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Oceanography >> Waves and Tides >> Tides
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4.6 - Tides
Objectives:
- To be able to find and read a tide table.
- To understand that the Moon causes the tides and that Spring tides are larger than Neap tides.
- To understand why the tides in Bermuda are less dramatic than those of the eastern and western edges of the ocean basins.
Bermuda has relatively small tides - mainly due to its location far from any continents. There are only a few locations around the island where there is an appreciable tidal flow (Flatt's Bridge, Watford Bridge, the wreck of the HMS Vixen and Castle Roads) and most islanders just notice the tides when they go to the beach or jump off cliffs. The south coast of England, where I grew up, has really big tides and bad things happened to any one on the water that did not respect and understand them! The largest tides are found in the Bay of Fundy, Canada. For the oceanographer, fisherman and sailor there are two aspects that we need to be aware of; height and flow.
The science of tides is complicated! There are a couple of ways to understand them:
In his great work, Principia, Newton codified the Laws of Motion and the Law of Universal Gravitation. The force of gravity follows an inverse square law - it gets rapidly weaker with distance. Ultimately the tidal forces that affect the oceans are due to the difference in the gravitational force due to the diameter of the Earth. The water moves as it is pulled sideways, almost parallel to the seabed by the tidal forces. The tides rise and fall as the Earth spins under the bulges.
In these diagrams it would appear that the high tide would coincide with the zenith of the Moon in the sky, but it doesn't happen that way. The ocean has to move and there is drag due to friction. This leads to a lag in the bulges. Local geography also plays a part as the water has to flow through openings and bays. Ultimately the Moon's kinetic energy is being slowly converted into heat by this friction. The Moon is very steadily moving away from the Earth due to this tidal friction.
The science of tides is complicated! There are a couple of ways to understand them:
- gravity
- harmonics
In his great work, Principia, Newton codified the Laws of Motion and the Law of Universal Gravitation. The force of gravity follows an inverse square law - it gets rapidly weaker with distance. Ultimately the tidal forces that affect the oceans are due to the difference in the gravitational force due to the diameter of the Earth. The water moves as it is pulled sideways, almost parallel to the seabed by the tidal forces. The tides rise and fall as the Earth spins under the bulges.
In these diagrams it would appear that the high tide would coincide with the zenith of the Moon in the sky, but it doesn't happen that way. The ocean has to move and there is drag due to friction. This leads to a lag in the bulges. Local geography also plays a part as the water has to flow through openings and bays. Ultimately the Moon's kinetic energy is being slowly converted into heat by this friction. The Moon is very steadily moving away from the Earth due to this tidal friction.
Diagram of the tidal forces acting on the surface of the Earth due to an orbiting satellite (the Moon). These are greatly exaggerated in scale. (Wikipedia)
Tides are not solely caused by the Moon - the Sun has an effect as well. The force of gravity between the Earth and the Sun is far greater than that between the Earth and Moon, but the distance from the Sun is far, far greater. This leads to a smaller gravity field gradient - which in turn leads to a smaller tidal force. The tidal force due to the Sun is about \(45\,\text{%}\) that of the Moon. These tidal forces are very weak and cannot "lift" the water, but they instead pull on it sideways. As the oceans are so huge, this can lead to the water piling up. For comparison - the width of the oceans is measured in thousands of kilometres, where the tidal range is generally only a few metres.
The effect of the Sun is noticeable. When the tidal forces of the Sun and Moon combine we get a larger tidal range than normal. This is known as SPRING tides. They occur TWICE a month, at a Full Moon and a New Moon. The weakest combined effect is when the Moon is perpendicular to the Earth-Sun axis. These are the NEAP tides and occur at the half-moons (First and Last Quarters).
The effect of the Sun is noticeable. When the tidal forces of the Sun and Moon combine we get a larger tidal range than normal. This is known as SPRING tides. They occur TWICE a month, at a Full Moon and a New Moon. The weakest combined effect is when the Moon is perpendicular to the Earth-Sun axis. These are the NEAP tides and occur at the half-moons (First and Last Quarters).
Tides are pretty much predictable and tide charts and tables are produced for every port around the world. When navigating in waters with a large tidal range, it is critical to know the tide heights, times and currents.
In the figure above, the morning tide is higher than the evening tide. This is caused by the Moon's orbit not being perfectly aligned with the equator. The orbit is tilted at an angle of about \(5^{/circ}\). If the Moon is north of the equator in the morning, it will be below the equator 12 hours later as the Earth spins under it.
The cycle of spring and neap tides shows up very clearly on the 30-day forecast from www.tide-forecast.com. Notice how the spring and neap tides coincide with the phases of the Moon. Another good rule of thumb that works very well in Bermuda is that the tides are usually reversed after a week. For example: if it is high tide at 0830 Saturday morning, then the following Saturday it will be low tide at that time.
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Apart from being tilted at an angle, the Moon's orbit is slightly elliptical. Sometimes the Moon is closer to Earth than its average and other times slightly further away. Every so often, the Moon's closest point of approach coincides with Full/New Moon and the tides are more extreme than usual, especially if the axial tilt places the Moon in the northern hemisphere. These are called King Tides and usually occur once a year. We see this in St George's as King's Square gets flooded. (names are NOT related!)
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ACTIVITY - Find a local tide table and find out when the spring and neap tides are. Plot a graph of tidal height as a function of date/time.
http://weather.bm/Tools/TideTimes.asp?Month=1&Year=2020
https://www.tideschart.com/Bermuda/Hamilton-city/
https://www.tide-forecast.com/locations/Bermuda-Esso-Pier-Saint-Georges-Bermuda/tides/latest
http://weather.bm/Tools/TideTimes.asp?Month=1&Year=2020
https://www.tideschart.com/Bermuda/Hamilton-city/
https://www.tide-forecast.com/locations/Bermuda-Esso-Pier-Saint-Georges-Bermuda/tides/latest
Harmonics
Tides can also be thought of as waves that have a very long period. This is borne out when tidal heights are plotted as a function of time. Fourier analysis shows that the two principal components have periods of \(12.42\,\text{hrs}\) and \(12\,\text{hrs}\). Whenever there are two waves of similar but slightly different frequencies we get 'beats' due to the interference between the waves. These beats are the spring and neap tides!
Tides can also be thought of as waves that have a very long period. This is borne out when tidal heights are plotted as a function of time. Fourier analysis shows that the two principal components have periods of \(12.42\,\text{hrs}\) and \(12\,\text{hrs}\). Whenever there are two waves of similar but slightly different frequencies we get 'beats' due to the interference between the waves. These beats are the spring and neap tides!
ACTIVITY - Use two browser windows to open the following link. Set the frequencies to be slightly different and hear the beats.
http://onlinetonegenerator.com/
Another great simulation of beats is shown below:
http://onlinetonegenerator.com/
Another great simulation of beats is shown below:
Image: www.ophysics.com
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Beyond Oceanography
Tidal forces do not just affect the world's oceans. They also affect the atmosphere to a far lesser extent. I noticed this when recording data aboard the RRS Discovery when crossing the ocean. A plot of the atmospheric pressure as a function of time showed the semi-diurnal atmospheric tides as well as the large scale changes due to weather.
If the tidal forces are strong enough on a celestial body it can cause 'tidal locking' where the forces have effectively stopped the rotation of that object. We think of the Moon as causing the tides on Earth, but the Earth in turn produces far higher tidal forces on the Moon - roughly \(20\) times the magnitude. The Moon is tidally locked by the Earth, which is why we can only see one side of it. Pluto and Charon are in a mutual tidal lock. In extreme cases the tidal forces can destroy the satellite - which is the origin of the rings of Saturn. The tidal forces of a Black Hole could cause 'spaghettification', where an objects falling in experiences far higher forces at the point closer to the Black Hole than away from it - so stretching the object until it breaks.
Tidal forces do not just affect the world's oceans. They also affect the atmosphere to a far lesser extent. I noticed this when recording data aboard the RRS Discovery when crossing the ocean. A plot of the atmospheric pressure as a function of time showed the semi-diurnal atmospheric tides as well as the large scale changes due to weather.
If the tidal forces are strong enough on a celestial body it can cause 'tidal locking' where the forces have effectively stopped the rotation of that object. We think of the Moon as causing the tides on Earth, but the Earth in turn produces far higher tidal forces on the Moon - roughly \(20\) times the magnitude. The Moon is tidally locked by the Earth, which is why we can only see one side of it. Pluto and Charon are in a mutual tidal lock. In extreme cases the tidal forces can destroy the satellite - which is the origin of the rings of Saturn. The tidal forces of a Black Hole could cause 'spaghettification', where an objects falling in experiences far higher forces at the point closer to the Black Hole than away from it - so stretching the object until it breaks.
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| 4.5_-_tides.pptx |