Tide Modelling Research Paper
Tide Modelling
Rationale: ¬¬¬¬¬¬¬
I have decided to centre this mathematical exploration on the features of the ocean. Initially I looked deeper at the stimuli provided by my schoolteacher. While being interested in many different topics for the explorations, this topic stood out to me, as I had never before thought about the mathematical significance of the height of waves. Would it be possible to predict the height of waves a day before? I did some research and investigation in the significance of lunar phases and the height of the waves however I was unable to find anything
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Introduction:
Gravity is one of the major forces that creates tides. Ocean tides result from the gravitational attraction of the sun and moon on the oceans of the earth. As the moon revolves around the Earth, its angle increases and decreases in relation to the equator. This is known as its declination. The two tidal bulges track the changes in lunar declination, also increasing or decreasing their angles to the equator. Similarly, the sun’s relative position to the equator changes over the course of a year as the Earth rotates around it. The sun’s declination affects the seasons as well as the tides. Through the following graph I have tried to explain my concept.
In this area tides are frequently changing their positions. Through the above secondary sites I have collated the data in the following way: Day 27th December 2003
Time Height
(m)
0.0 7.5
01.00 10.2
02.00 11.8
03.00 12.0
04.00 10.9
05.00 8.9
06.00
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Along the coast, the tides are of a particular interest. They are affected by the gravitational pull of both the moon and the sun. The high tides and low tides follow a periodic pattern that you can model with the sine function.
For example, on a particular winter day, the high tide in Bay of Fundy in Nova Scotia, Canada., occurred at midnight. To determine the height of the water in the harbor, use the equation .
Y = 5.8 sin (0.52x+0.20) + 6.5
where x represents the number of hours since midnight.
Analysis and interpretation:
Input the value of x into the equation to find the height at a particular time.
At midnight, the value of x is 0. Putting 0 in for x in the equation gives you
Y = 5.8 sin (0.20) + 6.5 = 7.65
And at the greatest height at π/2
Y = 5.8 sin (0.52 π/2 +0.20) + 6.5 = 11.94 ≈ 12
So it makes sense that the high tide would be when the formula uses the sine of that value. Determine the change in the height using the
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