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.
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?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:
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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.
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
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.
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.
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.
Thanks! Gerhard, Great answer, makes perfect sense. Any idea how far out into the bay you'd have to go to avoid this?
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.
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.
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.
Bill, I don't doubt that the phenomenon exists. I just want to understand WHY it exists!
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 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.
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.
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.
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
Sorry for repeating the question, I wanted to keep the discussion on track. If that is annoying, I won't do it again.
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.
https://www.space.com/17661-theory-general-relativity.html
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").
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
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Yes, nothing has changed. This horse is still dead.
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.
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.
