Question about Earth tides

[Hornblower]

Snipped from a post in Forum Feedback:

Can we discuss the wrong idea that there are two bulges? Or is just stating that considered ATM?

On a clean, simplified thought exercise planet with a spherically symmetrical ocean covering a spherically symmetrical lithosphere, it is my understanding that the sea water will form a pair of bulges while the underlying globe will be elongated by a lesser amount. On our actual Earth, the continental coastlines scramble the tidal bulges with the result that the water is sloshing around in complex patterns. If I am not mistaken, there are places such as Tahiti where there are one high tide and one low tide daily, instead of two of each. In most places we get two of each just as we would on an isolated island on the thought exercise planet, but they tend to be of greater amplitude on coastlines. The water piles up as the coastline runs up against its inertia.

As a sanity check, do some online research on tides. Don't take every detail of what I say as gospel. I have been known to make some errors and omissions.

[grant hutchison]

And, because the moon doesn't orbit over Earth's equator, even in an ideal model with an ocean of uniform depth and no continents, with neat double tidal bulges, there would still be once-daily tides at high latitudes, twice-daily tides at low latitudes, and mixed tides (of alternating high and low magnitude) in a region between.

Grant Hutchison

[Hornblower]

And, because the moon doesn't orbit over Earth's equator, even in an ideal model with an ocean of uniform depth and no continents, with neat double tidal bulges, there would still be once-daily tides at high latitudes, twice-daily tides at low latitudes, and mixed tides (of alternating high and low magnitude) in a region between.

Grant Hutchison

My bold. A few years ago we had the high side of this pattern from a "Super Moon" coincide with the peak of a nor'easter on the Virginia and North Carolina coastline near the December solstice. It was the worst possible tide-related timing for a storm of any given magnitude, and warnings of coastal flooding went up.

[Ken G]

Yes, we can certainly say that understanding tides starts with the shape of the equipotential of the effective gravity, which includes corrections to Earth gravity from the Moon's gravity and the Earth's orbital motion in the Earth-Moon system. That equipotential looks like two bulges of very small amplitude (the bulge only lifts the water about a foot above the average height), and that is pretty much what you find in the open ocean (though currents from the continents and the ocean floor affect that too). But that cannot end the discussion, because obviously tides on beaches have a much higher amplitude, and in inlets (like the Bay of Fundy) can be 10-20 times higher than that There can also be one tide per day, for the reason Grant gave (the bulges aren't on the equator), and due to more complicated resonances in the current flows along coastlines of various shapes. But all of this is caused by that double-bulge equipotential, no one could ever understand the first thing about tides without understanding those two bulges.

[a1call]

My 2 cents worth, i think there is a tendency to consider tides effect at points along the great circle which is perpendicular to the (apparent) axes of the revolution of the sun and the moon around the Earth.
On an ideal planetary system points on earth along these axes (the poles, assuming the sun and the moon over the equator) would be in equilibrium and would experience no tides.
Points in between would be a gradient of no tides to maximum tides.
ETA on second thought I can see problems with my description of the great circle considering the axes would not be the equilibrium points if the sun or moon are not on top of the equator considering it's mostly the Earth that rotates. The equilibrium points world still be there with no tides but I don't know how to verbally specify/describe them.
Perhaps someone could.
ETA II On third thought the equilibrium points would be moving on the surface of the Earth and any static point along this movement would experience tides.
ETA III Happy New year. Hopefully it will be a good year for all.

[grant hutchison]

You can find folk out there on the internet who claim that the general slosh induced by the continents, which prevents the oceans ever managing to follow the equipotential surface as it moves around the Earth, means that there are no tidal bulges at all on Earth.
And yet, the Earth-Moon system is demonstrably evolving tidally, with the Moon moving away from the Earth. So all that complicated sloshing must still be averaging down to an effect that looks gravitationally like tidal bulges from the vantage point of the Moon.

Grant Hutchison

[Ken G]

What's more, calculations of the equipotential bulge give about the same height (a foot above average) as the open oceans are said to rise up at those bulges. Thus, far away from continents, the oceans do seem to conform pretty well to the equipotential. One can say that tides are caused by the currents that attempt to fill those bulges, even when the presence of continents interferes with the ability to conform to the equipotential and can even cause overshoot when there is a resonance between the timescale for the equipotential to rise and fall, and the timescale for the currents to fill or empty those bulges. The equipotential bulge acts exactly like a local change in the strength of gravity, and periodicities in those gravitational changes can whip up currents that overshoot the bulges, as happens in the Bay of Fundy.

[Grey]

Here's a nice paper that I found when we were having an earlier discussion of the expected tidal distortion from a much larger or closer Moon. It gives a theoretical analysis of the deformation from the tidal influence of the Moon (and the Sun).

[grant hutchison]

Here's a nice paper that I found when we were having an earlier discussion of the expected tidal distortion from a much larger or closer Moon. It gives a theoretical analysis of the deformation from the tidal influence of the Moon (and the Sun).

That's nice.

I wrote my own attempt at explaining the tidal bulges without mathematics a while ago. It's here. I so far haven't got around to writing Part 2, which would be about the complicating factors we've mentioned on this thread.

Grant Hutchison

[grapes]

You can find folk out there on the internet who claim that the general slosh induced by the continents, which prevents the oceans ever managing to follow the equipotential surface as it moves around the Earth, means that there are no tidal bulges at all on Earth.

That may be where the comment from Gigabyte in the OP is coming from. I've found some of those folk, and I'm working through their objections.

And yet, the Earth-Moon system is demonstrably evolving tidally, with the Moon moving away from the Earth. So all that complicated sloshing must still be averaging down to an effect that looks gravitationally like tidal bulges from the vantage point of the Moon.

Here's a nice paper that I found when we were having an earlier discussion of the expected tidal distortion from a much larger or closer Moon. It gives a theoretical analysis of the deformation from the tidal influence of the Moon (and the Sun).

That paper references the NOAA Our Restless Tides, which I've criticized in the past (see ETA), and Stacey's Physics of the Earth, which I like a lot. The NOAA webpage seems to have been cleaned up a little but it still has this in the early summary:
https://tidesandcurrents.noaa.gov/restles2.html

At the surface of the earth, the earth's force of gravitational attraction acts in a direction inward toward its center of mass, and thus holds the ocean water confined to this surface. However, the gravitational forces of the moon and sun also act externally upon the earth's ocean waters. These external forces are exerted as tide-producing, or so-called "tractive" forces. Their effects are superimposed upon the earth's gravitational force and act to draw the ocean waters to positions on the earth's surface directly beneath these respective celestial bodies (i.e., towards the "sublunar" and "subsolar" points).

High tides are produced in the ocean waters by the "heaping" action resulting from the horizontal flow of water toward two regions of the earth representing positions of maximum attraction of combined lunar and solar gravitational forces. Low tides are created by a compensating maximum withdrawal of water from regions around the earth midway between these two humps. The alternation of high and low tides is caused by the daily (or diurnal) rotation of the earth with respect to these two tidal humps and two tidal depressions. The changing arrival time of any two successive high or low tides at any one location is the result of numerous factors later to be discussed.

It's difficult to read that in any way that makes it correct, as a summary.

ETA: https://forum.cosmoquest.org/showthr...663#post118663

[profloater]

There so called bulges are tiny and it is easy to show. The tides are sideways movements caused by tangential accelerations. All the fluids are free to slide sideways toward the moon (and the sun) as the earth rotates. The force is small and calculable per kg, sideways not radially, but integrated aver the half cycle to the fluids develop tangential momentum. Then the moving fluids encounter fixed barriers and the vertical tidal movement of water that we see at the coast occurs. Euler first spotted this I believe. The rotating bulge is completely wrong as explanation of the observed tides.

If there were no land masses on an ocean skinned planet, the waters would move without noticeable radial displacement. But we have the continental shelf and thus tides from momentum. The waters moving invisibly in porous rocks also experience these sideways accelerations, velocities and momentums.

[profloater]

The paper to my surprise ignores the integrated time of operation of the forces on the skin of the water surface, concentrating on the bulge and centrifugal force. Consider a point mass of water on the surface with the moon on the horizon. There is a simple Gmm/d^2 sideways force maintained over periods of hours. The force causes unopposed tangential acceleration giving significant velocity after say 6 hours. This velocity applies to all the neighbouring points in the water, it all moves sideways with actually huge momentum. Do I need to show the calculation? This is the cause of our tides.

[CJSF]

That makes no sense to me, profloater. The Moon would be at a point on the horizon for just about as long as any other position in the sky, including the opposite horizon. This would impart that force first toward one side, then up and across to the other horizon, and it would be doing this from every point on Earth. Making a bulge. ??? Wouldn't it?

CJSF

[Gigabyte]

You can find folk out there on the internet who claim that the general slosh induced by the continents, which prevents the oceans ever managing to follow the equipotential surface as it moves around the Earth, means that there are no tidal bulges at all on Earth.

Can you provide a source for that? It's not clear exactly what you are saying.

An equilibrium tidal bulge does not really exist on Earth because the continents do not allow this mathematical solution to take place. Oceanic tides actually rotate around the ocean basins as vast gyres around several amphidromic points where no tide exists. The Moon pulls on each individual undulation as Earth rotates—some undulations are ahead of the Moon, others are behind it, whereas still others are on either side. The "bulges" that actually do exist for the Moon to pull on (and which pull on the Moon) are the net result of integrating the actual undulations over all the world's oceans. Earth's net (or equivalent) equilibrium tide has an amplitude of only 3.23 cm, which is totally swamped by oceanic tides that can exceed one metre.

https://en.wikipedia.org/wiki/Tidal_...tum_and_energy

The various Wikipedia articles on tides actually at present explain the real situation, but it's not the first thing in any article.

But if you read them all, the information is actually there. The twin bulges following the moon do not actually exist.

The solid earth certainly has them, but the oceans do not.

[grant hutchison]

Can you provide a source for that? It's not clear exactly what you are saying.

Well, I presume you got this from somewhere:

The idea that there there are two tidal bulges always running around the worlds oceans is shown to be completely wrong by modern scientific data,...

That's an example of what I was talking about.
You can find another very long example here, under the heading There is no tidal bulge.

An equilibrium tidal bulge does not really exist on Earth because the continents do not allow this mathematical solution to take place. Oceanic tides actually rotate around the ocean basins as vast gyres around several amphidromic points where no tide exists. The Moon pulls on each individual undulation as Earth rotates—some undulations are ahead of the Moon, others are behind it, whereas still others are on either side. The "bulges" that actually do exist for the Moon to pull on (and which pull on the Moon) are the net result of integrating the actual undulations over all the world's oceans. Earth's net (or equivalent) equilibrium tide has an amplitude of only 3.23 cm, which is totally swamped by oceanic tides that can exceed one metre.

https://en.wikipedia.org/wiki/Tidal_...tum_and_energy

The various Wikipedia articles on tides actually at present explain the real situation, but it's not the first thing in any article.

But if you read them all, the information is actually there. The twin bulges following the moon do not actually exist.

The solid earth certainly has them, but the oceans do not.

Odd how Wikipedia manages to omit its legendary "citation needed" so often when a citation really is needed. I doubt the validity of that tenth-of-a-millimetre measure of the "equilibrium" tide (which isn't actually at equilibrium, as they've already said).
But the statement that "an equilibrium tidal bulge does not really exist" is not the equivalent of "there are no tidal bulges in the ocean" - and your Wiki quote describes how the bulges actually do show up in integrated sea surface height data.

Grant Hutchison

[profloater]

That makes no sense to me, profloater. The Moon would be at a point on the horizon for just about as long as any other position in the sky, including the opposite horizon. This would impart that force first toward one side, then up and across to the other horizon, and it would be doing this from every point on Earth. Making a bulge. ??? Wouldn't it?

CJSF

well here is a thought picture. Imagine the Earth with a small mass of water on the line between the earth and moon centres. The moon exerts a tiny force lifting the water a tiny amount. But the earth is spinning so the water point starts a journey around for twelve hours to the opposite side. During that twelve hours it starts to feel a sideways force maximised at the six hour point. While the moon cannot lift the water significantly it can move it sideways because all the water feels the same force so there is no resistance to motion to a first order. The force causes acceleration and all the water around the point chosen ends up moving towards the moon but at constant height. Ignoring waves obviously. That's all the local water now moving relative to the sea bed, sideways. After twelve hours the force is reversed.
Now all that water, say it's the Atlantic Ocean, moving sideways encounters say France, and the continental shallows. It's momentum causes faster flow and eventually a rise as it is blocked by the land. That is the tide we observe.

[Hornblower]

I know that any real planet that is deformed by external gravitational gradients will have some internal friction, but let's do a thought exercise with one that has none. My question is whether or not rotation in such a case will drag the tidal bulges off center. I have not been able to find anything written about this, but my educated opinion is that they will be off center. Here is my reasoning. A deformable body will seek an equipotential shape, but because of its inertia it will not spring to that shape instantly when the magnitude or direction of the perturbation is changed. A portion of the planet at quadrature will be below the undisturbed spherical lever, and as it comes around toward conjunction it will try to go to the equipotential level for any given angle but will lag because of its inertia. As it passes conjunction it is still a bit below the equipotential level and will thus keep rising a bit longer before starting to fall. Thus we will have an off-center ovoid subject to retrograde torque from the perturbing body. I would not consider my argument to be ATM because I have not seen it addressed anywhere, one way or the other.

[Ken G]

Ignoring the Sun for now, what is easy to calculate is the shape of the equipotential, and the fact that it rises up about one foot at maximum bulge, from where it would be without the Moon. So, all we need to do is ask how much the ocean height rises up at a point that the Moon passes directly over that is quite far from any continents. If the answer is about one foot, there you have it, the tidal bulge is alive and kicking.

It's actually pretty hard to get a straight answer to this question, but when I look at the ocean topography map at https://marinebio.org/oceans/currents-tides/, it looks like the Pacific is up about a foot, and the Atlantic about 90 degrees away is down by about a foot, roughly speaking (though it would help if they explain what this map is, like where is the Moon and the Sun and so on). So obviously there are important details due to all those continents, but the basic equipotential bulge idea seems like a pretty good way to see what is going on there. But I must confess I don't see two bumps and two dips, but that could just be because the map isn't made at a moment when both bulges, or both dips, are located in the open ocean. This is the kind of information that would actually be useful to discuss, in all that verbiage they do include. Were it me, I'd plot the ratio of the ocean height above average to the equipotential height above average, that would be a plot worth seeing.

One important number is that the time constant for the oscillations of the oceans is about 30 hours, meaning that if we somehow gave the ocean a huge kick, it would slosh around for some 30 hours before damping out. As this is longer than the 12 hour period of the tidal rises and falls of the equipotential, this certainly opens the possibility of resonant oscillations getting set up, overshooting the bulges in the equipotential, but not by a huge margin. On balance, one should only expect factor-2 kinds of accuracy in the open oceans when using the equipotential to predict ocean height, and of course much worse in regions strongly affected by the shape of the continents. Nevertheless, the equipotential bulges are certainly the starting point for understanding tides. The inaccuracies introduced are similar to what you get from concentrating on the change in the magnitude of the Moon's gravity with distance, rather than on its radial divergence focused on the center of the Moon, or what you get from ignoring the Sun.

[grant hutchison]

If you want to see a tidal bulge propagating around the Earth in sync with the moon, take a look at this animated gif that shows the movement of high and low tide around the amphidromes. There's a complicated rotary slosh within the ocean basins, driven by tidal forcing and Coriolis, but if you look at the Southern Ocean you can actually watch the southern amphidromes "hand off" the high tide to each other in a wave that moves continuously around the Earth from E to W.
And if you look at the tide magnitudes in this gif, you can see that the rotary movement in the ocean is less evident than you might expect from the amphidrome view, because not all high tides are of the same magnitude - there's a strong E to W progression in the north Atlantic and north Pacific, as well as the one previously noted in the Southern Ocean, and considerable sloshing and swirling elsewhere.

This is the interface between the equilibrium theory of tides (which deals with the idealized tidal bulges of Newton and Laplace), and the dynamic theory of tides, which deals with how the real oceans on a rotating world respond to forcing from the tidal potential.

Grant Hutchison

[profloater]

If you want to see a tidal bulge propagating around the Earth in sync with the moon, take a look at this animated gif that shows the movement of high and low tide around the amphidromes. There's a complicated rotary slosh within the ocean basins, driven by tidal forcing and Coriolis, but if you look at the Southern Ocean you can actually watch the southern amphidromes "hand off" the high tide to each other in a wave that moves continuously around the Earth from E to W.
And if you look at the tide magnitudes in this gif, you can see that the rotary movement in the ocean is less evident than you might expect from the amphidrome view, because not all high tides are of the same magnitude - there's a strong E to W progression in the north Atlantic and north Pacific, as well as the one previously noted in the Southern Ocean, and considerable sloshing and swirling elsewhere.

This is the interface between the equilibrium theory of tides (which deals with the idealized tidal bulges of Newton and Laplace), and the dynamic theory of tides, which deals with how the real oceans on a rotating world respond to forcing from the tidal potential.

Grant Hutchison

Those are fascinating gifs that I had not encountered before. I see the effect of the continental shelf adjacent to the land masses with small height changes in the open oceans. Thanks for finding and posting them. The natural period of the constrained oceans must also be very important as well as complex when the coriolis effects of north south transfers are included.. If you do a model of say a harbour with proper scaling factors you get the chaotic effect of occasional huge surges when forcing frequency hits one of the natural resonances. These chaotic coincidences smother any simple bulges.

[CJSF]

I am getting thoroughly confused here, as a layperson. What's the mainstream and who's arguing against it? Are there tidal bulges or not, and if so, are they relevant? Can you have the periodicity of tides without the bulges? What does it mean, "...the bulges actually do show up in integrated sea surface height data"?

CJSF

[grant hutchison]

The usual explanation given for the twice-daily tides is that the moon's gravity generates a "tide raising potential" on the Earth, creating two bulges in the ocean (and solid planet, and atmosphere), one facing towards the moon and one away from it. This is the "equilibrium theory of tides" produced by Newton (who emphasized the change in gravitational potential) and Laplace (who emphasized the tangential forces that help create flow towards the tidal bulges). It's the 101 "what causes the tides" explanation you'll find everywhere, and it is certainly mainstream - no-one argues that the "tide raising potential" doesn't exist.

The problem is that those neat bulges of water moving around the Earth can't exist in their "pure" form, because the continents get in the way and Coriolis effect deflects the flow of water. The result is that the tide-raising potential drives swirling motions in the various ocean basins (called gyres) around central points at which the water neither rises nor falls (called amphidromic points). So if you look at an animation of tidal movement in the open ocean, you don't see two big bulges sweeping around the Earth - you see a lot of complicated swirling instead. This also is mainstream - it's called "dynamic theory of tides".

Some people (like the one in a link I provided earlier) maintain that this swirling motion means there simple are no bulges at all. But if you look at the animations I linked to, there actually is a patchy but systematic drift of high and low water from east to west. And if you average out the gravitational effect of all the swirls in the sea surface height, then there is a net bulge (an excess mass of water) that is raised by the moon, and with which the moon interacts gravitationally, which is driving the outward evolution of the moon's orbit. You simply can't explain the orbital evolution of the moon (and the observed perturbation to artificial satellite orbits) without invoking a net bulge in the oceans, in addition to the tidal deformation of the solid earth.

So the ATM bit would be any sort of hard claim that there are no oceanic bulges of any kind. Just pointing out that there are no bulges corresponding to the simple equilibrium tidal theory of Newton and Laplace is entirely mainstream, and in fact would certainly have made Newton and Laplace say, "Well, duh."

Grant Hutchison

[Ken G]

And if you look at the tide magnitudes in this gif, you can see that the rotary movement in the ocean is less evident than you might expect from the amphidrome view, because not all high tides are of the same magnitude - there's a strong E to W progression in the north Atlantic and north Pacific, as well as the one previously noted in the Southern Ocean, and considerable sloshing and swirling elsewhere.

This is just the view I was hoping to see (though it would have been nice had they also plotted the two points opposite the Moon, and mentioned the lunar phase as well!). Indeed, we can presume that the color scale is in meters, so the yellow and teal colors that dominate in the open oceans correspond to height changes from the average of about a foot, which is just the scale of the changes in the height of the equipotential. So the equipotential bulge picture correctly predicts the scale of the height variations everywhere except against the continents where the simplistic tidal currents are strongly altered, and it also gives us the general sense of east-to-west variation. At the same time, I would freely admit that the picture we see here is not simply two points of a football moving around and stacking up when they encounter continents, there's also a lot of rotational sloshing in the circular basins between continents, that dynamical theory you mention. On balance, I would tend to say the equipotential bulge picture tells an important part of the story (in terms of overall scale and general phase coherence), but is only useful at a kind of factor of 2 level even in the open ocean.

[grapes]

This is just the view I was hoping to see (though it would have been nice had they also plotted the two points opposite the Moon, and mentioned the lunar phase as well!).

Yeah, whether the tide was neap or spring. The sun complicates things.

Also, the body tides are much more regular, the solid earth resonance modes do not interact as much as with the ocean tides.

Plus, as far the "two bulges", even in the ocean, they can be removed/isolated mathematically and the signature would probably be much more obvious, but even then they're going to be the sum of the solar tides and the lunar tides and are not going to be "textbook", even in the spring tides unless it's during eclipse time.

Indeed, we can presume that the color scale is in meters, so the yellow and teal colors that dominate in the open oceans correspond to height changes from the average of about a foot, which is just the scale of the changes in the height of the equipotential. So the equipotential bulge picture correctly predicts the scale of the height variations everywhere except against the continents where the simplistic tidal currents are strongly altered, and it also gives us the general sense of east-to-west variation. At the same time, I would freely admit that the picture we see here is not simply two points of a football moving around and stacking up when they encounter continents, there's also a lot of rotational sloshing in the circular basins between continents, that dynamical theory you mention. On balance, I would tend to say the equipotential bulge picture tells an important part of the story (in terms of overall scale and general phase coherence), but is only useful at a kind of factor of 2 level even in the open ocean.

[DALeffler]

...
Some people (like the one in a link I provided earlier) maintain that this swirling motion means there simple are no bulges at all

.

Ah, but I think there actually is a bulge (from Ken Gs link):

Origin of Tides

Tides originate in the southern oceans, the only place on Earth where a circumventing wave resulting from the tidal force of the Moon can travel with no restrictions from land barriers. The result is that in most places there are delays between phases of the Moon and effects on the tide. For example, spring and neaps are two days behind the new/full moon and first/third quarter in the North Sea.

When I read the above and looked again at those wonderful gifs you provided, it really clicked things into place for me.

[Gigabyte]

.
When I read the above and looked again at those wonderful gifs you provided, it really clicked things into place for me.

Really? Did anyone notice the clock? The "tidal bulge" in the southern ocean made it all the way around the pole in 12 hours.

Think about it.

[grant hutchison]

...
Some people (like the one in a link I provided earlier) maintain that this swirling motion means there simple are no bulges at all

Ah, but I think there actually is a bulge (from Ken Gs link):

So do I.

Grant Hutchison

[grapes]

Yeah, whether the tide was neap or spring. The sun complicates things.

Ha! So, we do have those records: Sep 1 2010 http://www.moonconnection.com/moon_september_2010.phtml
According to that, we have an exact mismatch, a neap tide. So, the bulges would be expected to be as indistinct as possible, since the sun signal interference with the lunar signal would be at a maximum

[01101001]

What's the mainstream and who's arguing against it? Are there tidal bulges or not, and if so, are they relevant?

I thought this was a spherical-cow matter, a lie we tell to children (Wikipedia), to help people to understand tides.

I'm surprised anyone would categorize this simplification as mainstream physics instead of simple mainstream pedagogy.

It's a germ of truth in a kernel of complexity.

[Gigabyte]

I'm surprised anyone would categorize this simplification as mainstream physics instead of simple mainstream pedagogy.

The original question was "how can you tell if it's mainstream?".

Obviously since NASA has animations showing there are no twin bulges following the moon across the Pacific ocean, as well as pages showing animations with two bulges (as the reason for the twice daily tides), the matter is a bit confusing.

NASA showing bulges

NASA showing a realistic view of the actual tides

It's why the matter came up.