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The Tides and Tidal Currents

The Tides and Tidal Currents. Professor Ian G Bryden The University of Edinburgh. The Sun the Moon and the Tides. In principle, the tides have been understood since the time of Newton. Their description represented a major step in our understanding of the physical universe

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The Tides and Tidal Currents

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  1. The Tides and Tidal Currents Professor Ian G Bryden The University of Edinburgh

  2. The Sun the Moon and the Tides • In principle, the tides have been understood since the time of Newton. • Their description represented a major step in our understanding of the physical universe • The tides arise from the orbital mechanics of the Earth, Moon and Sun.

  3. A Earth B Newton’s Theory of Tides Moon Earth and Moon orbit their common centre of mass every Lunar month CoM At point “A”, the gravitational attraction of the Moon is greater than that required to achieve the mutual orbit and there is a net “tidal” effect towards the Moon A Earth C At point “B”, the gravitational attraction of the moon is less than that required to achieve mutual orbit and there is a net “tidal” effect away from the Moon B

  4. New Moon:- “Spring Tide” In this configuration, the influence of the Moon and Sun reinforce each other to produce the large tides known as Spring Tides, or Long Tides. A similar superposition also exists at the time of Full Moon. solar tide Earth Sun Moon Lunar tide

  5. Moon solar tide Sun Earth Lunar tide Half Moon:- Neap Tides When the Sun and Moon are at 90o to each other, the effect is of cancellation as shown. This configuration results in Neap Tides, which are also know as Short Tides.

  6. Putting it all together, NOT to SCALE

  7. Influence of Flow Statistics • Obviously flow speed (and energy flux) varies with the state of the tide Mean Spring peak= 3.5m/s Mean Neap peak =1.75m/s

  8. “ diversion’ of outflowing water Open boundary “ diversion “of inflowing water Semi-enclosed Basin in the Northern Hemisphere • In flood, the water is diverted to the right towards the lower boundary. In ebb, the water is diverted towards the upper boundary. This results in a higher tidal range at the boundaries than at the centre. The net result is to generate a “tidal wave” which progresses anti-clockwise around a point in the centre of the “basin”.

  9. More Realistic Examples! Dynamic tide analysis can be applied, in principle, for any environment.

  10. η d h U V Δy Δx Temporal Streamwise Cross-stream Coriolis Pressure Bed friction term momentum term momentum term term gradient term term (i) (ii) (iii) (iv) (v) (vi) Wind stress term (zero-equation turbulence model) - eddy viscosity term (vii) (viii) Numerical Modelling: Formulation GOVERNING (SHALLOW WATER) EQUATIONS: Conservative form of the continuity equation: Conservative form of the x-directed momentum equation (momentum flux):

  11. Tidal Currents- world wide • The map below shows the global distribution of frictional energy dissipation due to tidal currents

  12. The Tides as a Mechanistic Process • The importance of the seas to commerce and defence have driven the science of tidal prediction • Machines have been developed to mimic the tidal processes and allow accurate tidal predictions

  13. Local Hot-Spots • Local geographical effects can result in quite massive local current speeds. • In the Pentland Firth, for example, there is evidence of tidal currents exceeding 7m/s. The energy flux in such a flow is considerable.

  14. BUT!: Turbulence • Tidal Currents are NOT smoothly varying, they are chaotic with drastic and violent changes in speed/direction • I suggest that we limit ourselves to extracting energy so that the speed varies less than the natural turbulent fluctuation • Turbulence will also have implications for design, installation, reliability etc Time(s) Also: Remember my passing comment about the 3 dimensional tidal flow equations?

  15. “Turbulence” in Three Dimensions (mm/s) • Turbulent flow is intensely complex in three spatial dimensions and in time • Our understanding must improve before the deployment of third generation devices 30 Height above sea bed (m) 20 Example of turbulent “eddy” 10 100 200 Time (s) The nature of this turbulence will affect design AND modelling of the flow itself Present generation tidal flow models do not adequately handle turbulence of this nature

  16. One for the Unbelievers Predicting flow speed reduction • Even the simple channel model includes the effects of friction, the free surface and pressure! • A simplified version can be used in a parametric form to make first stage predictions of flow speed reduction f is the ratio of energy extraction to the actual kinetic flux in a channel L is the channel length (m) g is the acceleration due to gravity (ms-2) Based upon multiple input to the simple channel model

  17. Questions

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