Thanks for the video! Very nice and well prepared explanation. Small remark - curl should be written as det of the matrix, or straight lines instead of the square brackets.
Hi Brian Storey Thanx for this excellent video on vorticity.But I am getting a problem in understanding Why red vortex pushes blue vortex forward ? Is there any mechanism through which I can guess why one vortex has an effect on other vortex. Thanx
:top side of the cross is having lower velocity than the velocity on the bottom side? Is it correct statement at 8:35 timestamp? shouldn't it be the other way around?
Professor in thin airfoil theory one of our assumption that we impose is that fluid is inviscid , then how we able to model vorticity in airfoil , shouldn't it be 0 as we have already said that okkk fluid is inviscid
Also..with the wave the change in direction of one arrow on the streamline cannt determine whether its vorticity free, we would need a second arrow perpendicular to it to see what the average of the two angular velocity is. Orienation of one may not change but the other may like in the boundary layer :)
Excellent video At 01:00 you are taking the determinant of the 3x3 matrix: You should put the matrix between two vertical lines to signify taking the determinant, or instead write "det" at the start of that line, because at the moment your equations is false. At 02:00 I prefer the simpler definition of circulation as Γ=int[v.dt] where dl is your differential tangent vector, equal to the unit tangent vector.differential element.
Well explained. But I have a doubt. At time stamp 24:45, wouldn't the pink and the green vortices have any effect on the red and the blue ones respectively as how the reverse is true? And then wouldn't the red and blue ones move more outwards rather than translating in the same horizontal direction?
Yes - all the vortices act on each other. The dominant interaction is from the closest ones, which I think I got right here. So the argument isn't 100% of the story, but I think I got the basic one correct. It is a pretty complex situation, but the basic phenomena I describe is what you observe in the lab. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Yydb9Mqg9TY.html
Thanks for the video Brian. Question 1. Does the material derivative of vorticity remain zero in the situation where spoon is accelarated (you assumed that total circulation remains zero)? Can the trailing vortices be generated witbout viscosity at all for you to apply Eulers? 2. Even with zero viscosity we must follow the same material points as you mentioned. In the example of accelerating spoon are you following the same material points? It seems like you just have one big circle and look at its content at two times. This is a control volume so it doesnt contain the same material points.
You cannot create vortices without viscosity. Once vorticity is created, we often can then start to ignore viscosity. So you can't really start to think about the material derivative of vorticity (in Euler's equation) until AFTER you have created the vorticity. In the spoon example, the idea is that we are looking at the whole loop to consider what is inside the loop, in total. The loop is far from the spoon. We also consider that the loop moves with the fluid - i.e. it is a material loop. Since the loop is far away, it basically stays fixed in space. Also, since the loop is far from the spoon assuming that viscosity is unimportant along that path seems like a reasonable thing to do. The weird thing is that for considering the circulation, we only really need to pay attention to what is happening along the loop of interest. Since there is zero NET initial vorticity in the loop when the spoon is still there is zero NET vorticity after. The circulation theorem only says the positive and negative must balance, it tells us nothing about the magnitude of the vortex. So considering the circulation explains what we see qualitatively, but not much else. Hope this helps and clears some things up.
Thanks. Perhaps I can ask my question this way: Is there a restriction on the use of the circulation theorem such that the fluid within should be free of viscosity. That means you can only apply the theorem once these vortices are created not before and then after.
What happens if you take the spoon and stir the fluid cyclically? It seems obvious that there would be some induced circulation, but why does this break Kelvin's theorem?
Yes, I have thought about this problem. I don't have a really simple answer to give you. Here are two cases I have thought about. If you imagine the stirring is by a sharp edged plate spinning, like this Then you will get two clockwise vortices on the top and bottom edge. However the plate is rotating counterclockwise and will induce some counterclockwise motion. Kelvin's theorem would tell us that all this should cancel, but it is not an experiment (or simulation) I have tried. So while I believe this is what would happen, fluids are surprising and I could be wrong. If you imagine instead of taking a cylinder at rest and spinning instantly at constant speed and hold until you reach equilibrium - what is interesting is that all the circulation ever created in this flow is created in the instant that you turn the cylinder on. However, in this case viscosity is what drives the flow, thus the kelvin theorem is not valid. Like I said, I have thought about this problem a lot, but I am not totally convinced. Someday, I will work on this problem for my own curiosity.
+Matias Rabbia I think we are both right (i.e. I probably wasn't clear). When we write grad P + rho (vector g) the plus or minus sign on the gravity term is embedded in the direction of g. When we write grad( P + rho g z) this is assuming that gravity is pointing downward in the z direction. I often do get the sign confused here, but I always do the simple check of looking at the case with no velocity and then (P+rho g z) would be a constant. So if we imagine the surface of the ocean as z=0 and negative z as diving down, the expression would say that the pressure increases as I dive down, which is the way I want it to be! Hope this makes sense and sorry that the video wasn't clearer on the sign.
+charan kumar The idea is that if the airfoil is initially at rest in a still fluid, the circulation is zero - nothing is moving. As we accelerate the airfoil, the total circulation enclosed by our loop must remain zero by the circulation theorem. If the total is zero then the circulation around the airfoil balances that generated by starting.
@@charankumar2996 The problem is that it isn't. This is theoretical stuff in real life there is heat and noise escapement. The acoustics generated over a mountain range is enough to replenish the storehouses of the snow spoken of in Job 38 to 41. www.jw.org/en/library/bible/nwt/books/job/38/ Compare: www.metoffice.gov.uk/weather/maps-and-charts/surface-pressure Oh dear; I think the USA has had it already, our turn tonight!
The magnitude if the particles in captured rotation will be evident to any observer of a wave or solon(?). If it is an ocean swell, the peak to trough can be measured in feet if it is rill of a stream the wave might be minute. In all cases the particle will be self evident, be it a ping pong ball or a small boat. Today over Stoke on Trent at about 15:30 the sky was full of vorticity. Over the hills there were markedly ragged clouds with hanging tendrils, further out past Mow Cop and towards the "Cheshire Gap" (lower plain, -flat land as far as the coast, there were roll clouds that are typical signatures for tornadoes in the USA. You pays your money and you takes your choices. The planet reacts to the solar system with a phenomenon called tele-connection. ocean.si.edu/planet-ocean/tides-currents/currents-waves-and-tides-ocean-motion is a tidal connection and is misleading. The image called the global conveyor is a composite of averages not a regular stream. The stream is controlled by earthquakes in the Southern Ocean off the cost of the peninsular continents at Falklands, Madagascar and New Zealand. Seismic signals are the reaction to the action of vorticity in fluids. Where the fluid rises the seismic signals delve. The barycentres may be 80 degrees apart. On a tidal river the current over the sandbars can submerge and turn over a small fishing boat. For the moon the mass is trillions of tonnes and its period of captured rotation is 27.3 days. You do the maths, I am dyscalculiac. Pay attention to what is happening with President Trump for all the lies being told about earth sciences are designed to blind you to what is happening. Seek and you will find, do not be lisled by thieves that are apostate. Pass this information out to general discussion before the Google horde of Magog hide my words from you. Don't respond to fools by their foolishness, teach fools as best you can. If they respond badly hand them back to their father.
He goes on to describe the generation of whirlpools and volcanoes in the Fijian Triangle following the tropical storms there. Or if he doesn't, I'll smack his botty -the naughty boy!
@@brianstorey7830 At around 5 min. You have that the material vorticity derivative equals the divergence of the velocity gradient. However, the temporal component (the partial derivative of vorticity with respect to time) is missing. Steady, perhaps?
Regarding contrails, they are actually generated by the engine exhaust interacting with water molecules in the upper troposphere. I see them up close quite often, particularly on the North Atlantic Track System. The lift coefficient at cruise is actually small since the speed is so high. Also, modern winglets and wing design greatly reduce the wingtip vortex at cruise. Wingtip vortices are most obvious during takeoff and landing (the lift coefficient is necessarily high at low speed) when there is a thin fog present.
Excellent lecture. Congratulations. At 17:32 it was stated that the circulation or vortex around the airfoil section may be imaginary, but if the air velocity on the upper section of a airfoil section in flight is always greater than that on the lower surface, does that not prove that the vortex around the wing is not imaginary but very real? It is to be noted that If a rotating ball is placed in the wind or it is moved forward, it is known to have lift. So if a wing moves forward and it lifts then it must have rotation! Fascinating subject, Congratulations again.
That is a great question, and I can't really defend my position of what is real or imaginary ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-OA3WGf9pX0A.html I guess I think of it as "imaginary" because there is not a little point vortex in the middle of the wing, but the flow is very closely modeled as the airfoil flow plus the vortex. I would say the net circulation around the airfoil is very real (you could measure the velocity field and compute it using the definition of the integral). But the existence of the vortex is not really there.
Brian Storey. Sir, thank you for replying. May I forward a suggestion which could indicate that the vortex around the wing is real. Let us take a ball rotating around its centre where the circumferential velocity is 20 mph . Now if the centre of the ball is moved with a speed of 100mph "forward" then one may assume that one part of the circumference would move at 120mph while the other part diametrically moves at 80mph. This state of affair will cause the ball to lift laterally due to its spinning and its forward motion, as the banana shots by great footballers, and since my name is Pule', Pele', the talented footballer who gave such kicks, was my favourite and we are the same age! And also note that the air with respect to the ball will all move backwards now, so rather than a round ball we could now put a body with a pointed trailing edge as the relative velocities are easily accommodated even if there is circulation!!!. It is well known that a flying wing moving forward will have the air on the top surface running faster than the that on the lower surface . Well, now, the forward movement is real, the difference in velocities on the two surfaces is real............. there is lift.................. so the vortex around the wing must be real lurking hidden somewhere! Incidentally the fact that the upper and lower surface velocities at the trailing edge of a wing are different ( but assumed to be moving in a flat two dimensional plane) what would happen is that as they go past the trailing edge, where the faster velocity will be disturbed , it will go into a helical three dimensional spin so that its axial velocity will equal to the slower streamline from below the wing, where this curling needs to be done in pairs and some time later the velocity and the pressure of the stream lines will equalise at a higher pressure. If the angle of attack of the wing is increased, then this multitude of pairs of helixes or vortices at the trailing edge will exist earlier on the top surface and the wing could/will stall. It is so interesting therefore that the inseen reality around a wing includes the following. 1, As the wing moves forward from stationary position, it leaves behind it one vortex, this must be accompanied by counter rotating one circulating around the chord of the whole wing. Hence a PAIR! 2, The vortices around the wing tips do and must come in counter rotating PAIRS 3, Due to the difference in the "planar" velocities emerging from the trailing edge they will break up into a three dimensional state with heixes or votrices spinning around each other causing turbulence till their pressures and velocities equalise . These must exist in PAIRS. and it is pairs of helixes counter rotating with each other that will cause oscillations as sine and cosine waves behind and above the trailing edges. 4. The total downwash at the trailing edge from above and below the wing whose change of momentum as compared with with what it was ahead of the leading edge must be equal to the lift. Pity we cannot see all this hidden but real wonders of applied engineering..............with its associated mathematical modelling. Again thank you for replying . I remember my Grads, Divs, and Curls, in younger days but at my old age , I would rather get my mind to imagine those air particles fitting in states which cause all this wonderful behaviour. Thanks for the company!
Interesting thoughts. I think it is important (or maybe it isnt) to distinguish between a vortex and circulation. The Kelvin circulation theorem is what demands your point 1 above. So whether we call the circulation around the airfoil a vortex or not is perhaps debatable, but that the airfoil must have circulation is not debatable and is easily measured. I guess when I say that it is "imaginary" I think of how the flow field around the airfoil is commonly modeled using potential (or irrotational flow). In potential flow you take the superposition of the airfoil flow computed for irrotational flow and an ideal vortex which has particular velocity field, v_theta = \Gamma/2 \pi r. You then set the strength of the vortex so the separation happens at the trailing edge (called the Kutta condition). Now there is no real reason that this particular superposition should work and is not something we can prove - it just kind of works well and agrees with reality. If all this potential flow stuff is unfamiliar to you, I could send you some references. Anyway, I would suggest also watching the vorticity movies from the 1960s national committee of fluid mechanics films - which you can find here on youtube. They deal with the circulation around the airfoil quite nicely and show some movies of the starting and stopping vortex experimentally.
Thank you for suggesting the vorticity movies, which I saw and apologies for me not distinguishing clearly between vortex and circulation. I just came across the many educational videos you produced, and I hope to follow them when I have time. Congratulations for your great effort, you have such a wide field of engineering coverage. You took my mind through a space walk through the eighty years of my life. Thank you.
