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MAR 110 LECTURE #22 Standing Waves and Tides 23 October 2007 MAR110_Lec22_tides_23oct07.doc 1 MAR 110 LECTURE #22 Standing Waves and Tides No Net Motion or Energy Propagation Figure 22.1 Wave Reflection and Standing Waves A standing wave does not travel or propagate but merely oscillates up and down with stationary nodes (with no vertical movement) and antinodes (with the maximum possible movement) that oscillates between the crest and the trough. A standing wave occurs when the wave hits a barrier such as a seawall exactly at either the wave’s crest or trough, causing the reflected wave to be a mirror image of the original. (??) Standing Waves and a Bathtub Seiche Figure 22.2 Standing Waves Standing waves can also occur in an enclosed basin such as a bathtub. In such a case, at the center of the basin there is no vertical movement and the location of this node does not change while at either end is the maximum vertical oscillation of the water. This type of waves is also known as a seiche and occurs in harbors and in large enclosed bodies of water such as the Great Lakes. (??, ??) 23 October 2007 MAR110_Lec22_tides_23oct07.doc 2 Standing Wave or Seiche Period l Figure 22.3 The wavelength of a standing wave is equal to twice the length of the basin it is in, which along with the depth (d) of the water within the basin, determines the period (T) of the wave. (ItO) Standing Waves & Bay Tides l Figure 22.4 Another type of standing wave occurs in an open basin that has a length (l) one quarter that of the wave in this case, usually a tide. In this case the node is at the inlet of the basin with the antinode at the closed end. The most commonly used example of this type of standing wave is the Bay of Fundy. (ItO) Figure 22.5 Bay of Fundy and Tidal Bores In regions with significant tides such as the Bay of Fundy it is not unusual for a tidal bore to form which is a wave or wall of water at the leading edge of the tide wave (right), particularly in rivers or narrow bays and passages. The tidal bore will continue upstream into the bay or river sometimes for a hundred miles or more (ex: the Yellow River in China). Since this wave or wall of water has the mass of the tide behind it, people can use it to push surfers or even boats upstream for long distances. (??, ItO, LEiO) 23 October 2007 MAR110_Lec22_tides_23oct07.doc 3 TIDES Twice-a-Day & Once-A-Day Forced LONG Waves Figure 22.6 Tides Tidal wave energy is concentrated at periods of approximately 12 and 24 hours. (ItO) OBSERVED Tides Semidiurnal Tide OBSERVED Tides twice-a-lunar day Sea Level Records Diurnal Tide once-a-lunar day Figure 22.7 Real Ocean Tides Sea level records from different locations reveal tides that are dominated by the twice-a-day or semidiurnal tide (top) ofr the once-a-day or diurnal tide (bottom). A mixture of the two period tides is more common. (LEiO) 23 October 2007 MAR110_Lec22_tides_23oct07.doc 4 Equilibrium Tidal Ocean CONDITIONS 1. Uniform Depth = 25km 2. No Continents 3. Sea Level “in Equilibrium” with Astronomical Forcing …..AT ALL TIMES! The tidal wave can “follow the forcing” Figure 22.8 Equilibrium Tidal Forcing The theoretical equilibrium tidal ocean covers the whole Earth deeply enough so that the shallow water tidal waves can follow astronomical forcing as the Earth rotates below. Basic Astronomical Dynamics is governed by Gravitational Attraction What if ….? the Earth were the size of the moon…then? Gravitational Attraction Figure 22.9 Gravitational Attraction A “body force” that draws mass together. (ItO) 23 October 2007 MAR110_Lec22_tides_23oct07.doc 5 Basic Astronomical Dynamics The “moon”- Moon system rotates to keep from “crashing together” Rotation Center Centrifugal Force Centrifugal Force balances balances Gravitational Gravitational Attraction Attraction Figure 22.10 Basic Dynamic Balance The centrifugal “force” of circular motion balances the gravitational attraction; so that our two “moons” do not crash into each other. (ItO) Basic Earth-Moon Dynamics The center of rotation is imbedded in the MASSIVE Earth Centrifugal Force Centrifugal Force balances balances Gravitational Gravitational Attraction Attraction ..and keeps the moon in “orbit” Figure 22.11 The Earth-Moon Dynamic The Earth is so massive that the center of Earth-Moon system rotation is located within the Earth. (ItO) 23 October 2007 MAR110_Lec22_tides_23oct07.doc 6 Tide-Producing Forces Double Bulge <= + Figure 22.12 Earth-moon System: Tide–Producing Forces The Moon’s gravitational attraction creates a stationary oceanic bulge on the side of the Earth facing the Moon. The centrifugal “force” due to the spinning of the System produces the oceanic bulge on the side of the Earth facing away from the Moon (ItO) Equilibrium Tide – Twice-a-day – Semidiurnal Figure 22.13 Twice-a-Day or Semidiurnal Tide An observer on the Earth rotates beneath a stationary double oceanic sea level bulge. An observer at the equator observes two high tides each lunar day, as indicated in the time chart to the right. (ItO, LEiO) 23 October 2007 MAR110_Lec22_tides_23oct07.doc 7 Equilibrium Tide – Once-a-day – Diurnal Figure 22.14 Once-a-Day or Diurnal Tide An Earth observer (the stick figure) standing on the Earth at a very high latitude observes a high tide once-a-day as indicated in the time chart below. (??) Spring - Neap Tides Figure 22.15 Spring – Neap Tides About every 14 days the range of the tidal sea levels cycles through a maximum called spring tides and a minimum called neap tides – as indicated by the sea level record to the left. This phenomena occurs because the sun and the moon each produce separate double oceanic sea level bulges, with the sun’s being about ½ that of the moon, as illustrated to the right. During spring tides (a time of full or new moon), the solar and lunar double bulges add to each other to produce the largest tidal ranges. During neap tides ( a time of half moon), the solar and lunar tidal bulges subtract from one another. In short, the spring neap cycle in tidal range arises from the constructive and then destructive interference of the solar and lunar tidal sea levels. (??) 23 October 2007 MAR110_Lec22_tides_23oct07.doc 8 Figure 22.16 Realistic Ocean Tides On the real Earth oceans are contained in basins bounded by the continents; not covered by the ocean. Thus the astronomical tidal forcing creates a standing tidal wave in our idealized ocean basin that is meant to model the Atlantic Ocean. (ItO) Rotary Standing TIDAL Wave A B Figure 22.17 Rotary Standing Wave in an Enclosed Basin The tidal waves in our idealized enclosed ocean basins are the rotary standing waves as illustrated above because of the effects of Earth rotation. Note how the sea level highs (and lows) rotate around a node in the center of the idealized basin – a point of no tide or amphidromic point in what is called an amphidromic system. (ItO) 23 October 2007 MAR110_Lec22_tides_23oct07.doc 9 Rotary Standing TIDAL Wave Figure 22.18 Cotidal Chart of an Amphidromic System The tidal action ina an amphidromic system can be neatly summarized in a cotidal chart, which looks like a wagon-wheel. Cotidal lines (the spokes) mark the location of high tide at each lunar hour during the tidal cycle. The corange lines (the circular wheel rim) mark the locations with the same tidal ranges. (ItO) North Atlantic Tides- similar patterns Figure 22.19 The Atlantic Ocean Amphidromic System The North Atlantic tidal system closely resembles an ideal amphidromic system with some deviation due to bathymetry. (ItO) 23 October 2007 MAR110_Lec22_tides_23oct07.doc 10 North Atlantic Tides DRIVE Bay of Fundy Tides Figure 22.20 Gulf of Maine/Bay of Fundy Tides The North Atlantic tidal excursions at the mouth of the Gulf of Maine (rather than direct astronomical forcing) drive the large tides in the Gulf of Maine/Bay of Fundy system, with the largest tidal ranges at the head of the Bay of Fundy. (ItO) Semidiurnal Tide Figure 22.21 (??) 23 October 2007 MAR110_Lec22_tides_23oct07.doc 11 Figure 22.22 (??) Equilibrium Tide – Diurnal + Semidiurnal – Mixed Figure 22.23 (ItO) .
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