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I do not see how a water molecule can distinguish between being in a 20 knot wind added to a 2 knot current vs experiencing 22knot wind in still water. All these are _relative to the bottom_ which is is the frame of reference we always use but the point is that the frame of reference does not matter as long as you are consistent.

That does not mean I doubt for one second that the phenomenon exists, the evidence based on the collective experience is overwhelming (your examples are very much to the point). So I must be missing something and I want to know what it is.
You are not missing anything; you are just asking the wrong question.

Well, if these waves come from thousands of miles away, what does the local wind have to do with them? Why should it matter which direction it comes from?
Exactly. It does not matter where the wind is from or if there even is a wind. It has been said above that it is not a question of wind vs current. It is a question of wave vs current.
 

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Discussion Starter #62
I've been wanting to jump into this discussion, but haven't had time. I'll have to keep it (sort of) short for now, and can provide more details later.

This whole concept of relative motion is classic Lagrangian frame of reference, where the "observer" is a moving particle of material (liquid or solid). This can lead to great simplifications of the equations of motion, where the relative fluid motion is all that matters, independent of the absolute motion of the frame of reference.

Unfortunately, those simplifications only apply when the frame of reference is non-accelerating, and inertial forces are weak relative to other forces such as viscous friction and gravity. Factoring the equations of motion into non-dimensional variables leads to dimensionless parameters such as the Reynolds number, Peclet number, Froude number. Of the many equations and dimensionless variables, the Navier-Stokes equation and Reynolds number are most relevant here, and with low Reynolds number the equations can usually be simplified to the more simple Stokes equations that can often be solved analytically without computers. Reynolds number is the ratio of inertial forces to viscous forces:



Unfortunately the geometry of the open seas has such a large characteristic length (typically the depth of the body of water) that any motion at all leads to a high Reynolds number, meaning that flow has a lot of inertia and very little viscous dissipation. This means that the energy of fluid motion has nowhere to go except to create eddies and waves, which are basically turbulence. Flow in narrow channels (or pipes) has a much smaller characteristic length, and if it's slow enough it will have a low Reynolds number leading to laminar flow, free of any eddies. In terms of energy transport, what happens is that the two major components of flow (momentum and vorticity) both diffuse to the rigid surface that encloses the liquid, taking energy away from the liquid and preventing turbulence and minimizing waves. But in the open seas, there is no such rigid surface nearby to absorb the energy, so the water churns away.

High Reynolds number flows require the full Navier-Stokes equations, which include nonlinear terms which are what lead to the eddies and turbulence. But Lagrangian frame of reference is almost impossible in this situation, requiring Eulerian frame of reference instead (where coordinate system is at rest). Wave action thus becomes dominated by non-linear effects that are more complicated than wind speed relative to water. In such a case, 10 kt wind against 3 kt current is very different than 16 kt wind with 3 kt current.

In low Reynolds number "creeping" flows, if the force that causes the flow is removed, the motion stops instantaneously (because there is no inertia). This is the situation where relative motion is all that matters.

In high Reynolds number flows, removal of forces (such as wind that's creating the waves) will eventually allow the seas to calm, but not instantaneously. Inertia causes the waves to propagate, sometimes for days and over thousands of miles, particularly in very deep seas where the is no solid surface to absorb the momentum or vorticity. That's why a storm in the North Atlantic can cause heavy swells in the Caribbean a week later.

As for the motion of the Earth, I think the surface actually moves about 1000 mph at the equator (not 24,000 mph). IIRC, the Earth's circumference is about 24,000 miles, and it spins once every 24 hours, so 24,000/24=1000.

The reason why Lagrangian frame of reference works on land (despite the high speed) is that the land mass of the Earth is a solid, and solid mechanics are different from fluid mechanics.
I don't understand what the Reynold's number has to do with this. I believe that an excellent approximation to the situation of waves and wind happening within the top ~10' of the surface of an ocean that is thousands of feet deep is to simply assume that the ocean is infinitely deep. No Reynold's number then. Then we have the much simpler situation of current in this ocean going into one direction, and wind either going in the same direction or the opposite one. If you want to talk frames of reference, it is neither Lagrangian nor Euclidean but just Galilean (with Galilean transformation between them, ie vector addition). Right?
 

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Discussion Starter #63
I'll try to elaborate on my prior message with a few targeted responses.

The frame of reference does matter, because it cannot be accelerating. If you were to pick a tiny element of water as your frame, it would be moving around in circles and getting faster and slower. Both are examples of acceleration, so the simplifications of only considering relative motion cannot completely describe all the energetics that are going on.

I'm not sure that Einstein has proven what you are claiming. Don't forget that the fundamental concept of special relativity is that speed of light appears to be the same regardless of frame of reference. That's a totally different thing from what we're discussing, but it is a good example of a situation where traditional Newtonian mechanics breaks down. It's also another example where "common sense" can lead us astray.
Well, I talked about Einstein because everybody associates relativity with that name. Of course what we are talking about is classical Newtonian mechanics and Galileo and Newton were well-familiar with that. Einstein was simply more consistent and got rid of the 'crutch' of Newton's 'fixed stars' reference frame, or (until Michelson-Morley) the 'ether' reference frame. So, I do maintain that Einstein has proven what I am claiming, even more thoroughly than all these other people before him, by showing that relativity applies EVEN for light, not only for water waves etc that everybody before would have agreed that only relative motion applies
 

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Discussion Starter #64
So yes, the wind direction can be a bit of a red herring, what matters is the direction the waves are traveling relative to the current, not so much the wind.
Is that what it is? So should we NOT talk about wind vs current but waves vs. current, where waves are NOT the ones generated by the wind that we are seeing but due to some far-distant source? Maybe it is but it is not what everybody seems to be saying. From this you certainly would not derive rules like 'any amount of Northern wind in the Gulf Stream is to be avoided.' This rule is about (local) wind.
 

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Discussion Starter #65
You are not missing anything; you are just asking the wrong question.



Exactly. It does not matter where the wind is from or if there even is a wind. It has been said above that it is not a question of wind vs current. It is a question of wave vs current.
Then why are sailors warned about Northern winds in the (North-setting) Gulf Stream? They should be warned about wave trains coming from New England or Greenland or something. But that is not the case.
 

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I don't understand what the Reynold's number has to do with this. I believe that an excellent approximation to the situation of waves and wind happening within the top ~10' of the surface of an ocean that is thousands of feet deep is to simply assume that the ocean is infinitely deep. No Reynold's number then. Then we have the much simpler situation of current in this ocean going into one direction, and wind either going in the same direction or the opposite one. If you want to talk frames of reference, it is neither Lagrangian nor Euclidean but just Galilean (with Galilean transformation between them, ie vector addition). Right?
No, the approximation that you describe is that of an infinite Reynolds number. You can simplify the equations of motion using that approximation if you choose to neglect all the other forces such as viscous drag and gravity.

However, the basic equations of motion only apply in a non-accelerating reference frame. If your frame of reference is accelerating, as it would be following a water molecule, there are additional fictitious forces that also must be considered, and render your suggestion of just considering the difference between the velocity of wind and water an incorrect formulation of the problem. A couple of simple examples of these forces are centrifugal force in a frame of reference that is spinning rapidly, or the (weak) Coriolis force in the slowly spinning reference frame of a spot fixed to the Earth. The forces emanating from the chaotic motion of a water molecule in the ocean would be very complicated, rendering the resulting solution intractable.
 

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Yes, you will get this effect at the mouth of the Potomac. We got the snot beat out of us on the way home from Annapolis one time (we live off the lower Potomac). The waves were not huge, maybe 4 or 5 feet or so, but the period was so short that they were square. We rattled that boat so much that an electrical wiring harness in the engine compartment came apart. This was on a 41' sailboat. What was interesting is that there was a traditional Chesapeake deadrise work boat that went past us and with that sharp bow just cut right through the chop. It was a miserable couple of hours, especially since it was our first day with the boat and we were just trying to bring it home!

Gerhard
Thanks! Gerhard, Great answer, makes perfect sense. Any idea how far out into the bay you'd have to go to avoid this?
 

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I'm not sure I can answer that question. Sorry. Seas on the bay can be steep and close together everywhere and where the effect of the outflow of the Potomac stops, I am really not sure. I would guess that if you were out as far as the main channel things would moderate, but again, not sure and you can get clobbered anywhere.

Gerhard
 

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Then why are sailors warned about Northern winds in the (North-setting) Gulf Stream? They should be warned about wave trains coming from New England or Greenland or something. But that is not the case.
For the last eleven years we have spent 5 or 6 months in the Bahamas crossing over from Florida and returning to the U.S. somewhere between West Palm and Cape Fear. For planning purposes we listen to Chris Parker and check the NWS Gulf and Tropical North Atlantic Briefing daily. I recommend that if you can listen to Chris Parker on HF in the morning, do so. He describes the Gulf Stream crossing conditions daily including the "why". You could also check out Gulf and Tropical Atlantic WX Briefing Package where you can see the wave and wind fields and develop an idea of their properties, extent, and interrelation and also ftp://tgftp.nws.noaa.gov/data/forecasts/marine/coastal/am/amz671.txt for a south Florida Gulf Stream wave forecast. It will take two weeks or so to see a whole cycle of the weather.

Bill
 

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Discussion Starter #70
No, the approximation that you describe is that of an infinite Reynolds number. You can simplify the equations of motion using that approximation if you choose to neglect all the other forces such as viscous drag and gravity.
Yup, that is exactly what I meant when I said 'no Reynolds number'. There simply is no body in the system that has a characteristic length so the concept of the Reynolds number makes no sense/is not applicable.

However, the basic equations of motion only apply in a non-accelerating reference frame. If your frame of reference is accelerating, as it would be following a water molecule, there are additional fictitious forces that also must be considered, and render your suggestion of just considering the difference between the velocity of wind and water an incorrect formulation of the problem. A couple of simple examples of these forces are centrifugal force in a frame of reference that is spinning rapidly, or the (weak) Coriolis force in the slowly spinning reference frame of a spot fixed to the Earth. The forces emanating from the chaotic motion of a water molecule in the ocean would be very complicated, rendering the resulting solution intractable.
The laws of motion apply in all frames of reference, accelerated or not. These additional 'ficticious forces' are simply ways to describe the dynamics of the system in a simple way. E.g. the Coriolios 'force' is not a force at all, it only makes it easier to understand the motion of a liquid (air) on a rotating sphere. If you are sitting on the sphere (in the frame of reference you are referring to), you can pretend that there is such a mysterious force and then the observed behavior of the air is explained in a simple way.

Let's do what Einstein did and do a Gedankenexperiment (thought experiment). Let's imagine a pot of water without a lid on top of a train (he loved to think about trains, of course ideal trains without vibrations from wheels and such details) going at 10 MPH. There is no wind, therefore the air is moving relative to the surface of the water at 10mph and creates little wavelets. If now, instead, you stop the train and start a fan that generates a 10mph wind, the speed of the water relative to the water is exactly the same, so the pattern of wavelets must be exactly the same. Why do we know that? If that were not the case, you would have an absolute frame of reference, ie if there were in fact a difference in wave patterns, you could use this difference to determine the absolute speed of the train relative to some imaginary frame of reference. Newton, in fact, thought that such an absolute frame of reference exists ('the fixed stars') but Einstein showed that there is none. Therefore, the wave patterns on our imaginary train must be the same in the two conditions.

My question remains, why is it that this does not seem to be the case in the practical situation of wind against current in the ocean, or even a river?
 

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Discussion Starter #71
For the last eleven years we have spent 5 or 6 months in the Bahamas crossing over from Florida and returning to the U.S. somewhere between West Palm and Cape Fear. For planning purposes we listen to Chris Parker and check the NWS Gulf and Tropical North Atlantic Briefing daily. I recommend that if you can listen to Chris Parker on HF in the morning, do so. He describes the Gulf Stream crossing conditions daily including the "why". You could also check out Gulf and Tropical Atlantic WX Briefing Package where you can see the wave and wind fields and develop an idea of their properties, extent, and interrelation and also ftp://tgftp.nws.noaa.gov/data/forecasts/marine/coastal/am/amz671.txt for a south Florida Gulf Stream wave forecast. It will take two weeks or so to see a whole cycle of the weather.

Bill
Bill, I don't doubt that the phenomenon exists. I just want to understand WHY it exists!
 

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Let's do what Einstein did and do a Gedankenexperiment (thought experiment). Let's imagine a pot of water without a lid on top of a train
Your example of a pan of water on a train has a very small characteristic length (size of the pan), making it very different from the middle of the sea. It's really irrelevant to unbounded seawater with wavelengths and inertial forces that are millions of times larger.

The laws of motion apply in all frames of reference, accelerated or not. These additional 'ficticious forces' are simply ways to describe the dynamics of the system in a simple way.
The laws of motion are differential equations that describe the dynamics of the system, basically a 4-dimensional force balance (3-D space + time). If you adopt an accelerating frame of reference, there must be additional terms (commonly referred to as fictitious forces) or the equations will not get the correct answer. Do not belittle the importance of these additional terms with words like "simple" and "pretend". The additional terms are essential, and if you don't include them you'll get a wrong answer (unless dimensional analysis proves that they're negligible). And I guarantee that when trying to model chaotic phenomena like ocean waves and turbulence, they are anything but simple.

Yup, that is exactly what I meant when I said 'no Reynolds number'.
This is still wrong. Reynolds number is the ratio of inertial forces to viscous forces. You have both in this situation. Inertia is huge because of the nearly infinite length scale. But you cannot neglect viscous forces either, because it is viscous drag of the wind against the water surface that transfers momentum across the boundary layers from air to water. If you assume no viscous forces, the equations of motion would predict that the wind has no effect in stirring up the water, which is clearly incorrect.

My question remains, why is it that this does not seem to be the case in the practical situation of wind against current in the ocean, or even a river?
You keep repeating this question, and the answer is hiding in plain view in my posts. If you consider motion of air relative to a molecule of water in the ocean (which is the Lagrangian frame of reference that you are proposing), your frame of reference is accelerating, so there are additional nonlinear terms in the equations of motion besides the simple difference between air and water speed. Those additional nonlinear terms are what explains the chaotic waves, eddies, and currents that can propagate over thousands of miles and cause the ocean to continue churning for many days after the wind dies down. If you don't accept these additional nonlinear factors, you will continue asking the same question without getting a correct answer.
 

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Discussion Starter #73
Your example of a pan of water on a train has a very small characteristic length (size of the pan), making it very different from the middle of the sea. It's really irrelevant to unbounded seawater with wavelengths and inertial forces that are millions of times larger.
Ehm, no. Nowhere did I say anything about the size of the pan, or rely on it at any point in the argument. Remember, we are doing a Gedankenexperiment. Imagine the pan being a thousand miles wide, or a million if you want.

The laws of motion are differential equations that describe the dynamics of the system, basically a 4-dimensional force balance (3-D space + time). If you adopt an accelerating frame of reference, there must be additional terms (commonly referred to as fictitious forces) or the equations will not get the correct answer. Do not belittle the importance of these additional terms with words like "simple" and "pretend". The additional terms are essential, and if you don't include them you'll get a wrong answer (unless dimensional analysis proves that they're negligible). And I guarantee that when trying to model chaotic phenomena like ocean waves and turbulence, they are anything but simple.
Yes, the laws of motion are 4 dimensional PDEs, and they describe everything there is to know. When interpreting the results you get from them, it is often helpful for us to introduce imaginary 'forces' to get an intuitiive understanding (I don't belittle that, it is helpful). But that does not mean there actual forces. Everything is described in the equations, there is nothing 'additional.'

This is still wrong. Reynolds number is the ratio of inertial forces to viscous forces. You have both in this situation. Inertia is huge because of the nearly infinite length scale. But you cannot neglect viscous forces either, because it is viscous drag of the wind against the water surface that transfers momentum across the boundary layers from air to water. If you assume no viscous forces, the equations of motion would predict that the wind has no effect in stirring up the water, which is clearly incorrect.
Sorry, this is wrong. The Reynold's number has no meaning if there is no characteristic length in the system, like the diameter of a tube, the size of an airplane wing etc. The derivation on the wikipedia page is pretty nice and correct, see
https://en.wikipedia.org/wiki/Reynolds_number. It is incorrect that 'inertia is huge because of the nearly infinite length scale.' If you do not have a characteristic length the whole concept is meaningless and this statement is simply wrong.

That has nothing to do with neglecting inertia: the forces due to inertia acting on a local scale do not become infinite because the system is infinite.

You keep repeating this question, and the answer is hiding in plain view in my posts. If you consider motion of air relative to a molecule of water in the ocean (which is the Lagrangian frame of reference that you are proposing), your frame of reference is accelerating, so there are additional nonlinear terms in the equations of motion besides the simple difference between air and water speed. Those additional nonlinear terms are what explains the chaotic waves, eddies, and currents that can propagate over thousands of miles and cause the ocean to continue churning for many days after the wind dies down. If you don't accept these additional nonlinear factors, you will continue asking the same question without getting a correct answer.
Sorry for repeating the question, I wanted to keep the discussion on track. If that is annoying, I won't do it again.

But as I said before, the equations of motion describe the whole physics. Period. Of course there is turbulence but that does not make the system violate relativity. Again, if by blowing water over air you could determine ABSOLUTE motion relative to some fixed reference frame, the system would violate (special) relativity. As we know since Michelson and Morley (and explained by Einstein), this is incorrect. You can introduce as many nonlinear term in the description as you want, but none of that will violate relativity.
 

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Ehm, no. Nowhere did I say anything about the size of the pan, or rely on it at any point in the argument. Remember, we are doing a Gedankenexperiment. Imagine the pan being a thousand miles wide, or a million if you want.



Yes, the laws of motion are 4 dimensional PDEs, and they describe everything there is to know. When interpreting the results you get from them, it is often helpful for us to introduce imaginary 'forces' to get an intuitiive understanding (I don't belittle that, it is helpful). But that does not mean there actual forces. Everything is described in the equations, there is nothing 'additional.'



Sorry, this is wrong. The Reynold's number has no meaning if there is no characteristic length in the system, like the diameter of a tube, the size of an airplane wing etc. The derivation on the wikipedia page is pretty nice and correct, see
https://en.wikipedia.org/wiki/Reynolds_number. It is incorrect that 'inertia is huge because of the nearly infinite length scale.' If you do not have a characteristic length the whole concept is meaningless and this statement is simply wrong.

That has nothing to do with neglecting inertia: the forces due to inertia acting on a local scale do not become infinite because the system is infinite.



Sorry for repeating the question, I wanted to keep the discussion on track. If that is annoying, I won't do it again.

But as I said before, the equations of motion describe the whole physics. Period. Of course there is turbulence but that does not make the system violate relativity. Again, if by blowing water over air you could determine ABSOLUTE motion relative to some fixed reference frame, the system would violate (special) relativity. As we know since Michelson and Morley (and explained by Einstein), this is incorrect. You can introduce as many nonlinear term in the description as you want, but none of that will violate relativity.
You did say something about the size of the pan. You asserted that there are “tiny wavelets”, which I agree would exist in a small pan. If the pan is a thousand miles wide (and deep) motion would be dominated by large waves and eddies, as predicted by a large Reynolds number.

There is a characteristic length scale in the ocean. It’s the depth, which is very large but not infinite. Flow is dominated by eddies and waves, as with high Reynolds number flows.

Your continued invocation of Einsteinian relativity is an unnecessary complication. Velocities are nowhere near the speed of light, and gravity is 1G. Newtonian mechanics is sufficient to model this phenomenon, but it must include the nonlinear inertial terms, which is why the simple difference between air and water current do not fully describe the wave motion. Due to inertia, the relative direction causes a different behavior for 10 kt relative co-directional flow than 10 kt counter-directuinal flow. None of this violates relativity, or any other laws of physics.

Even Einstein’s Special Relativity requires selecting a non-accelerating reference frame, or the laws of physics are different (additional terms for fictitious forces):

Albert Einstein, in his theory of special relativity, determined that the laws of physics are the same for all non-accelerating observers
https://www.space.com/17661-theory-general-relativity.html

Your suggestion of setting the frame of reference moving with a single molecule of water would be an accelerating frame of reference due to the chaotic motion of the water.
 

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Then why are sailors warned about Northern winds in the (North-setting) Gulf Stream? They should be warned about wave trains coming from New England or Greenland or something. But that is not the case.
When asking a question about the *physics* of steepened waves, you must get the physical terms exactly right in order to get a meaningful answer; when asking a question about practical *sea conditions*, you will hear people use the terms of weather instead. At the time scale in which people create weather reports, and hear weather reports, and cast off, and get out to sea, the wind conditions are highly predictive of wave conditions. Hence its good enough to use rules of thumb (like the one talking about "northerly a component of wind near the Gulf Stream").

BTW, although they don't say "coming from Greenland", a good marine report will indeed mention the height, period, and direction of large swells.
 

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Discussion Starter #76
You did say something about the size of the plan. You asserted that there are “tiny wavelets”, which I agree would exist in a small pan. If the pan is a thousand miles wide (and deep) motion would be dominated by large waves and eddies, as predicted by a large Reynolds number.

There is a characteristic lenght scale in the ocean. It’s the depth, which is very large but not infinite. Flow is dominated by eddies and waves, as with high Reynolds number flows.

Your continued invocation of Einsteinian relativity is an unnecessary complication. Velocities are nowhere near the speed of light, and gravity is 1G. Newtonian mechanics is sufficient to model this phenomenon, but it must include the nonlinear inertial terms, which is why the simple difference between air and water current do not fully describe the wave motion. Due to inertia, the relarive direction gets a different behavior for 10 kt relative co-directional flow than 10 kt counter-directuinal flow. None of this violates relativity, or any other laws of physics.

Even Einstein’s Special Relativity requires selecting a non-accelerating reference frame, or the laws of physics are different (additional terns for fictitious forces):



https://www.space.com/17661-theory-general-relativity.html

Your suggestion of setting the frame of reference moving with a single molecule of water would be an accelerating frame of reference due to the chaotic motion of the water.
You are right in your first point, I did refer to the size of the container. I should not post at 2 am, did not read my own text (wiping some egg from my face :rolleyes:)

Unfortunately this is a very busy time for me and I can't reply now in detail. It may take until after the holidays that I will find the time. I agree with you that special relativity is likely not needed to understand this (though I don't agree with your statement that SR is valid only in non-accelerated frames, this is a common misconception). But the laws of physics are the same in all frames of reference, accelerating or not, and there are no 'forces' that are not described by the equations of motion. Everything else is a violation of relativity, even Galilean.
 

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But... if you are at beach and watch the waves breaking, wind DOES make a lot of difference.

With onshore winds, roughly the same direction of the wave trains, the waves tend to break earlier, less steep and crumbling from the top, releasing energy more gradually. With offshore winds, the waves tend to get steeper and break harder, forming tubes and releasing a lot of energy in one go.

So, the effect of the wind on the waves is somewhat similar to the effect of the current.



Cheers,

Ismael :ship-captain:
 

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Been away for a bit. Wow, this is still not settled. Maybe its because there is more to the earth, wind and sea than molecules and momentum. Im happy to just go with that, and know that the condition exists.
Mic drop.
 

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Discussion Starter #80
Sorry for being quiet for a week. I have now some time to reply to your posting.

You did say something about the size of the pan. You asserted that there are “tiny wavelets”, which I agree would exist in a small pan. If the pan is a thousand miles wide (and deep) motion would be dominated by large waves and eddies, as predicted by a large Reynolds number.

There is a characteristic length scale in the ocean. It’s the depth, which is very large but not infinite. Flow is dominated by eddies and waves, as with high Reynolds number flows.
First, again my apologies for not reading my own text. You are right of course that I implicitly referred to the size of the pan ('tiny wavelets'). But I believe it does not make a difference, see further down.

As for your second argument, I would argue depth is NOT a characteristic length scale in the ocean as far as wind-driven waves are concerned. The depth is so large that it is in fact infinite as far as these waves are concerned because they do not interact with the bottom. In other words, the waves would have identical behavior if the ocean were infinitely deep as if it were, say, 1Km deep. In other words, you could not distinguish at the surface between the two conditions.

You are of course right that there is turbulence in the wave layer but this is not captured by the standard Reynolds number which is relative to the dimension of some fixed object, like the diameter of a pipe or an air foil. I do not know enough hydrodynamics to give a precise definition what it is in the case of ocean waves but I believe it is something like the distance between the ocean surface and the boundary layer between turbulent and non-turbulent flow (perhaps the van Dorn book that you recommended addresses this; I have received it but it came just before I flew out and I am now on a different continent, so I can not consult it). This boundary layer is not a fixed object so the simple derivation of Re from the Wikipedia article does not apply. But in any case, the ocean floor can not be the 'object' used in the derivation of Re because then it would mean that the whole ocean is turbulent. Instead, turbulence occurs only in a very thin layer (on the order of 10m), everything below that is laminar.

Nevertheless, in spite of differences in the details, I think we agree in the main part, namely that there is turbulent flow at the top of the ocean. However, I believe this does not address the question of relative motion, see below.


Your continued invocation of Einsteinian relativity is an unnecessary complication. Velocities are nowhere near the speed of light, and gravity is 1G. Newtonian mechanics is sufficient to model this phenomenon, but it must include the nonlinear inertial terms, which is why the simple difference between air and water current do not fully describe the wave motion. Due to inertia, the relative direction causes a different behavior for 10 kt relative co-directional flow than 10 kt counter-directuinal flow. None of this violates relativity, or any other laws of physics.

Even Einstein’s Special Relativity requires selecting a non-accelerating reference frame, or the laws of physics are different (additional terms for fictitious forces):

https://www.space.com/17661-theory-general-relativity.html

Your suggestion of setting the frame of reference moving with a single molecule of water would be an accelerating frame of reference due to the chaotic motion of the water.
OK, there is more to answering this than I want to type here. You are right that you don't need Einstein's theory of relativity. As far as 'Newtonian mechanics' it depends on what you understand by it. Newton seemed to believe that there is an absolute frame of reference (the 'fixed stars' that I referred to earlier) which he thought was necessary to explain, e.g. that if you rotate a bucket of water around its long axis the water will climb up the walls. In contrast, if you imagine that you yourself accelerate around the bucket, you might get dizzy but you will not see the water rise up the walls of the bucket. His explanation was that this difference arises because the bucket moves relative to this absolute frame of reference. To make this mathematically treatable, 'fictious forces' were introduced in the presence of acceleration (not sure if Newton did this already, I am not a historian of science). Many have argued that this makes not much sense (like Ernst Mach, and even before that) but it was Einstein who made everything crystal-clear.

The laws of physics are the same in all frames of reference, accelerating or not. It is a common misconception that special relativity only applies to non-accelerating frames of reference. The first sentence in the space.com site that you refer to, "In 1905, Albert Einstein determined that the laws of physics are the same for all non-accelerating observers" is correct but misleading: the laws of physics are also the same for all ACCELERATING observers. A few lines down in that article is a sentence that is clearly wrong: "Einstein then spent 10 years trying to include acceleration in the theory and published his theory of general relativity in 1915". This is nonsense, the difference between special and general relativity is not that the first does not include accelerating frame but that the first is valid in the special case of a flat space-time, ie in the absence of gravity (or constant gravity), and the latter does include gravity.

This issue of fictional forces is explained at https://en.wikipedia.org/wiki/Inertial_frame_of_reference. I can't explain it shorter or better than they do. The most important sentence from that essay is this:



"In practical terms, the equivalence of inertial reference frames means that scientists within a box moving uniformly cannot determine their absolute velocity by any experiment. Otherwise, the differences would set up an absolute standard reference frame.[21][22]" Ref. 21 is Einstein's book, ref 22 is a collection of lectures by one of my favorites, Dick Feynman (I had the pleasure of seeing him lecture in person, he was even more clear then than in the books that collect his lectures in writing). Neither is easy reading but Feynman starts at the basics and the book is available for free: https://nirstern.files.wordpress.com/2016/04/six-not-so-easy-pieces.pdf.

The sentence in red is one of the foundations of physics, just like the conservation laws of mass/energy, momentum etc. No violation of them has ever been found so we take them as gospel. Therefore, imagine you have a mass of water large enough that you can neglect the effects of its boundaries (which otherwise would establish a frame of reference) with a given current (vector) of velocity v_c. Now you blow wind over it, say with a strength v_s in the same direction as the current. The relative velocity of the wind over the water is (v_s-v_c). This will create some kind of wave pattern. Now take the same ocean with current velocity 0 and wind velocity v_s-v_c (same values as before). The wave pattern (and anything else) must be IDENTICAL in the two cases. Because, if that were not the case, we could define an absolute frame of reference, e.g. as that one that generates the first wave pattern. This is impossible. Therefore, any complications that you introduce (nonlinear interactions, fictitious forces, whatever) that you introduce can not violate any of these fundamental laws. If they do, something is wrong with these additions.
 
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