REVIEW OF TIDES (Garrison, p257-271) (by Andrew Aubrey) Tides - Periodic, short-term changes in the height of the ocean surface at a particular place caused by a combination of the gravitational force of the moon and the sun and the motion of the Earth. Tides are caused by gravity where the tide generating force is expressed by the following equation: m m T G 1 3 2 r As you can see, the distance is very important to the overall tide generating force (T). G is the universal gravity constant, m1 is the mass of the earth, and m2 is the mass of the sun or moon. The farther the distance away, the lower the tide generating force. Although the sun is more massive than the moon, the fact that the moon is so much closer than the sun makes it have more of an effect upon the Earth’s tides. The relationship is approximately: TMoon 2 TSun Or that the tide generating force of the moon on the Earth’s oceans is twice that of the Sun’s tide generating force (TGF). The moon exerts its gravitational attraction on the Earth’s oceans on the side that it is aligned. However, the Earth’s movement around the center of mass of the Earth-moon system creates a bulge on the opposite side of the moon’s location (Fig 11.4), due to centrifugal force. This creates an even tidal bulge on the side of the earth close to the moon and the side farthest from the moon. When the moon is in the equatorial plane, it produces tides in the following orientation (Fig 11.7). Notice that the time between high-tides is 12 hours 25 minutes. The total time that it takes the moon to be overhead in one spot on earth again is equal to 24 hours 50 minutes. This is because as the earth rotates about its axis, the moon proceeds along its 1 month rotation around the earth. Because the moon rotates around the earth in the same direction as its rotation about its axis, the moon rises (in the East) 50 minutes later each day. Here is another diagram that explains why the time between high tides is 12:25 and the time that it takes the moon to be directly overhead again is equal to 24:50. This is explained by the fact that there is motion associated with the moon around the earth in the time that it takes the earth to rotate once around its axis (Fig 11.8). Figure 11.11 shows the phases of the moon with the Earth-Sun-Moon system and how it affects the tidal bulge (and therefore tidal range). The true tidal bulge is the average between the moon’s tidal bulge and the sun’s tidal bulge. The sun and moon’s gravitational forces work together to deform the tidal bulge in Full Moon and New Moon situations (a), resulting in Spring tides, or the conditions of largest tidal range. The gravity of the sun and moon work against each other in 1st and 3rd Quarter situations (b), resulting in neap tides, or the conditions of smallest tidal range. When the moon is drawn above the earth, keep in mind that the moon’s position is really directly behind the earth in this picture, not above the earth as it is drawn. The largest tidal ranges would occur in spring tide situations (New Moon or Full Moon conditions) when the moon is at perigee (closest to earth), so called perigean spring tides. Even larger tides would result if the earth were at the perihelion location in its orbit around the sun. Conversely, the smallest tidal range would occur in neap tide situations (1st or 3rd Quarters) when the moon is at apogee (farthest from earth). Even smaller tides would result if the earth were in the aphelion location in relation to the sun. Figure 11.12 shows the relationship between the phase of the moon and the tidal range. Understand how the phase of the moon leads to large tidal ranges (spring tides) and small tidal ranges (neap tides). The moon’s rotation around the earth is not always along the equatorial plane. In fact, the true movement is a rotation about the earth that places it ~28.5 degrees above the equator (week 0), and two weeks later, ~28.5 degrees below the equator. In between these extremes, the moon passes once in the equatorial plane (week 1) and through the equatorial plane once again in week 3. Daily inequalities result when the moon is out of the equatorial plane and they are larger when the moon is at the largest angle out of the equatorial plane (28.5 degrees). See how the tidal bulge is changed when the moon is out of the equatorial plane (Fig 11.10). Keep in mind that the moon’s orbit is also not a perfect circle. There are times when the moon is closer to the earth in its rotation (perigee), resulting in larger tidal ranges. There are also times in the moon’s orbit when it is farther away from the Earth (apogee), resulting is less gravity on the earth’s ocean, and smaller tidal ranges. The earth’s orbit around the sun is elliptical rather than circular. This results in a time in the year of perihelion, when the earth is closest to the sun and the sun’s gravity on the oceans is largest, and aphelion, when the earth is farthest from the sun. The perigee and apogee have more of an effect on tides than the perihelion and aphelion conditions because the moon is so much closer to the earth than the sun. Here is a record showing the tides at various locations on the earth. Understand that the daily inequality is equal to the difference between the high high-tide and low high-tide, or the difference between the low low-tide and the high low-tide (Fig 11.13, c). Keep in mind that the mixed tides situation (c) can also be designated as semi-diurnal because there are 2 high tides and two low tides per 24 hours, 50 minutes. Be familiar with amphidromic systems in confined basins (Garrison, p. 267-268). Realize that this is mostly due to the shape of the basin and how the tides propagate through these areas.
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