Tidal Teaser Solution

After posting a 'teaser' on the tides in the general section, there was an initial flurry of good and not so good responses. It was however quite clear that there is some lack of understanding about what causes the coastal tides. This Blog entry summarizes the salient points of the solution.

I found the proper story on this NOAA site, but it took quite a bit of analysis to figure out how it actually works. NOAA, unfortunately, still first tell the old fashioned story of centrifugal forces around the barycenter of the Moon/Earth system, before getting to the 'real' explanation, so before going there, read on...

Not to hold you in suspense for any longer, it is the horizontal 'tractive forces' created by the tidal gravity of the Moon and the Sun that create circulating tidal currents in the deep ocean. These currents cause the tides when they hit continents.

The figure below shows an equatorial cut of a hypothetical Earth with no continents, viewed from the South Pole (S.P.), with the Moon above and assuming that the Sun is in the same general direction, i.e., it's new moon.

The four quadrants are labeled "accelerating" and "decelerating" as measured in the direction of Earth's rotation (clockwise from the S.P.). Earth drags the water around at a surface speed of about Mach 1.5 relative to the Moon. The Moon's tidal gravity then tries to accelerate and decelerate the water molecules as indicated.

The dark blue arrows indicate positive tidal flow relative to the surface and the red ones negative flow, with lengths indicating relative flow rates. In the hypothetical continuous ocean, this will create 'bulges' in the ocean with a 45-degree lead angle, as shown. Continents tend to get in the way of these currents, but it does not prevent them from forming in any wide-open and deep waters.

The open sea tidal currents are slow, very slow (20 to 40 m/h), but they pack a mighty punch because they work equally at all depths. This is in contrast to the thermal currents, which are fast, but operate only in narrow depth bands at any one location. When a tidal current hits a continent or a shallow water shelf, much of the considerable kinetic energy is converted into potential energy, hence raising the water level.

The figure below shows a map of Earth with the thermal currents, by www.physicalgeography.net. Superimposed on this map are the positions of the Sun and the Moon for a specific equinox full Moon at about 01h GMT. The fat arrows show the main tidal current directions for mid-southern latitudes (I used this in a local presentation). This is roughly high tide time in South Africa and low tide time in South America and Australia.

I think the diagram (however poorly readable due to the insert method) speaks for itself. The main currents approach Southern Africa and withdraw from South America and Australia. The situation in the northern hemisphere is roughly the same, except that there are obviously no currents where there is no open, deep water. Even the Med does not show significant tides.

To complicate things further, natural hydrodynamic frequencies of basins obviously tries to force their rhythms onto the water. Where natural frequencies more or less coincide with the 12h20m rotating tidal current frequency, stronger currents and higher tides usually happen due to resonance. Where a 24-hour resonance is very strong, single highs and lows per day can be the result. Where no resonance happens, very small or erratic tidal movements can result.

A more descriptive treatment of tidal gravity and the coastal tide phenomenon is given in the chapter 'Tidal Gravity' of my eBook. The chapter can be downloaded for free from this page. I will post something on tidal prediction in this Blog later.