide. On the same day, a person located at the equator would experience a semi-diurnal tide.

C. Elliptical Orbits - Neither the Earth's orbit around the sun nor the moon's orbit around the Earth is perfect circle. So the distance between the Earth and the sun change during the course of the year and the distance between the Earth and the moon change during the course of the month. This results in variations of the magnitudes of the tidal bulges caused by the sun and the moon.

XI. Dynamic Tidal Analysis

A. Because tidal waves are very long-wavelength waves, they behave as shallow water waves, even in the deepest part of the oceans. That is their paths are affected by the local bottom topography. This means that the configuration of the local coastline can concentrate or disperse tides at different places leading to very large tidal ranges in some areas and very small tide ranges in other places.

1. Bay of Fundy has almost a 40-foot tidal range whereas Nantucket (just to the South) has a range of only about 1.5 feet.

B. Also, in the mouths of some rivers, the incoming tide meets the outflowing current and stacks up, forming tidal bores. These are fast-moving currents that travel as a wave front or wall of water up and down a bay or river. The bores are usually less than a meter in height, but can be as high as 8 meters. A steep-fronted wave sometimes results. This can influence the progress of the tidal wave to upstream locations.

1. Some tidal waves are so consistent that surfers can ride them for many miles (e.g. a spot along the Amazon River)

C. Because the continents separate oceans the tidal wave is discontinuous. It starts at one shore of an ocean basin and stops at the other.

1. Only in southern latitudes around Antarctica does the ocean go all around the earth without a "continental interruption".

2. The tidal wave is also reflected from the continental edges creating strange interference patterns.

D. Coastal bays and channels are often long and narrow. They have an open end toward the sea and reflection of the tidal wave occurs only at the head of the basin. This leads to a complex interference pattern for tidal waves that varies with the size and dimensions of the bay. The dimensions of the Bay of Fundy are such that interference of the tidal wave with itself yields a 2-meter tidal range at the mouth of the bay and an 11-meter range at the head of the bay.

E. The weird tides in Gulf of Mexico result because all the water must get in and out of the Gulf through the narrow Florida Straits.

F. All these factors combine to make prediction of tides very complicated, so published tide tables are mainly based on historical records of the progression of the tides in a given region.