Introduction to Earth Sciences I

2.6 Marine Tides

Every one who has been to the beach or spent any time near a shore line knows something about the behavior of tides. They appear to the beachgoer as the advance and retreat of the high water line. In fact, we all know that what is happening is that the water level is rising and falling throughout the day. Tides are a very predictable feature of the Earth and result from the interactions of the Earth, Moon and Sun, together with the rotation of the Earth and Moon.

The basic features of tides are well known:

• In most places there are two high and two low tides each day.
• The height of the high tide varies, having two maxima in a month.
  
  The figure below shows these features in tide gage readings (the height of the tide) at several locations around the world for the same one month period. You can see that in some places there are two high and two low tides a day (called semi-diurnal) and in others there is only one (called diurnal). Note also that the maximum height of the tide changes throughout the month. Look carefully and you will also see that the time at which the tide reaches a maximum advances a little each day.
  

  
  Figure 2.6.1

  
  
  
• Tides are very different from place to place throughout the Earth.
  
  The figure below shows how the tidal heights actually vary throughout the world. The pattern is very complex in detail and cannot be explained by the simple theory we cover in the following. Note that the animation at the very end of this section shows how this complex pattern varies through a month.

  
  Figure 2.6.2

These basic features can be explained by the "equilibrium" theory of tides.

Tides are caused by the gravitational attraction of the Moon and Sun. The Moon's effect is about 54% of the total - gravitational force is proportional to the masses of the interacting bodies, but inversely proportional to the square of the distance separating the bodies so, although the Sun outweighs the Moon by a factor of 10 million the fact that it is almost 400 times further away than the Moon gives the Moon the gravitational edge.

Water is very weak and will respond to gravitational attraction or "pull" by trying to move in the direction of the force. So the water covering the Earth distorts by making a bulge toward the Moon.

Figure 2.6.3

As the Earth rotates, points on the surface move in and out, under the bulge, and hence experience high and low tides. But there's a problem with this model of tides; it can't account for there being two high and two low tides each day. It can only explain one high and one low as the Earth rotates beneath the one bulge. Our simple model is incomplete because it doesn't take account of the rotation of the Earth/Moon system. We generally think of the Moon rotating around the Earth on a monthly basis while, in fact, the Earth and Moon rotate around each other. The gravitational attraction acts to "connect" the two bodies and they rotate in unison. If they were of equal mass they would rotate about their mid-point like a baton thrown in the air by a majorette. Because the Earth's mass is much greater than the Moon's, the point about which Earth and Moon rotate together (CM) is near the Earth's surface.

Figure 2.6.4

The animation that is available at
http://plabpc.csustan.edu/general/tutorials/PlanetaryMotion/PlanetaryMotion.htm shows you how the motion of two bodies rotating around each other is affected by the relative sizes of the masses. You can use the sliders to change the masses. You will see how making the masses more nearly equal causes the center of rotation to be somewhere about half-way between the bodies, while if one mass is much greater than the other the center of mass, and hence the rotation point is actually within the more massive body. That's the way it is with the Earth/Moon system.

The critical effect this has is that it gives rise to a second force - the centrifugal force - that acts in the opposite direction and wants to create a water bulge on the opposite side of the Earth, away from the Moon.

Figure 2.6.5

These two forces, in combination, give rise to equal size bulges on both sides of the Earth, and explain why there are usually two high and two low tides a day. This explains one of the most basic observations about tides.

We also know that the basic pattern of daily tidal variations changes from place to place. Usually there are two high and two low tides but the height of the two "highs" is usually not the same. In some places there is only one high tide in a day and in others the signal appears mixed between the two. The gross features of this variable behavior are explained by remembering that the Earth's rotational axis is tilted with respect to the plane of the ecliptic by 23.5° as we know from our previous studies, and the Moon is inclined at about 5°. The net effect is that the tidal bulge is 28.5° off the equator.

Figure 2.6.6

That's almost everything. All that's left is to explain why the height of the tides change during a month.

Figure 2.6.7

Figure 2.6.8

Another way of looking at it:

Figure 2.6.9

Video resource: World Tides Video (QuickTime ~7MB) | World Tides Video (Streamed Real Media)

This is due to the combined effect of Moon and Sun. When the two are aligned the gravitational attractions of the two reinforce and create very high tides. This occurs when the Moon is "full" and "new". When the Moon and Sun are maximally out of line, at the Moon's "quarter" positions, the tides are lowest. The high tides are called Spring tides and the lowest are rip tides. We often hear news reports that describe the destructive effects of storms that surge at the same time as a Spring tide - just about the worst combination.

In reality, tides are even more complex than have been described above and we need a more complete theory (or model) to explain their exact behavior. Missing from our simple model are the continents (our equilibrium model has a fully water enshrouded Earth) and the topographic effects of the seafloor including bays and inlets. Even the friction between the seafloor and the water layers must be factored in. These effects are very complex and no fully complete model of tides actually exists. All are approximations.

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