Oops. I mean “time derivative,” not “gradient.”
Think of a hurricane, which is a very large vortex. The hurricane has mass and it moves, so it has momentum. But is not a discrete object; some air near the hurricane gets caught in the vortex, other air within the hurricane gets ejected out. The air around it has low pressure, so air from other regions flows in to create equilibrium. If you look at the entire atmosphere, there is zero net momentum, but that doesn’t mean that any given parcel has zero net momentum.
Quantguy Thanks for summarising the new direction of this thread.
I dont buy Apex Rogers and QED’s explanations.
Forget vortexes and torroids for the moment. Consider a puff of air moving throught the air (easy thought-experiment for smokers). Make it spherical for simplicity.
The puff is moving forward.
Air in front of the puff is moving back around the puff (lamillar flow) and closing in behind the puff. The amount displaced is the same volume and thus (ignoring compression) same mass as the puff.
The overall momentum of the system is zero, however there is a concentration of momentum (or energy) in the movement of the puff. The backward flow is dissipated around the spherical puff.
When the puff encounters an object, the momentum is concentrated in one spot. Look at a cross section of the puff (90 deg to motion) as it encounters a surface. The velocity gradient (vector parallel to motion) is greatest inside the puff, whereas the negative velocity is much less and spread out around the boundary of the puff.
This is pretty much what I was saying, only you’re confusing the frame of reference, just like the OP. The puff is moving through the air, displacing it; the air is not moving backward around the puff, since there is no force acting on it to cause it to.
So the pressure exerted by the puff (force/area) against the surface is greatest at the centre of the puff, the outside air produces insignificant backward pressure against the surface.
bbeaty I just re-read your OP about boats adn oars, with the discussion of vortexes in mind. I can just imagine your boat with an air cannon out the back propelling itself by fireing smoke rings backwards. Like something off whacky races. 
Why is sand different from a fluid. Shear forces are transferred though the fluid like you say. And you could argue that sand is fluidised when running over it.
I will have to read your treatise on flight in more detail.
Please do. But think about what he’s saying in it. I interpretted it as saying the vortices are actually responsible for holding the plane up. This is almost as scary (but at least not as easy to convince someone) as the thought that airplane wings work through simple deflection of air.
Vortices are losses and undesirable. They exist because a relative inflexible and undeformable object (wing/oar) are moving through a low viscosity fluid. SOME fluid flows from the high pressure side to the low pressure side around the edges. This creates a circular motion and the vortex is born. This is energy created by the wing/oar that doesn’t contribute to lifting/propulsion, instead it is dissipated by setting in motion the fluid around it.
Let’s get the causality right.
I’ll agree that vortices are undesireable, but necessary losses. I was arguing the point that vortices do carry momentum, not that they are the sole carriers of momentum in the systems cited in the OP. Just to clarify my position.
The energy in a vortex created in this way is balanced (at least in part) by drag on the object that created it. An oar is only useful if it has very high drag, so in this case wouldn’t the vortices be desirable? This is a minor point, but for a wing you want to decrease drag by decreasing any losses which lead to drag. For an oar, you want to increase drag as much as possible, or, more precisely, set the drag so that it is just possible to move it through the water with the available force at the desired rate.
This is the crux. Equal rearward flow. Zero net momentum. And it’s rubbish. As I said above:
The equal “rearward” (and probably should read “retrograde”) flow is only a flow of mass. Not of momentum. The mass might be the same, but the velocity definitely is not. The exhaust from a SR-71 simply *does not * ultimately flow forward (retrograde) at supersonic speed.
Granted that the oar and a wing are doing different things. But consider this:
if the water had infinite viscosity (ok, so then the oar couldn’t get into the water, but let’s use our imaginations…) then the oar would remain stationary relative to the water, and ALL the energy of the stroke would go towards moving the boat forwards. As the viscosity of the fluid drops, some of the fluid escapes from the stroke by flowing around the oar (losses). The stroke loses efficiency, and this fluid flow around the oar creates the vortex.
Of course vortices carry momentum.
They are a moving mass. It isn’t any more difficult than that.
That’s what I’ve been trying to say, but the OP can’tquite graps why. Maybe you can word it better than I have thus far.
ok…I’ll take a stab…
There are really two things that confuse the issue. First, we’re talking about an air vortex moving in air, or a water vortex in water. You have to separate the vortex from the rest of the fluid to think about it.
Second, the frame of reference can be confusing. A stationary vortex can contain a lot of energy, but if you draw your boundary layer outside the entire vortex, there is no apparent motion and therefore no momentum. Particles inside the vortex, though, all have momentum; they just cancel each other out when summed. It’s just that when your frame of reference is bigger than the vortex, there is no motion at that scale.
Note that with an airplane wing, the vortices move downward and outboard, thus must have momentum beyond just the circular motion.
That’s not a frame of reference, that’s a “control volume”. If your control volume is larger than the vortex and there’s no flow across the boundary of the CV then there’s no momentum exchange.
A frame of reference is the system of axes you use to measure spatial coordinates. An inertial reference frame can be moving as long as it’s not accelerating, so it is common to use a reference frame moving with an object to study an object. This is why wings are often modeled as stationary with air flowing past them when in the “real world” reference frame, the air is stationary and the wing moves through it.
The biggest problem in this thread seems to be a confusion on reference frames. Several posters indicate that the ambient fluid rushes backward past a moving object whether that object is a wing, a baseball in a pipe, or a vortex. This is true in a reference frame which moves with the object you’re studying, but if you’re trying to look a momentum balances in a fixed (non-moving) reference frame then you have to realize that the “rushing backward” fluid is actually stationary or actually moving forward at a velocity slightly less than the moving object. From the point of view of the object, the fluid is moving backward, but you can’t take “backward” velocities from that reference frame and use them to compute momentums in another fixed reference frame.
A moving vortex has momentum. All the rotational momentums cancel out, but the fact that the vortex is moving as a whole means all those fluid elements have a velocity component in the direction the vortex is moving in addition to their rotational component. There is no ambient fluid rushing backwards past the vortex to balance the momentum of its bulk motion. If you want to look at a reference frame moving with the vortex (assuming the vortex isn’t accelerating) then you get exactly the same answer. In this case there is fluid rushing past the vortex but the vortex itself is fixed. You can set your reference frame in any way that makes the calculations convenient, but you can’t take measurements from one frame and use them in calculations for another.
In retrospect, I can see how my bold “exactly” in the above post might be misinterpreted. My point is that you cannot pick a reference frame to conveniently zero the momentums. If you pick a fixed frame, the moving vortex has momentum. If you pick a reference frame moving with the vortex, the the ambient fluid is moving and has momentum. But you can’t combine the moving ambient fluid in one frame with the moving vortex in another frame to get zero momentum.
I’m perfectly aware of the reference frames. Even in the laboratory frame, though, there is, in fact, a movement of fluid backwards around the projectile. An extreme example might make this more clear, though the same principle applies to any closed system of incompressible fluid. Consider a cylinder, sealed at both ends. One half of the cylinder is almost completely filled with a plug, with just a little bit of clearance around it. The rest of the cylinder is filled with a liquid of the same density as the plug. So you’ve got fluid on the left end of the cylinder, and a solid plug on the right end. Now move the plug through the fluid, over to the left end. Where’s the fluid now? The right end, of course! The fluid moved from left to right, and while the plug was moving (and at all other times), there was exactly zero net momentum in the system. The same will be true in a system of any finite size, so long as the fluid doesn’t compress.
Note that you can have a concentration of momentum, which could be enough to knock over a caardboard target. You just can’t have a net momentum.
No no no. NOT the relative motion of the whole environment. I’m doing everything relative to the fixed “atmosphere” in the room in which the smoke-ring is moving.
Look, please glance at this crude animated gif:
See? Yes it’s very crude and oversimplified. But I’m trying to illustrate a point:
If the red chunk of fluid moves forward, it DISPLACES a volume of ambient fluid. The red chunk also leaves a SPACE BEHIND IT when it moves forward. Therefore, as the red chunk moves forward, there has to be an equal rearward flow, otherwise there would be a buildup of fluid on the left as the red chunk moved towards the left. (Part of the requirements is NO BUILDUP OF FLUID ANYWHERE, constant density in other words.)
Therefore if some fluid moves from right to left, other fluid MUST move from left to right.
Smoke rings are misleading because the smoke only follows the vortex core, as if the smoke-filled core was the only real motion.
Ah, I know. What if a CLEAR vortex moves through a smoke-filled room? In that case you’d be able to see the “nimbus” of rearward-flowing air which surrounds the forward-moving donut of clear air. Yes yes yes the specific molecules in that rearward flow don’t accompany the donut of air on its journy. But the PATTERN of rearward flow certainly does! And that rearward flow has momentum which is opposite to the momentum in the donut.
Maybe the momentum in the rearward flow is less than the momentum in the forward-moving donut? If so, then that’s the key to my misunderstanding. But my thought-experiments always end up showing that the momentums are equal and opposite, so the travelling vortex-pattern carries zero momentum as it goes.
I don’t think so. I’m describing “motion” relative to the atmosphere. On the other hand, if I was following the ring-vortex along as it moved, then I’d see the whole atmosphere travelling backwards, but I’d also see a pattern of air surrounding the donut which was going backwards EVEN FASTER.
Please look at that animation. Imagine trying to drag a wooden cylinder through a block of soft wet mud. The mud must get out of the way. But the cylinder tries to leave a hole behind itself in the wet mud. Mud in front of the wooden cylinder has overpressure, and mud behind has underpressure, so the mud flows backwards to occupy that space being vacated by the cylinder. It’s not a backwards flow relative to the cylinder, instead it’s a backwards flow relative to the whole block of mud! In other words, the wooden cylinder TRADES PLACES with the volume of mud ahead of it, and as the cylinder goes forwards, it trades places with mud which flows backwards to fill the volume where the cylinder had been. Wood cylinder forward, “mud cylinder” backward.
bbeaty, I can’t seem to get your animated gif to load properly, only the first image shows. with that in mind, it is my impression from what you said that the backward flow moves at the same rate as the forward moving vortex. This is not the case; the flow moving to replace the void from the particles displaced by the moving vortex will fill it in at a slower rate than the vortex, thus achieving a net momentum for the system.
I’ve never been confused. I suspect that you never viewed the animated GIF that I mentioned early on in this thread. Sixteen animation frames are worth 16,000 words?
Yes, the smoke-filled vortex core does move across the room. But as I understand it, the core is surrounded by a pattern of genuine rearwards flow, (rearwards motion relative to the unmoving distant parts of the atmosphere), yet the PATTERN of rearwards flow moves forwards and accompanies the smoke-filled vortex.
Just because the air in the room isn’t filled with smoke, that doesn’t mean it’s a vacuum! The smoke-filled vortex ring cannot move forward because there is air in the way. Can it push that air out of the way? No, because it would have to compress the air to do so. However, the air immediately ahead of the smoke-filled part of the vortex can move backwards at the same time as the smoke-filled air moves forwards. That way no overpressure is created ahead of the vortex, and no underpressure is created behind it. The smoke-filled air trades places with the non-smoky air immediately ahead. But to do this the non-smoky air has to move backwards when the smoke-filled air moves forwards.
When you shoot a smoke-ring across a room, you cannot see this backwards-moving region of air. After all, it doesn’t contain any smoke! However, this region of backwards-moving air accompanies the smoke-ring on its journey. The backwards-moving region is not air, it’s not travelling mass, instead it’s a PATTERN OF MOTION. But this pattern of motion carries some momentum with it. And since the mass-parcels within this moving pattern are travelling backwards relative to the rest of the atmosphere, this means that the momentum in the travelling pattern is opposite to the momentum in the forward-moving smoke-filled region of the vortex.
Another very crude GIF animation:
