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### The Engineer's Notebook

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# Tidal Teaser Solution

Posted November 15, 2006 11:00 PM by Jorrie
Pathfinder Tags: Tidal gravity Tides

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.

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Anonymous Poster
#1

### Re: Tidal Teaser Solution

11/17/2006 1:57 PM

Jorrie, if this is the correct picture, it is brilliant - but I have my doubts though!

For one thing, the tides in most place in the world do not seem to agree with the 45° lead angle that you portray - OK, I must qualify: not at high tide during full moon.

I have read the NOAA pages and they do not give exactly this picture. I must confess that I do not see them giving any clear picture for any place on Earth!

Have you got more evidence for your picture?

Guru

Join Date: May 2006
Location: 34.02S, 22.82E
Posts: 3817
#2

### Re: Tidal Teaser Solution

11/17/2006 10:22 PM

Guest wrote: "For one thing, the tides in most place in the world do not seem to agree with the 45° lead angle that you portray - OK, I must qualify: not at high tide during full moon."

You must also remember what the 'portraying' above said: "hypothetical continent-free Earth" and "specific equinox full moon...". There are many, many factors that change this idealistic picture. One that I did not mention is the fact that the Moon has a quite bizarre path around Earth.

Things that I did mention is that the basins of Earth have natural frequencies and that it changes the ideal picture. In fact, for virtually no place on Earth can the tidal heights and times be calculated analytically from first principles.

The method used all over the world is to set up an empirical model and measure some constants for every port and the predict on that basis. More about that in a follow-on post.

BTW, have you read the pdf that I mentioned above?

__________________
"Perplexity is the beginning of knowledge." -- Kahlil Gibran
Anonymous Poster
#3

### Re: Tidal Teaser Solution

11/19/2006 12:53 AM

OK Jorrie, I see your point about the complications, but then, what is the point of the whole debate about what causes the tides? I mean, if it is all set up empirically and constants determined by measurement, who cares what the precise mechanisms are?

Yep, I did read your pdf, good stuff! Are you sure that the tides reach the western coast of Southern Africa before they reach the eastern shores? Sounds bizarre to me! From the map in your post, it appears that equal currents approach from both sides at the same time, so should the high tide not be roughly at the same time on both sides?

Guru

Join Date: May 2006
Location: 34.02S, 22.82E
Posts: 3817
#4

### Re: Tidal Teaser Solution

11/19/2006 11:38 AM

Hi Guest, good points you are making! To your "I mean, if it is all set up empirically and constants determined by measurement, who cares what the precise mechanisms are?"

I can only reply: human curiosity! Actually, what made me dig into the causes was your 2nd question and the "anomalies" that I noticed on the tide tables...

"From the map in your post, it appears that equal currents approach from both sides at the same time, so should the high tide not be roughly at the same time on both sides?"

Consider what happened, say, two hours earlier than what the map portrays, when the Moon and Sun were still ~30° further east. Shift the arrows accordingly and there would have been a stronger tidal current flowing towards the west coast, compared to the east coast, where water may actually still be withdrawing!

And me too thought that the tides come with the Moon, from the east!

__________________
"Perplexity is the beginning of knowledge." -- Kahlil Gibran