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The text book reading assignment that corresponds with this pwr pt is Trujillo and Thurman chapter 8 pp

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4 TIDAL PHENOMENA

5 tides and tidal phenomena are studied because : tides are the regular rise and fall of sea level on a daily basis this variation is caused by extremely long wavelength and period waves safe coastal navigation requires know- ledge of the tide stage and flow dispersion/aggregation of shore-line materials are affected by tides flooding can be enhanced or reduced by tide range and phase large tide ranges can be used to run generators and supply power

6 The longest oceanic waves are those associated with tides. A tide is observed as a rhythmic rise and fall of sea level over a period of several hours.

7 Diurnal Tides fluctuations are largely due to the changes in the Moon’s declination (angle from the celestial equator) Semidiurnal Tides fluctuations are due to the relative positions of the Sun and Moon Mixed Semidiurnal Tides the most commonly seen waveform reflecting local basin geometry and the moon’s declination Types of Observed Tides

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9 There are two kinds of tide-generating forces: gravitational attraction between masses and centripetal force, a center-seeking force, that is related to earth’s circular motion The EQUIIBRIUM THEORY was developed by Isaac Newton with several assumptions: the tide-generating forces are everywhere in balance; the earth is completely covered by an ocean that is extremely deep; progressive tide waves propagate without any continental boundaries or friction against the bottom Newton’s theory predicts two opposed tidal bulges and explains spring and neap tides twice a month … it does not predict the times that tides occur nor tide phases nor different kinds of tides. How is the balance struck ?

10 Isaac Newton’s law of universal gravitation quantizes the forces between the Earth, moon and sun in terms of their masses and the distances between them. A gravitational force that exists between any two masses depends on the product of their masses and, further, is inversely proportional to the square of the distance between them. We know what such a force is like but not why it is there. Each of these gravitational forces results in a deformation of the hydrosphere by generating individual bulges directed along a line between the respective masses. Superposition of the individual bulges forms an overall tidal bulge. The earth’s tidal bulge has a resultant extension toward the moon because of the relatively short distance between earth and moon and its effect on the the relative size of the earth-moon and earth-sum forces. There is another bulge on the opposite side of the Earth that is often described in terms of a centrifugal force related to the rotation of the Earth-Moon system about its center of mass. No working physicist would use such a force concept but invoking such does make it easier for most of us understand the tidal bulges. One can accept and go on with 251 impunity.

11 Centrifugal force Tide-producing force Gravitational force due to Moon the centrifugal force [thin white vector] within earth and moon system balances the forces of gravitational attraction [blue vector ] between earth and moon the resultant of centrifugal and gravitational forces is known as the tide-producing force [thick white vector] there is a force known as the tractive force; it is a component of the tide-producing force along the sea surface : the tractive force is the one that makes the water move. To moon

12 tractive forces that raise the tidal bulges

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16 An Explanation of Spring and Neap Tides

17 An Explanation of the Different Types of Tides : diurnal, mixed, and semi-diurnal

18 tide observations can be explained by mathematically combining amplitudes and phases of harmonic tidal components

19 One process of mathematically disassem-bling waves into their components and using them identify related physical phenom-ena is known as Fourier Analysis. That is, Fourier when the basic components are assumed to be sinusoidal ones that are called fundamental and/or harmonic waves. The composite [left,bottom graph] is very close to an actual recorded wave form. Notice that their are components identified with moon and sun forcing that give rise to both semi- and diurnal wave forms. There are as many as 65 different components that can be used to generate a composite tide prediction.

20 The dynamic theory of astronomical tides considers the motion of the waves over ocean basins under the influence of bottom topography, earth’s rotation, and blocking effects of continents on propagation. The model forms a wave that rotates counter-clockwise in the northern hemisphere around a basin, once a day in a diurnal case and twice for semi-diurnal. In a time sequence, a high tide at the western edge of a basin creates a pressure gradient sloping down and away to the east. A geostrophic analysis of this gradi- ent yields a current that moves water toward the equator. At the equator, waters gather, a pressure gradient sloping downward to the north supports the notion of geostrophic flow eastward and so on, until the basin has been boxed. This semi-circular motion naturally defines an inner location around which the wave turns and at which there is no tide elevation or motion; it is known as an amphidromic point, normally one per geographic basin. From each of these points, lines that define the position of any phase of the wave emanate in a wavy fashion that indicates the influence of the bottom topography on the speed of the wave’s propagation.

21 world ocean tidal amphidromic points and cotidal lines

22 a simple model of a rotating dynamic tide model; consider the left and right sides of the rectangular flat bottom basin as the North American and European continents

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24 examples of cotidal and corange lines for two models and corresponding actual basins

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26 Hurricane Celia track July-August 1970

27 Hurricane Celia winds and pressure

28 Hurricane Celia High Water Profile

29 Hurricane Carla’s Galveston Sea Level Record

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