Sunday, September 22, 2013

Global Tidal Variations Explained

Tides are periodic variations of the ocean surface caused by the gravitational attraction of the moon and the sun. On a fundamental level, tides can also be considered as waves. Since these tidal waves have extremely long wavelengths, they are essentially shallow water waves(Shallow water waves are waves which travel over depths lower than 1/20th their wavelength). This means that the speed of the tidal wave is proportional to the depth. The depth of the ocean basin, the time of year and month, latitude and earth's rotation affect the type and magnitude of tides. While the exact relationship between all these variables can be somewhat complex, certain scientific theories and models help simplify and explain the behavior of tides.

Depending on the occurrence of high and low tides, tidal patterns are classified into three types. These are,
1. Diurnal tides
2. Semi-diurnal tides
3. Mixed Tides.
If the tidal wave shows 1 crest and 1 trough within a period of 1 lunar day(24hrs and 50mts), then it is called a diurnal tide. If it shows two crests and two troughs or vice versa in one lunar day, it is called a semi-diurnal tide. Mixed tides are a mixture of these two, often with significantly different amplitudes.

While tidal variations can be attributed to the gravitational attraction of both the sun and moon, the effect of the moon is significantly larger. "The Equilibrium theory of tides" attempts to explain these variations with the following assumptions.
-the ocean is indefinitely deep
-no land masses are present
-no inertial forces
With these assumptions, the key tide generating forces are, gravitation and centripetal force. These two forces act differently on different locations on the earth. While the gravitational force directs to the center of the moon, the centripetal forces at different locations are parallel to each other. This is because, centripetal force is the force that keeps an object in circular orbit, and the different locations have their own circular orbits parallel to each other.

Source : Trujillo,Alan P.Essentials of oceanography / Al Trujillo, Harold Thurman. 10th ed.

The gravitational attraction provides the required centripetal force to keep the earth in orbit. However, the gravitational attraction and the required centripetal force are unequal at different locations on the earth. These two are equal only at the center of the earth. The difference between these two forces creates a resultant force which acts as shown in the diagram. It is this resultant force that is responsible for the generation of tides. This is also why, tidal bulges appear on both sides of the planet, because the resultant forces at the two sides of the earth are oppositely oriented. 

The orbital plane of the moon is inclined by approximately 28.5 degrees to the earth's axis of rotation. This causes the tidal bulges also to orient as shown below. The earth rotates through these tidal bulges. This explains the occurrence of diurnal and semi-diurnal tidal patterns explained above. By inspecting the diagram below it can be seen that high latitude locations receive diurnal tides, equatorial regions receive semi-diurnal tides and mid latitude locations receive mixed tides. 

Source : Trujillo,Alan P.Essentials of oceanography / Al Trujillo, Harold Thurman. 10th ed.

This shows how the equilibrium theory explains the occurrence of the diurnal and semi-diurnal tides. This means that, tidal patterns on earth should be related to latitude. According to the above diagram it is also seen that tidal heights should also vary with latitude, with the highest tidal heights in mid latitude regions. However, the following tide map of the world shows that no such connection between tidal characteristics and latitude can be observed. This is where the equilibrium theory of tides fails.

-world tidal patterns- Source : Invitation to oceanography / Paul R. Pinet. — 5th ed.

The equilibrium theory of tides does not take into account the depth variations of the ocean basins. It also neglects the effect of the earth's rotation. To overcome these issues, another theory, "The Dynamic Theory of Tides" was proposed. Proposed in the 18th century by Pierre Simon Laplace, it attempts to explain tidal variations with the Coriolis Force.

To illustrate this theory, consider a large rectangular ocean basin in the northern hemisphere. when the water level rises in the upper portion of the basin due to the tidal action, the Coriolis force deflects the mass of travelling water towards the right. this causes the water to build up in the upper right corner of the basin. The resulting pressure gradient causes the water to flow downwards, but is again deflected to the right by the Coriolis force. This cycle continues, and it results in a counterclockwise oscillation of the water mass. The nodal point where the water does not oscillate is known as an "Amphidromic Point."

Source : Invitation to oceanography / Paul R. Pinet. — 5th ed

If the ocean basin is situated in the southern hemisphere, the Coriolis force will deflect the water towards the left side, and the resulting oscillation would be clockwise. While ocean basins found on earth are not ideal basins like the above explained, several Amphidromic Points can be identified in the earth's oceans through tidal action. This amphidromic system of tides better explains the tidal variations depicted in the above tidal map. Since the amphidromic system is an oscillatory system, tides can undergo resonance. If the natural period of the ocean basin equals the period of the tides, tidal resonance will occur creating a massive tidal wave. An example of this is the Bay of Fundy where tidal ranges of over 17metres have been observed.

Global Amphidromic Points - Source : Invitation to oceanography / Paul R. Pinet. — 5th ed
The depth of ocean basins also affect tidal heights. As explained above, tides being shallow water waves, have speeds that are proportional to depth. This means that a lower depth would cause the tidal wave to slow down, and due to the conservation of energy, the amplitude of the wave would increase, thus creating a higher tide. Taking all these factors into consideration, tides can be accurately modeled and predicted.

This understanding of tidal action opens up means of using it as an energy source. In places where a high tide variation is present, tidal energy can be tapped into by building dams to trap the incoming tidal flood current, and then channeling them through turbines like in a hydro-power plant. Power plants of this type are already in operation around the world, an exmaple is the La Rance tidal power plant at St. Malo, France. Tidal power plants do not pose a significant threat to the environment and are therefore are a good alternate source of renewable energy.

No comments:

Post a Comment