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TIDES

Explore the science behind ocean tides, gravitational and centrifugal forces, equilibrium tides, non-astronomical factors influencing tides, tidal wave characteristics, constituents of tides, and more.

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TIDES

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  1. TIDES Tide - generic term to define alternating rise and fall in sea level with respect to land and is produced by the balance between the gravitational acceleration (of the moon and sun mainly) and the centrifugal acceleration. Tide also occurs in large lakes, in the atmosphere, and within the solid crust Gravitational Force (Newton’s Law of Gravitation): F = GmM/R2 G = 6.67×10-11 N m2/kg2

  2. EQUILIBRIUM TIDE Centrifugal Force F = GmM/R2 Moon’s Gravitational Force (changes from one side of the earth to the other) Tide Generating Force (Difference between centrifugal and gravitational) Center of mass of Earth-Moon system ~1,700 km from Earth’s surface (because Earth is 81 times heavier than Moon)

  3. How strong is the Tide-Generating Force? Gravitational Force at A: B S A P Centrifugal Force at A: Imbalance (Tide-generating force at A): Tide-generating Force at A: Tide-generating Force at B:

  4. How strong is the Tide-Generating Force? B S A P Tide-generating Force at A: Tide-generating Force at B: The mass of the sun is 2x1027 metric tons while that of the moon is only 7.3x1019 metric tons. The sun is 390 times farther away from the earth than is the moon. The relative Tide Generating Force on Earth = [(2x1027/7.3x1019)]/(3903) or = 2.7x107/5.9x107 = 0.46 or 46%

  5. EQUILIBRIUM TIDE

  6. What alters the range and phase of tides produced by Equilibrium Theory? Non-astronomical factors: coastline configuration bathymetry atmospheric forcing (wind velocity and barometric pressure) hydrography may alter speed, produce resonance effects and seiching, storm surges In the open ocean, tidally induced variations of sea level are a few cm. When the tidal wave moves to the continental shelf and into confining channels, the variations may become greater.

  7. Keep in mind that tidal waves travel as shallow (long) waves How so? Typical wavelengths = 4500 km (semidiurnal wave traveling over 1000 m of water) Ratio of depth / wavelength = 1 / 4500 C = [ gH ]0.5 Then, their phase speed is: The tide observed at any location is the superposition of several constituents that arise from diverse tidal forcing mechanisms. Main constituents:

  8. The Form factor F = [ K1 + O1 ] / [ M2 + S2 ] is customarily used to characterize the tide. When 0.25 < F < 1.25 the tide is mixed - mainly semidiurnal When 1.25 < F < 3.00 the tide is mixed - mainly diurnal F > 3 the tide is diurnal F < 0.25 the tide is semidiurnal

  9. When 0.25 < F < 1.25 the tide is mixed - mainly semidiurnal When 1.25 < F < 3.00 the tide is mixed - mainly diurnal F > 3 the tide is diurnal F < 0.25 the tide is semidiurnal Superposition of constituents generates modulation - e.g. fortnightly, monthly This applies for both sea level and velocity

  10. Subtidal modulation by two tidal constituents

  11. In Ponce de León Inlet: M2 = 0.41 m; N2 = 0.09 m; O1: 0.06 m; S2: 0.06 m; K1= 0.08 m F = [K1 + 01] / [S2 + M2 ] = 0.30 GNV

  12. Panama City In Panama City, FL: M2 = 0.085 m; N2 = 0.017 m; O1: 0.442 m; S2: 0.035 m; K1= 0.461 m F = [K1 + 01] / [S2 + M2 ] = 7.52

  13. From Pinet (1998)

  14. Co-oscillation Independent tide - caused by gravitational and centrifugal forces directly on the waters of a basin -- usually negligible effect for typical dimensions of semienclosed basins Co-oscillating tide - caused by the ocean tide at the entrance to a basin as driving force The wave propagates into the basin and may be subject to RESONANCE and RECTIFICATION -- alters tidal flows and produces subtidal motions

  15. Resonance of Tidal Wave At the mouth x = L, L at x = L Substituting into and The natural period of oscillation is then: For resonance to exist, the denominator should tend to zero, i.e.,

  16. u L For an estuary with length < λ /4, u is zero at the head and maximum at the mouth For longer estuaries u is zero at x = 0, λ / 2, 3 λ / 2,… or where sin κx = 0 and maximum at x = λ /4, 3 λ / 4, 5 λ / 4, …, i.e., where sin κx is max

  17. Merion’s Formula Mode 1 (n =1)

  18. Solution: Effects of Rotation on a Progressive Tidal Wave in a Semi-enclosed basin R = C / f KELVIN WAVE

  19. Effects of Rotation on a Standing Tidal Wave in a Semi-enclosed Basin Two Kelvin waves of equal amplitude progressing in opposite directions. Instead of having lines of no motion, we are now reduced to a central region --- amphidromic region-- of no motion at the origin. The interference of two geostrophically controlled simple harmonic waves produces a change from a linear standing wave to a rotary wave.

  20. Two Kelvin Waves in Opposite Directions Distance (m) Distance (m)

  21. Two Kelvin Waves in Opposite Directions km

  22. Effects of Bottom Friction on an amphydromic system (Parker, 1990)

  23. Virtual Amphidromes (Parker, 1990)

  24. Virtual amphidromes in Chesapeake Bay

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