27 October 2007 MAR110_Lec22_standing Waves_tides_27oct07.doc 1 MAR 110 LECTURE #22 Standing Waves and Tides Coastal Zone Beach Profile Figure 22.1 Beach Profile Summer Onshore Sand Transport Breaking Swell Currents Erode Bar Sand. & Build the Summer Berm Figure 22.2 Beach Evolution Summer Onshore Transport
27 October 2007 MAR110_Lec22_standing Waves_tides_27oct07.doc 2 Winter Offshore Sand Transport Winter Storm Wave Currents Erode Beach Sand. to form sandbars Figure 22.3 Beach Evolution Winter Offshore Transport No Net Motion or Energy Propagation Figure 22.4 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. (??)
27 October 2007 MAR110_Lec22_standing Waves_tides_27oct07.doc 3 Standing Waves and a Bathtub Seiche Figure 22.5 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. (??,??) Standing Wave or Seiche Period l Figure 22.6 Seiche Period 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)
27 October 2007 MAR110_Lec22_standing Waves_tides_27oct07.doc 4 Standing Waves & Bay Tides l Figure 22.7 Bay Tides and their Period 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 22.8 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)
27 October 2007 MAR110_Lec22_standing Waves_tides_27oct07.doc 5 TIDES Twice-a-Day & Once-A-Day Forced LONG Waves Figure 22.9 Tides Are Waves Tidal wave energy is concentrated at periods of approximately 12 and 24 hours. (ItO) Semidiurnal Tide twice-a-lunar day OBSERVED Tides Sea Level Records Diurnal Tide once-a-lunar day Figure 22.10 Observed 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)
27 October 2007 MAR110_Lec22_standing Waves_tides_27oct07.doc 6 Equilibrium Tide Diurnal + Semidiurnal Mixed Figure 22.11 Equilibrium Tides An observer on the Earth rotates beneath a stationary double oceanic sea level bulge. An observer at the equator observes two high tides of different height each lunar day, as indicated in the time chart to the right. (ItO, LEiO) Spring - Neap Tides Figure 22.12 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. (??)
27 October 2007 MAR110_Lec22_standing Waves_tides_27oct07.doc 7 Figure 22.13 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 B A Figure 22.14 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)
27 October 2007 MAR110_Lec22_standing Waves_tides_27oct07.doc 8 Rotary Standing TIDAL Wave Figure 22.15 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 22.16 The Atlantic Ocean Amphidromic System The North Atlantic tidal system closely resembles an ideal amphidromic system with some deviation due to bathymetry. (ItO)
27 October 2007 MAR110_Lec22_standing Waves_tides_27oct07.doc 9 North Atlantic Tides DRIVE Bay of Fundy Tides Figure 22.17 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)