Tides. 1. The dynamic theory of tides. The equilibrium theory is of limited practical value, even though certain of its predictions are correct:

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1 Tides 1. The dynamic theory of tides 2. Amphidromic systems and shallow water effects 3. Predicting tides by the harmonic method 4. Real tides 5. Tidal currents. 6. Tidal power (and energy) 1. The dynamic theory of tides The equilibrium theory is of limited practical value, even though certain of its predictions are correct: i. The spring tides will occur in full and new moon; ii. There are (in some places)two high waters and two lows per day; iii. The tidal (daily) inequality is related to the declination of the moon. 1

2 However there are a number of reasons why tides do not behave as equilibrium tides: i. The inertia of the water masses; ii. The Earth is not covered by water uniformely. The presence of the land masses prevents the tidal bulges from directely circumnavigating the globe. Only in the southern ocean surrounding Antartica can happen; iii. The Coriolis force (the geostrophic effects...). Due to rotating Earth the flow of the water due to the tide is deflected. iv. Frictional forces betwen the bottom of the ocean and the water masses. The dynamic theory uses the same tide-producing force but accounts for all the complicating factors: i. Depths and configuration of the ocean bassins; ii. The Coriolis Force; iii. Inertia of the water masses iv. Frictional forces (bottom...) We talk now about tidal waves and not about tidal bulges as in the equilibrium theory. These waves are produced by the same tideproducing forces so they will have the same periodicity. 2

3 2. Amphidromic systems and shallow water effects From the greek: Amphi: around Dromas: running The water will oscilate in the oceans that will act as bassins. We can think of a forced oscillation due to the tide-producing force in the bassins. Let us see a simple explanation! If the shape of the bassin is appropriate the osccilation will increse and a resonant condition exist. 3

4 The central point is called the amphidromic point 4

5 Co-tidal lines Co-range lines 5

6 The range of tides in the mid-ocean is small. However when the tidal wave invades the comparatively shallow waters of the continental shelf, the height is increased, especially within gulfs and embayments on the coast. Tides can be classified as Micro, Meso and Macrotidal Note: The virtually land locked seas sach as the Mediterrenean, Black, Red and Baltic seas are microtidal! 6

7 3. Prediction of the tides by the harmonic method. The harmonic method is the pratical application of the dynamic theory of tides. It makes use of the knowledge that the observed tide is the sum of a number of harmonic components (sinusoids). Each component as a period defined by the periodic movements of the system Earth-Moon-Sun. 7

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9 4. Real tides. There are a great variety of tides around the world. The semi-diurnal tide predominates but other types are possible. The type of tyde can be classified acording to the factor (K 1 +O 1 )/(M 2 +S 2 ) 9

10 5. Tides and currents in shallow water. Tidal currents (horinzontal) typically reach speeds of 1 to 2 knots (0.5 to 1.0 m/s). Tidal currents have the same periodicities as the vertical oscillation of the tide (remenber the model of the bassin oscillating). In a restricted channel they will flow in opposite directions in flood and ebb. In wide estuaries and in the open sea they tend to follow an elliptic path. Tidal currents can transport sediments and cause erosion: coast of France, lagoon entrances... 10

11 6. Tidal power (and energy). Power can be generated by holding incoming and outgoing tides behind a dam, using the head of water so produce to drive turbines for electricity generation (as in conventional dams in rivers). A minimum tidal range is necessary for economical reasons. 11

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13 Another way to produce energy is two use directely the tidal current (the same ideia as in the wind). This is an emerging technology but with some problems to be solved. Can you think of some of them? Tagus estuary. Flow field in ebb close to mid t 13

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15 Traditional use of tidal energy: tidal mills! Tidal mill La Richardais (France) 15

16 Tidal Mill Birlot (France) Tidal Mill Grand Traouiaéros (France) 16

17 Tidal mill. Questions 1. What are the main reasons why tides do not behave as equilibrium tides? 2. What is the tiddal range on the amphidromic point? 3. What is the effect of the Coriolis force in creating amphidromic systems? 4. Give examples of places where the tide is microtidal. 5. How is the tide predicted using the harmonic method? 6. Stuying real tides one can find: semidiurnal; mixed predominately semidiurnal; mixed predominately diurnal and diurnal. How can we know in advance from the tidal constituents? 7. Tidal currents have the same periodicity of the vertical oscillation of the tide. True or false? 8. Power can be generated with tides. Explain how! 17