Chapter 11 – Tides. A tidal bore is formed when a tide arrives to an enclosed river mouth. This is a forced wave that breaks. . Tidal range can be very large .
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Chapter 11 – Tides A tidal bore is formed when a tide arrives to an enclosed river mouth. This is a forced wave that breaks. Tidal range can be very large
Tide - rhythmic oscillation of the ocean surface due to gravitational & centrifugal forces (‘inertia’) between the Earth, Moon and Sun. Tide Patterns - regular, cyclic patterns of low water-high water Tidal cycle – one low tide and one high tide consecutively diurnal tide - one low tide, one high tide a day; semidiurnal tide - high water-low water sequence twice a day; 2 high, 2 low, about the same level semidiurnal mixed tide - same as semidiurnal but 2 highs and 2 lows do not reach/drop to the same level; may be the result of a combination of tide types
diurnal tide semidiurnal tide semidiurnal mixed tide Tide Patterns - regular, cyclic patterns of low water-high water
Semidiurnal tides Diurnal tides Mixed tides d (ft) (m) Mixed tide, Los Angeles Diurnal tide, Mobile, Alabama Semidiurnal tide, Cape Cod 14 4 Higher high tide 10 3 High tide Lower high tide High tide 6 2 4 1 0 0 Lower low tide Higher low tide –4 –1 Low tide Low tide 0 6 12 18 24 30 0 6 12 18 24 30 36 42 48 0 6 12 18 24 30 36 42 48 36 42 48 a Time (hr) b Time (hr) c Time (hr) Most of the world’s ocean coasts have semidiurnal tides.
Flood Tide: tide wave is propagating (onto shore) onshore – water level is rising High Tide: water level reaches highest point Ebb Tide: tide is moving out to sea – water level is dropping Low Tide: water level reaches lowest point Slack tide: period when tide wave is reversing – low current velocity Water currents are generated by the tides, the speed of the incoming tide is about the same but in the opposite direction of the outgoing tide. Moving waters have to slow down and reverse, from flood to ebb and vice versa (slack tide). This is a good time for navigation through narrow places, particularly those characterized by strong tides (East River, for example).
Mean Tide Level = MTL - computed from measurements taken at a place over many years and averaging all water levels. Mean High-Water = MHW. Mean Low-Water = MLW. For mixed tides: Mean Higher High Water = MHHW Mean Lower Low Water = MLLW tidal range– difference between MHW and MLW (water level at high tide and water level at low tide)
Study of Tides • Equilibrium Tidal Theory - ideal approach to understand basic principles, assumes an earth covered with water • Assumptions: • 1: entire Earth surface covered in water • 2: infinitely deep basin (no shoaling) • 3: tidal bulge fixed relative to the moon • Dynamical Tidal Analysis - realistic approach, studying the tides as they occur on earth, accounts for modification due to landmasses, geometry of ocean basins, earth’s rotation. Tides are caused by the difference in gravitational forces resulting from the change of position of the Sun and the Moon relative to points on Earth * centrifugal (‘inertia’) and gravitational forces*
universal law of gravitation F= G m1 m2 / R2 G = universal gravitational constant m1, m2 = mass of bodies R = distance between centers of mass of bodies B & C = gravitational forces
1,650 km (1,023 mi) Earth’s mass is 81 times the mass of the moon Moon (81/82) r (1/82) r Average Earth–moon distance (r) Figures in textbook The moon’s gravity attracts the ocean toward it. The motion of Earth around the center of mass of the Earth – moon system throws up a bulge on the side of Earth opposite the moon. The combination of the two effects creates two tidal bulges.
(with figures 11.5 & 11.6 in textbook) The Tide Producing Force (difference between gravitational forces and centrifugal forces at the earth surface) is proportional to GM/R3
The Tidal Day = 24 hr 50 min Lunar Cycle: the Earth – Moon system has a period of 29.5 days Diurnal = 24 hr 50 min Semidiurnal = 12 hr 25 min
A (and B & C) = gravitational forces A’ (and B’ & C’) = centrifugal forces Add the Sun
The Sun Tide Spring & Neap Tides
Declination Tide Moon’s declination cycle 28.5N – 28.5S = 29.5 days Sun’s declination cycle 23.5N (summer solstice) – 23.5S (winter solstice) = annual
Orbital Influence on Tides Astronomical High Tide: Moon at perigee, Sun at perihelion, and Earth-Moon-Sun system at syzygy (full or new moon)
Dynamic Tidal Analysis A mathematical study of tides as they occur. It looks at the tide wave, which is similar to the tide wave of the ideal water covered earth, but varies from place to place. * Continents break up wave propagation * Tide wave moves continuously around the globe only in the Southern Ocean (Antarctica). * shallow-water wave: speed is controlled by depth of ocean * standing wave: oscillates because it is contained in ocean basins (wave ‘contained’ in ocean basin) * reflected by continents, refracted by changes in depth, and diffracted (spread of energy sideways) as it passes through gaps * Coriolis affects the water movement because it is a large scale phenomenon.
Amphidromic Point Amphidromic System Cotidal Lines
Tidal Patterns Center on Amphidromic Points The development of amphidromic circulation (a) A tide wave crest enters an ocean basin in the Northern Hemisphere. The wave trends to the right because of the Coriolis effect (b), causing a high tide on the basin’s eastern shore. Unable to continue turning to the right because of the interference of the shore, the crest moves northward, following the shoreline (c) and causing a high tide on the basin’s northern shore. The wave continues its progress around the basin in a counterclockwise direction (d), forming a high tide on the western shore and completing the circuit. The point around which the crest moves is an amphidromic point (AP).
Tidal Patterns Vary with Ocean Basin Shape and Size How do tides behave in confined basins? The tidal range is determined by basin configuration. (a) An imaginary amphidromic system in a broad, shallow basin. The numbers indicate the hourly positions of tide crests as a cycle progresses. (b) The amphidromic system for the Gulf of St. Lawrence between New Brunswick and Newfoundland, southeastern Canada. Dashed lines show the tide heights when the tide crest is passing.
Tidal Patterns Vary with Ocean Basin Shape and Size Tides in a narrow basin. (a) True amphidromic systems do not develop in narrow basins because there is no space for rotation. (b) Tides in the Bay of Fundy, Nova Scotia, are extreme because water in the bay naturally resonates (seiches) at the same frequency as the lunar tide.
Bay of Fundy 10 meter range
Tidal Resonance British Columbia 10 meter range
Calculate the speed of the tide in the open ocean. • Calculate the resonant period of the tide in Long Island Sound Tidal Resonance Length = 110 miles Avg Depth = 78 feet
Chapter 11 – Summary Tides are huge shallow-water waves-the largest waves in the ocean. Tides are caused by a combination of the gravitational force of the moon and sun and the motion of Earth. The moon's influence on tides is about twice that of the sun's. The equilibrium theory of tides deals primarily with the position and attraction of the Earth, moon, and sun. It assumes that the ocean conforms instantly to the forces that affect the position of its surface, and only approximately predicts the behavior of the tides. The dynamic theory of tides takes into account the speed of the long-wavelength tide wave in water of varying depth, the presence of interfering continents, and the circular movement or rhythmic back-and-forth rocking of water in ocean basins. It predicts the behavior of the tides more accurately than the equilibrium theory. Tides have the longest wavelengths of the ocean's waves. These huge shallow-water waves are forced waves: never free of the forces that cause them and so act in unusual but generally predictable ways.