Introduction to Ocean Sciences

Chapter 12: Tides

Guide to Reading and Learning

When we visit the shore in some locations the water level rises and falls rhythmically during the day. At others it either changes much less or almost not at all. If we watched closely, we would notice that in some locations the sea rises and falls just once each day but goes through this cycle twice a day in others, and that the time that the water begins to rise or fall changes each day. These motions are the tides. Tides have been important to mariners for centuries, as many ports and harbors are not deep enough to enter when the tide is low and ships can sometimes pass safely over shallow sand bars and reefs only at high tide. However, did you know that tides are important to many marine species, including such well known species as turtles, and that many species match their reproduction to the tides, some spawning at times that are as specific as at the peak of the highest tide of a specific month each year?

The tides are created by the interaction between the gravitational attraction of the moon and sun on the Earth and the centripetal forces needed to keep these bodies in their orbits around each other. The chapter starts with an explanation of how the tide generating force is created. This is tricky and may be hard going for some readers but the reward for achieving an understanding of this basic process is that you will then have no difficulty in understanding why tides can occur once or twice a day, why they are larger in some locations than others, and why the relative locations of the Earth, sun, and moon during each month cause the height range of the tides to become larger and smaller twice a month—spring tides and neap tides. You will also understand why the moon has a bigger influence on the tides that the sun despite the sun’s much larger size.

The general characteristics of tidal motions are easy to understand on a hypothetical ocean covered Earth, but the tides that we do observe are not quite so simple. The tide is like a very long wave that moves east to west as the Earth rotates with respect to the moon and sun, but in doing so it runs into the continents. Also, at every place except the regions near the poles, the tide wave cannot move fast enough to keep up with the sun. The details of exactly how the tide wave is modified are somewhat complex. However, the important things to understand are why the wave cannot travel fast enough to keep up with the sun and generally how the continents modify the tide.

Tidal currents are more complex that the tides themselves. Many people hold the simple idea that the tidal current will be zero when the tide is at its highest and at its lowest point. However, this is rarely the case. Tidal currents generally flow inshore for part of the tidal cycle and toward the sea during the remainder of the tidal cycle in estuaries and bays. However, the patterns are complicated because the tide can behave like a progressive wave or a standing wave, or have characteristics of both these wave types. In addition, the tide’s character can be changed by factors such as the amount of fresh water flowing into the estuary. Some examples are given in the chapter, but if you are going to sail in an estuary or bay near you, you will have to review the studies of local tidal current motions. Tidal height predictions are very accurate for most coastal areas and are published in local newspapers but tidal currents are much more difficult to predict and are not related in any systematic way to tidal heights. This means that sailors need much local knowledge for each port that they visit if they are to make best use of the tides to navigate within the estuary.

Chapter 12 Essential to Know 

Critical Concepts used in this chapter

CC.12

12.1 Tide-Generating Forces

Gravity

  • Newton’s law states that all particles of mass have a gravitational attraction for all other particles, and that the gravitational force is proportional to the sum of the two masses and inversely proportional to the square of the distance between their centers of mass.
  • The gravitational attraction between the moon and the Earth is very small compared to gravity felt by an object at the Earth’s surface due to the Earth itself. Although the sun has a much greater mass than the moon it is much further from the Earth and the gravitational attraction between the sun and the Earth is smaller than that between the moon and the Earth.

Orbital Motions and Centripetal Force

  • In any two body system, such as the Earth and moon or the Earth and sun, one body does not orbit around the other. Rather the two bodies orbit around a common balance point that is closer to the larger body. For the Earth and moon, this balance point is beneath the Earth’s surface but not at the Earth’s center, Similarly the common point of rotation between the Earth and sun is inside, but not at the center of, the sun
  • Any body in orbit must be held in that orbit by a centripetal force that can be supplied by the gravitational attraction.
  • Centripetal force varies with distance from the center of rotation. All points within each rotating body follow the same diameter circle of rotation, and centripetal force is the same at all points on and within each of two orbiting bodies.
  • The gravitational force varies with the square of the distance and is slightly higher on the side of a body facing the other orbiting body and slightly lower on the opposite side.

The Balance between Centripetal Force and Gravitational Force

  • The small imbalance between centripetal force and gravity at different points on the Earth is responsible for tides.
  • The Earth’s own gravity is millions of times larger than the gravitational attraction of the moon or sun at the Earth’s surface and, therefore, the imbalance between centripetal force and gravity can be compensated by an immeasurably small change in an object’s weight if the force imbalance is directed in the same direction as Earth’s gravity (vertically toward Earth’s center).

Distribution of Tide-Generating Forces

  • The moon’s gravitational attraction and the required centripetal force are exactly balanced at all points along a ring around the Earth drawn almost exactly midway between the point closest to and farthest away from the moon
  • At the points directly toward the moon and directly on the opposite side of the Earth from the moon, Earth’s gravity and the imbalance between the moon’s gravitational attraction and the required centripetal force is completely compensated by an immeasurably small change in an object’s weight.
  • At all other points on the Earth there is a component of the imbalance between the moon’s gravitational attraction and the required centripetal force that acts parallel to the Earth’s surface and so cannot be compensated. This component is the tidal force.
  • The tidal force acts toward the moon on the moon’s side of the Earth and away from the moon on the opposite side.
  • The tidal force is zero at the points directly toward and directly away from the moon, increases away from these points, and then decreases to zero again at points along the ring around the Earth drawn almost exactly midway between the point closest to and the point farthest away from the moon, where the moon’s gravitational attraction and required centripetal force are balanced.

Relative Magnitude of the Lunar and Solar Tide-Generating Forces

  • The tide-generating force exerted by the sun is approximately one-half of that exerted by the moon because the sun is much further from Earth than the moon, even though the sun is much more massive than the moon.

12.2 Characteristics of the Tides

Diurnal, Semidiurnal, and Mixed Tides

  • Tides are of three types: diurnal, mixed, and semidiurnal.
  • The three types of tides are the result of the angle of the Earth’s axis relative to the plane of the moon’s orbit..
  • The lunar tidal day is 24 hours and 49 minutes long because the moon orbits in the same direction that the Earth spins and has moved further along in its orbit by the equivalent of 49 minutes when the Earth has spun through 360o (one day).
  • Diurnal tides have one high tide and one low tide each tidal day.
  • Semidiurnal tides have two high tides and two low tides each tidal day, with the two highs and the two lows having approximately equal heights.
  • Mixed tides have two high tides and two low tides each tidal day, with the two highs and the two lows having substantially different heights.

Spring and Neap Tides

  • Tidal range varies during each month. Spring tides occur when the tidal range reaches a maximum and neap tides occur when the tidal range reaches a minimum in a given location. There are two sets of spring tides and two sets of neap tides each lunar month.

12.3 Tides on an Ocean-Covered Earth

The Fundamental Equilibrium Tides

  • On a hypothetical ocean covered planet, the declination of the moon (the angle between the plane of the moon’s orbit and the Earth’s equator) would cause lunar tides to be diurnal near the poles, semidiurnal at the equator, and mixed everywhere else on the Earth.

The Origin of Spring and Neap Tides

  • Spring tides occur when the lunar high tide and the solar high tide occur at the same place at the same time. At such times the lunar high tide and the solar high tide are added while the lunar low tide and solar low tide are also added, causing the tidal range to be at a maximum.
  • Neap tides occur when the lunar high tide and the solar low tide occur at the same place at the same time. At such times the lunar high tide and the solar low tide partially offset each other while the lunar low tide and solar high tide also partially offset each other, causing the tidal range to be at a minimum.
  • Spring tides occur at new moon and full moon. At new moon, the Earth, sun, and moon are aligned so that the moon is located between the Earth and sun; at a full moon the Earth is located between the moon and sun.
  • Neap tides occur at the first quarter and third quarter phases of the moon, when the moon-to-Earth direction is aligned at 90o to the Earth-to-sun direction.
  • There are two sets of spring tides and two sets of neap tides as the moon rotates around the Earth in each lunar month (29½ days).

Other Tidal Variations

  • Tidal heights and times of high and low tide are the sum of both the solar and lunar tides. They have periodicities of 12 hours and 24 hours, 49 minutes respectively (two highs and two lows per rotation).
  • However, tidal heights and times are also affected by variations in the orbits of the Earth, sun, and moon that include changes of distance within the orbits (which are not quite circular) and changes in the declinations. There are many tidal components and each contributes a variation called a partial tide that must be added to compute the tidal height at any location and time.

12.4 Tides in the Earth’s Oceans

  • On the Earth tides are not determined entirely by relative movements of the Earth, moon, and sun because they are affected by the continents, latitude, and the Coriolis effect.

Effects of Continents and Ocean Depth

  • Because the tide wave wavelength (about 20,000 km) is always greater than 1/20 of the ocean depth (maximum of 11 km), tide waves behave as shallow-water waves and are refracted and reflected by the seafloor and continents.
  • As a shallow water wave the tide wave moves at approximately 700 km·h–1. However, the orbital velocity due to the Earth’s spin is greater than this value at low latitudes, so the tide wave tends to lag behind the moon’s overhead location but is continuously recreated so that the lag is reduced and the wave is called a forced wave.
  • Because the tide wave cannot pass over the continents, the the east to west flowing wave is blocked by the east coasts of continents and must be recreated on the west coasts.

Latitudinal Variation of the Earth’s Spin Velocity

  • Tide waves are forced waves at most latitudes because the tide-generating forces move faster than the speed of a shallow water wave of the tide wave wavelength. The tide lag is at a maximum at the equator and is reduced at higher latitudes.
  • At high latitudes above about 65o there is no tidal time lag, and at even higher latitudes the tide wave even tends to run ahead of the moon’s orbital motion. Thus, the tide wave is well developed at high latitudes in the Southern Hemisphere where there are no continents to interfere with its progress.

Coriolis Effect and Amphidromic Systems

  • Tide waves are deflected by the Coriolis effect.
  • Some components of open ocean tides form rotating tidal waves in some basins that are similar to standing waves and called amphidromic systems.. These systems are well developed where the tide wave can be deflected and flow around the basin to arrive back at its original location exactly when the next (or a subsequent) east to west moving tide wave arrives, so the oscillation is tuned.
  • Amphidromic systems flow counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.

12.5 Tides in the Open Oceans

  • The interaction of landmasses and the Coriolis effect with the tides tends to create amphidromic systems within most major ocean basins.
  • In the Atlantic Ocean, the east to west tide wave is poorly developed because the ocean is relatively narrow. The well developed tide wave that flows around Antarctica is deflected into the South Atlantic Ocean so the tide wave flows north through the South Atlantic Ocean and then enters the counterclockwise rotary motion of an amphidromic system in the North Atlantic Ocean.

12.6 Tidal Currents

  • Orbits of water particles in tide waves are so flattened that they are essentially oscillating horizontal currents.

Open-Ocean Tidal Currents

  • Open-ocean tidal currents are weak and rotary, usually clockwise in the Northern Hemisphere, rotating 360o in 12 hours 24½ minutes where tides are semidiurnal—and in complex looping patterns where tides are mixed.

Temporal Variation of Tidal-Current Speeds

  • Contrary to common belief, the times when tidal current speeds are at their minimum do not usually coincide with high and low tide..
  • If the tide wave was a pure progressive wave, the current speeds would be at a maximum at high and low tides.
  • If the tide wave was a pure standing wave tide, the highest current speeds would occur at mid-tide.
  • Because most tide waves have some progressive and standing wave components or characteristics, there is no fixed relationship between the times of high and low tide and the times of maximum and minimum currents. Tidal height tables cannot be used to predict tidal currents.

Tidal Currents in Estuaries and Rivers

  • In very shallow water the crest of the tide wave moves in deeper water than the trough and so moves faster. As a result, the period of time between high and low tide may be much longer than between low and high tide.
  • Tidal currents are oscillatory in the open ocean and reversing in bays and estuaries. In most locations, the times of maximum and minimum tidal currents must be determined by direct observations at the location, and these times are not contiguous with the times of high and low tide.
  • In areas with large tidal ranges and where a channel or bay narrows markedly, a tidal bore can develop when the tide wave moves faster than the shallow-water wave speed at that depth and the leading edge of the wave forces its way up the bay or estuary.
  • Tidal currents within bays and estuaries can behave as if the tide wave were a progressive wave, a standing wave, or a combination of both.

12.7 Tide Prediction

  • Tidal time and height predictions are very accurate and are based on harmonic analysis of observations of tidal fluctuations over months or years at any given point.
  • Tidal current predictions are less accurate and must be based on actual measurements taken over a period of months or years at each location for which prediction is to be attempted.

12.8 Marine Species and the Rhythm of the Tides   

  • Tides are important to many marine species, especially those which coordinate their spawning or egg-laying cycles to a particular tidal phase. Some of these species place eggs and larvae above the normal high tide line to protect them from predators.  Others spawn when tidal currents are strong to maximize dispersion of eggs and larvae, and yet others spawn synchronously to overwhelm ability of predators to consume the eggs and larvae.

12.9 Energy from the Tides

  • Energy can be extracted from tides in a few locations only by placing turbines and, for efficient extraction of available energy, a dam across a bay mouth within which the natural tidal range is very large.

 

Critical Concept Reminders:

CC.12 The Coriolis Effect (pp. 313, 314, 323, 324)

  • Water masses move freely over the Earth’s surface while the solid Earth itself is constrained to move with the Earth’s rotation. This causes moving water masses, including long wavelength waves that comprise the global tide wave motion, to appear to follow curving paths across the Earth’s surface. The apparent deflection is called the Coriolis effect. Coriolis deflection can create a rotary motion of the tide wave, called amphidromic systems, within certain ocean basins. Amphidromic systems rotate counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere. To read CC12 go to page 32CC.

 

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