TIDES

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Tides are generated by the gravitational attraction of the sun and moon on the oceans. This force is:

Tide generating force (TGF) is proportional to (moon mass*sun mass)/(r**3)


The mass of the sun is 2x10**27 metric tons while that of the moon is only 7.3x10**19 metric tons. The sun is 390 times farther away from the earth than is the moon. If we substitute these in the equation we find:


Relative TGF = [(2x10**27/7.3x10**19)]/(390**3)

or = 27x10**6/59x10**6 = 0.46 or 46%

For each particle on the earth there is an associated centripetal or center-seeking force which is required to keep each particle following the same orbit as the earth. If we swing a rock on a string around our head, the string provides the centripetal force to the rock. If it breaks, the rock flies off in a straight line tangent to the circle.

On the average, the centripetal force is equal to the gravitational attraction, but the two are not equal at all points on earth. The centripetal force is directed toward the center of each particle's orbit. The gravitational attraction of the moon is greater for particles closer to the moon and is directed toward the center of the moon.

The difference in the magnitude and direction of these two forces can be determined by vector subtraction. The tides result from this net force. The moon is at zenith when it is directly overhead and at nadir at the opposite side of the earth. If we pass a plane through the center of the earth perpendicular to a line connecting the centers of the moon and the earth, there is no tide generating force along the circle, nor at zenith or nadir. At all other points, there is a slight lateral force. These lateral forces produce the bulges of water that are the tides. These forces reach a maximum along circles which are at 45o from the previously described circle.

If we treat the earth as if it were uniformly covered by water and that there is no friction between the water and the ocean floor, we can examine the theoretical, predicted tides. These tides are called equilibrium tides. Once we develop an understanding of these oversimplified tides, we can consider the effects of varing ocean depth, the presence of land masses and frictional forces. These tides are called the dynamic tides.

Equilibrium Tides

The important things here are: 1) the combined effect of the earth's rotation around the sun and the moon's rotation around the earth produces tides that have two highs and two lows at the equator every 24 hours and 50 minutes. This is due to the length of the lunar day; 2) the combined effects of the sun and moon produce spring and neap tides depending on their alignment which varies over the course of one month; 3) the effects of declination cause seasonal changes in the northern and southern hemispheres and cause the bulges of water to be centered in the regions north and south of the equator rather than always being centered on the equator; and finally 4) the annual changes in the distances between the earth and the sun and the moon produces annual changes that affect the tides.

The diurnal inequality refers to the fact that the heights of successive high or low tides are unequal. This is due to the inclination of earth on its axis.

Dynamic Theory of Tides

As previously stated, the tides are an extreme example of a shallow water wave with a wavelength of about 20,000km and a speed of 1600km/hr in the equilibrium situation. Tides are measured with tide guages. In order for this to happen, the depth of the ocean would have to be 22km. We know the average depth is slightly less than 3.9km. This means these waves travel slightly less than 700km/hr (much slower than the rotation of the earth). In addition the continents interrupt the free movement of the tide waves. These factors cause the tide waves to break up into a number of cells.

In the open ocean the crests and troughs of these cells rotate as a standing wave around a point in the center called an amphidromic point ("running around"). Each amphidromic point is analgous to the node of a standing wave and has cotidal and corange lines associated with it to predict time and heights of tides. Once a tide wave rotates into a cell, the direction of rotation is to the right in the northern hemisphere. Because of the interaction of tides and land masses, the amphidromic points in the ocean are complex.

Types of tides - diurnal - one high and one low; common in the Gulf of Mexico; tidal period of 24hr 50min. Semidiurnal - two highs and two lows, with high approximately equal and lows approximately equal; common along the Atlantic coast of the US; tidal period approximately 12hr 25min. Mixed tides generally have two highs and two lows, but their heights are noticeably unequal; the period is 12hr 25min; the will become diurnal for a day or two during the month; most common throughout the world.

These complexities are due to the fact that there are seven components involved in producing the observed tides. In certain areas there are extreme tides due to basin topography and resonance. One such area is the Bay of Fundy where tides are about 17m. In some rivers, tidal bores are produced.

ENERGY EXTRACTION

OTEC -ocean thermal energy conversion - utilizes the thermocline to vaporize a low boilong point liquid to turn a turbine and condense it with cold water from below the thermocline.

Power from waves - projects have been tried, but no commercial production yet

Power from tides (2362) - only certain locations promising; only produces power during certain times of the tidal cycle which will change each day