The direct forces felt by Earth’s oceans due to the Moon’s gravitational field is extremely small, at about one nine millionth of the force they feel from Earth’s own gravitational field. Therefore our ocean tides are not caused by the simple lifting of the oceans due to the direct pull from the Moon.

If it was that simple we would have only one tidal movement per day when the Moon is overhead and the oceans would pile up against the east coast of continents as the Earth rotates. Instead, most coastal areas experience two high tides per day at any position of the Moon, and the oceans don’t pile up against east coasts. For example, the sea level at the Western end of the Panama cannel is slightly higher than the Eastern end. So let’s examine what is really happening so we can explain how such small forces, mainly due to the Moon, can cause our oceans to move.

Our Moon does not simply travel in a circle with Earth at the centre, but instead the Earth and Moon is a gravitationally coupled system that orbits a ‘barycentre’ over a period of about 27.3 days. This ‘barycentre’ can be thought of as being the centre of mass of the Earth Moon system and is, on average, 4671 km from the Earths centre and always in the direction of the Moon.

This factor is particularly important because our Moon is relatively large. A moon is usually between 10 to 100 times smaller in diameter than the parent planet but our Moon’s diameter is only about 4 times smaller than Earth diameter. Dynamic stability for the Earth Moon system is provided by the gravitational pull of the Moon on one side of the barycentre being balanced by the centrifugal pull from the Earths mass on the other side of the barycentre.
Because ‘force’ is a vector quantity (that is magnitude and direction) Earth’s surface responds to these tidal forces where the pull due to the Moon’s gravity, or Earth’s centrifugal force, is sufficiently different in direction, from the pull due to Earth’s own gravity. It should be emphasized that the important factor is the direction of these external forces relative to the direction of the force due to Earth’s own gravity.

The pull, on Earth’s surface, due to Earth’s own gravity is always towards Earth’s centre, whereas the external forces, that we are now considering, are parallel to the orbital plane of the Moon. This tangential component of force, felt by Earth’s crust and oceans, is referred to as the ‘tractive force’. Tractive forces are zero at Earth’s equator and gradually increase to a maximum at about 60 degrees latitude north and south. The all important factor is that the direction of these tractive forces is either toward the Moon on the near side or away from the Moon on the far side. These ‘tractive force’, at 60 degrees latitude north and south, tends to press the ocean water in the general direction of the equator to form a total of four pressure zones. Although these pressure zones are stationary relative to the Earth Moon system pressure waves do propagate around the Earth’s surface at over 1000 km/hr due to Earth’s rotation.

Earth’s crust is approx 2.8 times denser than its oceans and the physical properties of the crust allows the ‘tractive force’ pressure wave to propagate in phase with Earth rotation with relatively small energy loss. However these same pressure waves cannot travel fast enough through the oceans to keep pace with Earth’s rotation. Therefore the resulting pressure waves in the oceans that we refer to as tidal action, are much more complicated.

The Earth, with its oceans, rotates on an axis that is on average 4671 km away from the centre of gravity of the Earth Moon system (the barycentre). Therefore the oceans feel regular pressure wave oscillations from the ‘tractive force’ as the Earth rotates. These pressure waves can’t travel fast enough through the water of the oceans to stay in phase with Earth’s rotation so instead they form ‘standing waves’ that can stay in phase with Earth’s rotation. But only in the oceans that have natural ocean harmonics that are receptive to the twice daily pressure wave oscillations. The Mediterranean, for example, feels little resonance therefore has negligible tidal movement. The resulting ‘standing waves’ are seen as spiral arms, radiating from central nodes, that rotate twice daily in synchronies with Earth’s rotation relative to the Moon. (Ref. internet ‘animated map of the tidal nodes of the Earth’).

What we know as ‘tides’ are ‘standing waves’ or resonant pressure waves that rotate around ‘nodes’ in phase with Earth’s rotation. The direction of tidal progression around a node is usually, but not always, anti-clockwise in northern oceans and clockwise in southern oceans. Tidal movement tends to be minimal near the nodes and then increases with distance away from the nodes until the pressure wave fades away due to interference from land-masses or other pressure waves. It must be remembered that, in the open ocean, the only water movement associated with a passing resonant pressure wave (a tide) is a slow raising and lowering at the surface, even although the associated pressure waves can propagate through the oceans at speeds up to 800 km/h.

The Sun also contributes to the tidal action on Earth. The dynamics involved are similar to the explanation above however the forces felt by Earth’s oceans are less from the Sun than from the Moon. Although the mass of the Sun is large, so is its distance from Earth, and distance is the dominant parameter in the algorithms determining the forces due to gravity. When the Sun, Moon and Earth are in line, at either ‘New Moon’ or ‘Full Moon’, the tidal forces add together to increase the ocean tidal movement. At in between times the interaction between these two gravitational systems becomes more complex and the actual ocean tidal action can behave strangely at some locations around the globe. There are also approximately five other minor pressure wave ‘nodes’ that have small influences on ocean tides but these are even more complicated.

The actual tidal movement at any location is also very dependent on; ocean currents, geological features around and under the ocean, as well as the ocean’s harmonic characteristics. Most, but not all, coastlines experience a high and low tide twice per day. The ocean tides do follow patterns that are predictable, for any particular location on the Earth surface. Up until recently tide tables have been compiled from historical data however in recent times our understanding of tidal action is improving and computer modeling programs are being developed.

The first satellite to accurately measure ocean surface heights and ocean pressure path patterns was Sea-sat in 1978 and it achieved this by using synthetic aperture radar. This satellite only lasted 106 days, so we are told, but it did confirm tidal nodes and encouraged more satellites dedicated to oceanographic studies. However it is also possible that Sea-sat did not fail but instead the information became classified after 106 days because it revealed the pressure waves generated by secret submerged submarines. It took more than ten years before more ocean pressure wave information became publically available. Satellites such as Topex/Poseidon launched in 1992; Jason 1 launched in 2001 and Jason 2 launched in 2008 has allowed very complex and detailed information to be compiled about the size and shape of the radiating tidal arms extending from all of the tidal nodes.

Observations made by these satellites shows that New Zealand has tidal anomalies because what is actually observed on the tidal behaviour of surrounding oceans does not correspond exactly with data provided by current standard computer tide modeling programs. It is also interesting to note that New Zealand is at a tidal node and the tidal propagation is anticlockwise and not clockwise as expected. New Zealand’s coastline experiences a high tide and a low tide at the same time but on opposite sides of the islands. This means that Cook Strait can have high tide one side and close to low tide on the other side and vice versa.

Ocean harmonics refers to how the regularly occurring pressure wave oscillations from the ‘tractive forces’ interact with the natural resonant frequencies of the ocean and coastline concerned. If there was to be a change in the oceans; density, depth or coastal geology it would cause a change in the characteristics of ocean harmonics that in turn would cause a change in the local tidal action. This means that in some cases a small change in ocean characteristics will cause an existing out of phase tidal movement to become in phase, and resonate to enhance the tidal movement. Populated coastal areas close to sea level that currently have small tidal movement only because of favorable ocean harmonic conditions would need to consider flooding if ocean harmonic characteristics change because this would cause larger tidal movement.
Tidal action can be drastically enhanced due to storm surges that are associated with cyclones. The two main factors causing tidal surges are reduced barometric pressure above an area of ocean close to land and strong winds pushing surface water towards land. When these conditions occur in conjunction with a high tide the water level will increase well above normal to cause flooding of coastal areas. It is unlikely that we will be able to stop cyclones but we should be able to identify coastal regions that are likely to be flooded by the action of tidal surge. This means that it is now becoming possible to predict coastlines that could be in danger from increased tidal movement due to changes in ocean harmonic characteristics.

The Earth, with its own gravitational field, rotates on its axis once a day. However this takes place inside a second gravitational field, due to the Earth Moon system, that is rotating about its barycentre once a month. The direction of rotation for both Earth’s rotation and the Moon’s orbit is anticlockwise when viewed from the North Pole. The power required to drive the tidal action on Earth comes from the energy stored in the rotating Earth. Power is being lost from the rotating Earth at the rate of 3.75 terawatts and most of this is absorbed by ocean tidal action.

The Moon exerts a gravitational pull on Earth’s surface, in effect slowing down Earth’s rotation, and the Earth’s surface exert an equal and opposite pull on the Moon that causes the Moon to speed up. In order for the Earth Moon system to maintain dynamic equilibrium the distance between Earth and Moon must be continuously increasing to satisfy Newton’s laws of motion.

We have been measuring this increasing distance for several decades now and the increase per year is about 38mm. We know that Earths rotational speed is slowing down because our ‘standard time’ regularly needs to have the insertion of ‘leap seconds’ in order to synchronize with the solar day. Since 1972 there has been 27 occasions when it has been necessary to insert a ‘leap second’ and the last correction was made December 31st. 2016.

This article was prepared by Bruce Furze for the U3A Science 2 Group