ZGT 372 Introduction to Oceanography Tides PDF

ZGT 372 Introduction to Oceanography Tides Prepared by: Syarawi Sharoni SyarawiSharoni2024 1 Aim & Learning Outcome To understand the equilibrium theory of tides. To understand the dynamic theory of tides. To understand sev...

ZGT 372 Introduction to Oceanography Tides Prepared by: Syarawi Sharoni SyarawiSharoni2024 1 Aim & Learning Outcome To understand the equilibrium theory of tides. To understand the dynamic theory of tides. To understand several important effects of tides. SyarawiSharoni2024 2 A) Tides As Ocean Waves SyarawiSharoni2024 3 A) Tides As Ocean Waves 1) Introduction Tides are periodic and 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 sun, the motion of Earth, and the inertia of water. With a wavelength that can equal half of Earth’s circumference, tides are the longest of all waves. These huge shallow-water waves are never free of the forces that cause them and thus are called forced waves. The pull of gravity between two bodies is proportional to the masses of the bodies but inversely proportional to the square of the distance between them. The forces that actually generate the tides vary inversely with the cube of the distance from Earth’s center to the center of the tide-generating object (the moon or sun). The sun is about 27 million times as massive as the moon, but the sun is about 387 times as far away as the moon, so the sun’s influence on the tides is only 46% that of the moon’s. SyarawiSharoni2024 4 A) Tides As Ocean Waves 2) Tides Theory There are two dominant theories of tides. 1. Equilibrium Theory Deals primarily with the position and force attraction of Earth, moon, and sun. Does not factor in the influence of ocean depth or the positions of continental landmasses. The equilibrium theory would accurately describe tides on a planet uniformly covered by water. 2. Dynamic Theory Takes into account the speed of the long-wavelength tide wave in relatively shallow water, the presence of interfering continents, and the circular movement or rhythmic back-and-forth rocking of water in ocean basins. SyarawiSharoni2024 5 B) Equilibrium Theory of Tides SyarawiSharoni2024 6 B) Equilibrium Theory of Tides 1) Basic Principle Tidal potential is derived from the gravitational attraction of masses of the moon and the sun. The equilibrium theory explains ocean tides by examining the balance and effects of the forces that allow a planet to stay in a stable orbit around the sun, or the moon to orbit Earth. The assumptions; i. The seafloor does not influence the tides. ii. The ocean conforms instantly to the forces that effect the position of its surface. iii. The ocean surface is presumed always to be in equilibrium (balance) with the forces acting on it. SyarawiSharoni2024 7 B) Equilibrium Theory of Tides 2) Gravitational Force and Inertia First, look at the moon’s effect on ocean surface. Earth and the moon don’t smash into each other (or fly apart) because they are in a stable orbit; their mutual gravitational attraction is exactly offset by their inertia (centrifugal force). Earth–moon system revolves once a month (27.3 days) around the system’s center of mass, located 1,650 kilometers inside Earth. The moon’s gravity attracts the ocean surface toward the moon. Earth’s motion around the center of mass of the Earth– moon system throws up another bulge on the opposite side of Earth. Two tides bulges result. SyarawiSharoni2024 8 B) Equilibrium Theory of Tides Four places on Earth’s surface are marked with numbers 1 through 3) Tractive Forces 4. Each place has three arrows drawn to represent forces: the outward-flinging force of inertia is shown in blue, and the inward- pulling force of gravity is shown in brown. Combined, they are called tractive forces, red arrows. Tractive forces is the net force of inertia and gravitational attractions. Points 1 and 2 are closer to the moon, so gravitational attraction at those points slightly exceeds the outward-moving tendency of inertia. Water there tends to be attracted toward the moon so is pulled along the ocean surface toward a SyarawiSharoni2024 spot beneath the moon. 9  At points 3 and 4 , slightly farther B) Equilibrium Theory of Tides from the moon, inertia exceeds 3) Tractive Forces (cont.) gravitational attraction. Water at those points tends to be flung away from the moon so moves along the ocean surface toward a spot opposite the moon. Together, the tractive forces cause the two small bulges in the ocean, one in the direction of the moon, the other in the opposite direction Note that there is no point on Earth’s surface where the force of the moon’s gravity exactly equals the outward-moving tendency of inertia. Only at point CE—the center of Earth—are the inward pull of gravity and the outward-moving tendency of inertia exactly equal SyarawiSharoni2024 and opposite. 10 B) Equilibrium Theory of Tides 4) Rhythm of Tides In the idealized equilibrium model, the bulges tend to stay aligned with the moon as Earth spins around its axis. As Earth rotates eastward beneath the bulges, an island on the equator is seen to move in and out of these bulges through one rotation (1 day). The bulges are the crests of the planet-sized waves that cause high tides. Low tides correspond to the troughs, the area between bulges. Theoretically, the wavelength of these tide waves is as long as 20,000 kilometers! The bulges tend to stay aligned with the moon as Earth spins around its axis. The key to understanding the equilibrium theory of tides is to see Earth turning beneath these SyarawiSharoni2024 bulges. 11 B) Equilibrium Theory of Tides 5) Lunar Tides Complications The moon have unique orbital specifications that modified the gravitational and inertial interaction of the moon and Earth. 1. Longer Tidal Day A complete tidal day is 24 hours 50 minutes long, because the moon, moves through about 1⁄27 of its orbit in a day. Thus, the highest tide also arrives 50 minutes later each day at the same location. 2. Equator Offset The moon does not stay right over the equator; each 𝟏 month, it moves from a position as high as 28𝟐° 𝟏 above Earth’s equator to 28 ° below. When the 𝟐 moon is above the equator, the bulges 1 are offset accordingly. When the moon is 282° north of the equator, an island north of the equator will pass through the bulge on one side of Earth but miss the bulge on the other side. SyarawiSharoni2024 12 B) Equilibrium Theory of Tides 6) Solar Tides Solar tides caused by the gravitational and inertial interaction of the sun and Earth. The sun’s influence on the tides is only 46% that of the moon’s. The sun’s tractive forces develop in the same way as the moon’s, and the smaller solar bulges tend to follow the sun through the day. Like the moon, the sun also appears 𝟏 to move 𝟏 above and below the equator (𝟐𝟑 °N to 𝟐𝟑 °S), so the position of the solar bulges 𝟐varies like 𝟐that of the lunar bulges. Earth revolves around the sun only once a year, however, so the position of the solar bulges above or below the equator changes much more slowly than the position of the lunar bulges. SyarawiSharoni2024 13 B) Equilibrium Theory of Tides 7) Astronomical Tides Tides caused by the simultaneous response of inertia and the gravitational force from the sun and moon combined are called astronomical tides. Spring Tide = If Earth, moon, and sun are all in linear alignment, the lunar and solar tides will be additive, resulting in higher high tides and lower low tides. Neap Tide = If the moon, Earth, and sun form a right angle, the solar tide will tend to diminish the lunar tide, resulting high tides are not very high and low tides not very low. Because the moon’s contribution is more than twice that of the sun, the solar tide will not completely cancel the lunar tide. Both tides occur alternately at 1 week interval SyarawiSharoni2024 14 corresponding to the moon phase. B) Equilibrium Theory of Tides 7) Astronomical Tides (cont.) Because Sun’s and Moon’s orbits are ellipses, they are closer to Earth at some times than at others. The difference between apogee (the moon’s greatest distance from Earth) and perigee (its closest approach) is 30,600 kilometers. Because the tidal force is inversely proportional to the cube of the distance between the bodies, the closer moon raises a noticeably higher tidal crest. The difference between aphelion (Earth’s greatest distance from the sun) and perihelion (its closest approach) is 3.7 million kilometers. If the moon and sun are over nearly the same latitude, and if Earth is also close to the sun, extreme spring tides will result. SyarawiSharoni2024 15 B) Equilibrium Theory of Tides 8) Tidal Frequency As earth to spin about its polar axis. The frequency of changing tidal potential at a fixed geographic coordinate on earth is calculated. The period of the solar hour angle is a solar day of 24 hr 0 m. The period of the lunar hour angle is a lunar day of 24 hr 50.47 m. Earth’s axis of rotation is inclined 23.45◦ this defines the ecliptic Earth orbiting sun varies between δ = ±23.45◦ with a period of one solar year. Moon’s orbit is also elliptical, but a description of moon’s orbit is much more complicated. The moon’s orbit lies in a plane inclined at a mean angle of 5.15◦ relative to the plane of the ecliptic. And lunar declination varies between δ = 23.45 ± 5.15◦ with a period of one tropical month of 27.32 solar days. SyarawiSharoni2024 16 C) Dynamic Theory of Tides SyarawiSharoni2024 17 C) Dynamic Theory of Tides 1) Newton Incomplete Explanation Newton knew his explanation was incomplete. The maximum theoretical range of a lunar tidal bulge is only 55 cm and of a solar tide is only 24 cm, both considerably smaller than the observed 2-meter average tidal range. The reason is that the ocean surface never comes completely to the equilibrium position at any instant. Remember that tides are a form of wave. In Equilibrium model, tides bulge appear to move across the idealized water-covered Earth at a speed of about 1,600 km/h. For a tidal crest to move at 1,600 km/h, the ocean would have to be 22 km deep. But the average depth of the ocean is only 3.8 km. SyarawiSharoni2024 18 C) Dynamic Theory of Tides 2) Tidal Patterns As Earth turns, landmasses obstruct the tidal crests, diverting, slowing, and otherwise complicating their movements. This interference produces different patterns in the arrival of tidal crests at different places. The shape of the basin itself has a strong influence on the patterns and heights of tides. Water in large basins can rock rhythmically back and forth in seiches. For these and other reasons, some coastlines experience; Semidiurnal (twice daily) tides: two high tides and two low tides of nearly equal level each lunar day. Diurnal (daily) tides: one high and one low. Mixed (or semidiurnal mixed) if successive high tides or low tides are of significantly different heights throughout the cycle. This pattern is caused by blending diurnal and semidiurnal tides. SyarawiSharoni2024 19 C) Dynamic Theory of Tides 3) Amphidromic Points As water moves north in a Northern Hemisphere ocean, it moves toward the eastern boundary of the basin; as it moves south, it moves toward the western boundary. A wave crest moving counterclockwise will develop around a node if this motion continues to be stimulated by tidal forces. The node near the center of an ocean basin is called an amphidromic point. The colors indicate where tides are most extreme An amphidromic point is a no-tide point (crests and troughs (highest highs, lowest lows), with blues being least extreme. White lines radiating from the cancel each other), around which the tidal crest rotates points indicate tide waves moving around these through one tidal cycle. points. Blue, indicating little or no apparent tide. These convergent areas are called amphidromic points. Tide waves move around these points. Because of the shape and placement of landmasses around ocean basins, the tidal crests and troughs cancel each other at these points. Due to Coriolis effect, tides move counterclockwise around the amphidromic point in the Northern Hemisphere and clockwise in the Southern Hemisphere. The height of the tides increases with distance from an amphidromic point. Crest radiates toward distant shores. SyarawiSharoni2024 20 C) Dynamic Theory of Tides 4) Tidal Datum The reference level to which tidal height is compared is called the tidal datum. The tidal datum is the zero point (0.0) seen in tide graphs. This reference plane is not always set at mean sea level, which is the height of the ocean surface averaged over a few years’ time. On coasts with mixed tides, the zero tide level is the average level of the lower of the two daily low tides (mean lower low water, or MLLW). On coasts with diurnal and semidiurnal tides, the zero tide level is the average level of all low tides (mean low water, MLW). SyarawiSharoni2024 21 C) Dynamic Theory of Tides 5) The Influence of Ocean Basin Shape The tidal range varies with basin configuration. The tidal range is not the same over a whole ocean basin, it varies from the coasts to the centers of oceans. The largest tidal ranges occur at the edges of the largest ocean basins. If a basin is wide and symmetrical, a miniature amphidromic system develops that resembles the large systems of the open ocean. If the basin is narrow and restricted, the tide wave crest cannot rotate around an amphidromic point and simply moves into and out of the bay. SyarawiSharoni2024 22 C) Dynamic Theory of Tides 5) The Influence of Ocean Basin Shape (cont.) SyarawiSharoni2024 23 C) Dynamic Theory of Tides 6) Tidal Bore / Tidal Wave If conditions are ideal, a tidal bore will form in some river inlets, exposed to great tidal fluctuation. Here, is a true tidal wave—a steep wave moving upstream generated by the action of the tide crest in the enclosed area of a river mouth. The confining river mouth forces the tide wave to move toward land at a speed that exceeds the theoretical shallow-water wave speed for that depth. Their potential danger is lessened by their predictability. SyarawiSharoni2024 24 C) Dynamic Theory of Tides 7) Tidal Current The rise or fall in sea level as a tide crest approaches and passes will cause a tidal current of water to flow into or out of bays and harbors. Flood Current = Water rushing into an enclosed area because of the rise in sea level as a tide crest approaches. Ebb Current = Water rushing out because of the fall in sea level as the tide trough approaches. Tidal currents reach maximum velocity midway between high tide and low tide. Slack Water = a time of no currents, occurs at high and low tides when the current changes direction. SyarawiSharoni2024 25 C) Dynamic Theory of Tides 8) Tidal Constituents There are many components (or constituents) that make up the total tides, characterize by their amplitude, phase, and period. The main lunar tide has a period of 12.42 h and the main solar tide a period of 12 h respectively. These tidal constituents (or tidal components) are called M2 and S2. The influence of the sun is characterized by the letter S, the influence of the moon by the letter M. The index 2 refers to phenomena that occur twice daily. The amplitudes and phases of these two constituents vary with the location at the earth. SyarawiSharoni2024 26 C) Dynamic Theory of Tides 8) Tidal Constituents (cont.) Constituents: One of the harmonic elements in a mathematical expression for the tide- producing force in corresponding formulas for the tide or tidal current. Each constituent represents a periodic change or variation in the relative position of the Earth, moon, and sun. Amplitude: One-half the range of a constituent tide, may be applied also to the maximum speed of a constituent current. Phase: Phase lag, may be expressed in angular measure as 360 degree. Period: Time between two consecutive like phase of the tide or tidal current. SyarawiSharoni2024 27 C) Dynamic Theory of Tides 8) Tidal Constituents (cont.) SyarawiSharoni2024 28 C) Dynamic Theory of Tides 9) Tidal Prediction If tides in the ocean were in equilibrium with the tidal potential, tidal prediction would be much easier. Unfortunately, tides are far from equilibrium. The shallow-water wave which is the tide cannot move fast enough to keep up with sun and moon. Therefore it is very complicated to predict the tide. We can separate the problem of tidal prediction into two parts; First deals with the prediction of tides at shallow water (ports, beach); Second at deep ocean. SyarawiSharoni2024 29 C) Dynamic Theory of Tides 9) Tidal Prediction – Shallow Water Tides in ports and shallow water can be measured by tide gauges. Two methods are used to predict tides at shallow water; Harmonic Method: Typically uses >19 years of data from a coastal tide gauge from which the amplitude and phase of each tidal constituent (the tidal harmonics) in the tide-gage record are calculated. Response Method: Calculates the relationship between the observed tide at some point and the tidal potential. SyarawiSharoni2024 30 C) Dynamic Theory of Tides 9) Tidal Prediction – Deep Ocean Tides in deep ocean can be measured by satellite altimeter. The satellite was placed into an orbit especially designed for observing ocean tides, and the altimetric system was sufficiently accurate to measure many tidal constituents. Hydrodynamic Theory: Purely theoretical calculations of tides that are not very accurate because the dissipation of tidal energy is not well known. Altimeter + Response Method: Several years of satellite altimeter data have been used with the response method to calculate deep-sea tides. Altimeter + Numerical Method: Altimeter data can be used directly with numerical models of the tides to calculate tides in all areas of the ocean from deep water all the way to theSyarawiSharoni2024 31 coast. C) Dynamic Theory of Tides 9) Tidal Prediction – Deviation Atmospheric forcing can influence the observed sea level especially near the shore. Storm surge, due to low atmospheric pressure can have a positive bulge on local sea level. Strong wind, seiches, can also change the level of local sea level. SyarawiSharoni2024 32 D) Several Effects of Tides SyarawiSharoni2024 33 D) Several Effects of Tides 1) Planetary Effects Tides dissipate 3.75 ± 0.08 TW of power, of which 3.5 TW are dissipated in the ocean, and much smaller amounts in the atmosphere and solid earth. The dissipation increases the length of day by about 2.07 milliseconds per century. The tidal have some known effects at a planetary scale. 1) Slowing Earth’s Rotation The daily rise and fall of the tides consumes a very large amount of energy, comes directly from the rotation of Earth, and dissipated as heat. Tidal friction is gradually slowing Earth’s rotation by a few hundredths of a second per century. Evidence suggests that 350 million years ago, a year contained between 400 and 410 days, with each day being about 22 hours long; and 280 million years ago, there were about 390 days in a year, each about 22 1⁄2 hours long. 2) Synchronous Tidal Locking Tidal friction affects other bodies. Tidal forces have locked the rotation of the moon to that of Earth. As a result, the same side of the moon is always facing Earth, and a day on the moon is a month long.SyarawiSharoni2024 34 D) Several Effects of Tides 2) Marine Organism Organisms that live between the high-tide and low-tide marks experience very different conditions from those that reside below the low-tide line. Within the intertidal zone itself, organisms are exposed to varying amounts of emergence and submergence. The animals and plants sort themselves into three or more horizontal bands, or subzones (supratidal, intertidal, subtidal zones). Each distinct zone is an aggregation of animals and plants best adapted to the conditions within that particular narrow habitat. SyarawiSharoni2024 35 D) Several Effects of Tides 3) Power Extraction Taking advantage of trapped high-tide water to generate electricity can be potential alternative to our growing dependence on fossil fuels. Tidal power is the only marine energy source that has been successfully exploited on a large scale. At high tide, seawater flows from the ocean through the generators into the estuary. At low tide, the seawater and river water from the estuary flow out through the same generators. Power is generated in both directions. Another way to generate tidal power is through turbines that submerged in the open water. SyarawiSharoni2024 36 Exercise Time! Put your short name in ‘Subject’ section. Section 11 – Tides Q1: What is the basic principle and assumptions hold in the equilibrium theory of tides? Q2: What are the advancement of dynamic theory of tides as compared to the equilibrium theory? Q3: What is tidal constituent? How the observed tides can be different from its prediction? SyarawiSharoni2024 37 Important Concepts 1. Tides are periodic short-term changes in ocean surface height. Tides are forced waves formed by gravity and inertia. 2. The equilibrium theory of tides explains tides by examining the balance of and effect of forces that allow our planet to stay in orbit around the sun, or the moon to orbit Earth. Because of its nearness to Earth, our moon has a greater influence on tides than the sun. 3. The dynamic theory of tides takes into account the tide-wave properties, seabed contour, basin shapes and tide-wave inertia. 4. Together, the equilibrium and dynamic theories allow tides to be predicted years in advance. 5. Tides can have a planetary effect, influence marine organism activity, and extracting power. SyarawiSharoni2024 38