Tidal forces and their influence

Tidal motion in the ocean and atmosphere occurs due to gravitational interaction between the Earth and the other bodies in the solar system, principally the Moon and the Sun. The impact of the interaction of the Moon and Earth on a fluid envelope around the Earth is shown in Fig. 2.19. The two planets rotate about a common centre of mass, which, due to the greater mass of the Earth, is some 1700 km beneath the Earth's surface. A gradient of gravitational force pulling the fluid towards the Moon exists across the Earth because the force on an individual fluid parcel is proportional to the inverse square of the distance to the Moon. A second force acts due to the rotation of the Earth about the Moon-Earth centre of mass. This is a centrifugal force, directed away from the Moon everywhere over the Earth (see Fig. 2.19). The combination of these two forces on the fluid envelope is to create bulges of fluid on the portions of the globe facing the Moon and opposite this, as shown in Fig. 2.19. The rotation of the Earth about its axis every 24 hours means that, for a given point on the Earth's surface, two peaks in sea level or surface atmospheric pressure pass over each day. This can be seen in the sea level trace shown in Fig. 2.20. It should be noted

Centrifugal force exceeds gravity

Gravitational force exceeds centrifugal force

Centrifugal force exceeds gravity

Gravitational force exceeds centrifugal force

Fig. 2.19. The basic forces causing the lunar tide. The Earth-Moon system rotates about a centre-of-mass. On the Moon side of the Earth the influence of the Moon's gravitational force is greater than the centrifugal force felt by the Earth due to this rotation (which should not be confused with the daily rotation of the Earth). On the side of the Earth away from the Moon, the Moon's gravitational field is weaker while the centrifugal force is the same. The net result is a bulge in the water surface on both sides of the Earth.

Fig. 2.20. A predicted sea level curve for Cromer, England for four days in July 2002. The times refer to GMT rather than BST.

Fig. 2.19. The basic forces causing the lunar tide. The Earth-Moon system rotates about a centre-of-mass. On the Moon side of the Earth the influence of the Moon's gravitational force is greater than the centrifugal force felt by the Earth due to this rotation (which should not be confused with the daily rotation of the Earth). On the side of the Earth away from the Moon, the Moon's gravitational field is weaker while the centrifugal force is the same. The net result is a bulge in the water surface on both sides of the Earth.

that the atmospheric tide (Fig. 2.21) is due to pressure changes from the diurnal heating cycle of stratospheric ozone rather than smaller gravitational forces.

Tidal motion shows rather more complexity than this simple model suggests. The declination of the Earth leads to unequal amplitudes of the two daily peaks, the superposition of the tidal effects of the Sun and Moon leads to bi-monthly modulation of tidal amplitudes, and the shape and depth of ocean basins results in oceanic tidal flow around basins rather than around the entire Earth.

The effect of the tides on the circulation and mixing of the atmosphere is essentially non-existent. By contrast, the tidal impact on the oceans can be substantial, particularly in coastal waters. The amplitude, phase and depth variation of the flow in such regions can be dominated by the tidal motion (see Fig. 2.22). Mixing of the ocean in regions of vigorous tidal currents can also be significant. This can be particularly true in regions of strong stratification and pronounced tidal amplitude because the internal tide (between layers of differing densities) can be of much greater amplitude than the surface effect.

For much of the discussion in the rest of this book, however, tidal effects are likely to be of limited importance. Exceptions to this will occur for processes

Fig. 2.21. A barograph trace recorded in Norwich, England, from 0800 GMT on 30 October 1993, to 1700 GMT on 1 November 1993. Superimposed on the gradual decline in pressure over this period is a twice daily oscillation, the peaks of which are indicated by arrows. This oscillation, about 1 mb in amplitude (the vertical scale is in millibars), is due to the atmospheric tide. [Trace courtesy of John Green.]

Fig. 2.21. A barograph trace recorded in Norwich, England, from 0800 GMT on 30 October 1993, to 1700 GMT on 1 November 1993. Superimposed on the gradual decline in pressure over this period is a twice daily oscillation, the peaks of which are indicated by arrows. This oscillation, about 1 mb in amplitude (the vertical scale is in millibars), is due to the atmospheric tide. [Trace courtesy of John Green.]

S2 Current ellipse at sea-surface S2 Current ellipse at sea-bed

Fig. 2.22. Magnitude of the S2 oceanic tide (the semi-diurnal solar tide), calculated from a numerical model of the tides of the European shelf. The tide at the sea surface and sea bed is shown in the form of tidal ellipses. Following a vector around the ellipse formed from the two right-angled axes at a given location describes the evolution of the tidal current through a full tidal cycle. Along the east coast of Scotland, for example, the tide essentially completely reverses direction between ebb and flood tide. However, southwest of England there is a strong circular element to the tidal variation. [Fig. 7 of Davies (1986). Reproduced with permission from Kluwer Academic Publishers.]

where coastal or topographic effects are significant in the oceanic budget and these will be highlighted when encountered. One recently discovered tidal effect of importance to the global circulation is through the impact of tides around steep deep ocean bathymetry on vertical mixing in the deep ocean. This will be explored in more detail in ยง2.12.

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Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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