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post #61 of 80 Old 12-10-2018
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Re: Why is wind against current a problem?

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Originally Posted by MastUndSchotbruch View Post
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.

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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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Re: Why is wind against current a problem?

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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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Re: Why is wind against current a problem?

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Originally Posted by TakeFive View Post
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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Re: Why is wind against current a problem?

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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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Re: Why is wind against current a problem?

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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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Re: Why is wind against current a problem?

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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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Re: Why is wind against current a problem?

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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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Re: Why is wind against current a problem?

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.

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Re: Why is wind against current a problem?

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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/foreca.../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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Re: Why is wind against current a problem?

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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.

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Originally Posted by TakeFive View Post
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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