Captain Hook: Help me! Help me!
Peter Pan: You know the rules, Hook. A good captain always goes down with his ship.
Captain Hook: I dont want to be a good captain!
~~Return to Never Land (2002)
A smoke ring is a great example of a vortex ring. If you were to slice a smoke ring down the middle, it would leave you with something that looks like half a bundt cake - a u-shape. Each end of the "u" would appear to you as a vortex, giving you two vortices. The two vortices rotate in different directions, one clockwise and the other counter-clockwise. As we are in the Northern hemisphere, bias dictates that clockwise is anticyclonic. Thereby, the vortex moving in the counter-clockwise direction is cyclonic. As part of a closed system, the two vortices are known as dipolar vortices. With the dipolar vortices working together like this in a closed loop system, you get a vortex ring, a ring donut.
According to Bernoulli's Principle, the density of a fluid increases with pressure. The density increases as pressure increases. A slower moving fluid exerts a higher pressure than fast moving fluids. An anticyclone is a high pressure system, meaning that pressure increases as you move from the periphery to the centre, because the fluid is moving more slowly at the centre. Certain weather conditions are associated with high and low pressure systems. The dynamics of a high pressure system is that fluid moves downward vertically, as opposed to a cyclonic, low pressure system where fluid moves vertically upward.
High pressure areas, or highs, are shown by "H" symbols. In a high pressure system, air pressure is greater than the surrounding areas. This difference in air pressure results in wind, or moving air. In a high pressure area, air is more dense than in areas of lower pressure. The result is that air will move from the high pressure area to an area of less density, or lower pressure. Winds blow away from high pressure areas toward areas having lower air pressure. http://www.ussartf.org/predicting_weather.htm
It is possible to find examples of the vortex ring where it has been "halved" in such a way to expose the dipolar vortices, and is commonly referred to as a U-vortex, or horseshoe vortex. The horseshoe vortex is well-known in aviation, where they are produced by the wings of a plane as it moves through the fluid of the air. The horseshoe vortex is responsible for the trailing vortices that you might see leaving the wing tips of aircraft. The vortices are only visible because the lower pressure in the region lowers the temperature, and if it drops below the local dew-point, we see the condensed water vapor. In fluid dynamics it is accepted that the horseshoe vortex is not open as such, but is in reality part of a closed vortex loop.
A C-17 Globemaster III from the 14th Airlift Squadron, Charleston Air Force Base, South Carolina. flies off after releasing flares over the Atlantic Ocean near Charleston, South Carolina, during a training mission on Tuesday, May 16, 2006. The "smoke angel" is caused by wing vortices at the plane's wingtips.
Another place where the horseshoe vortex appears, somewhat surprisingly, is beneath the feet of the humble water-strider. The dipolar vortices appear on the surface of the water either side of the water-strider's leg - one rotating clockwise and the other anticlockwise. The vortices are joined beneath the water in a U-shape. These vortices carry sufficient backwards momentum to propel the animal forwards. Thanks to the Nature journal, I found an excellent illustration of how these horseshoe vortices appear beneath the feet of the water-strider:
Vortices carry the momentum to move animals forwards in both air and water, but their pattern varies with the style and speed of locomotion.
"In a series of experiments, mathematician David L. Hu and coworkers showed that during the rowing stroke, water striders drive their middle legs backwards without penetrating the surface, and can attain speeds of up to 1.5 m/s.
Water striders can stand effortlessly on water due to their non-wetting legs. Writing in Nature, biophysicists Xuefeng Gao and Lei Jiang show that the water resistance of the legs is due to the "special hierarchical structure of the legs, which are covered by large numbers of oriented tiny hairs (microsetae) with fine nanogrooves". They go on to demonstrate that this physical structure is more important than the chemical properties of the wax coating of the legs.
Gao and Jiang used Cassie's law to show that air is trapped in spaces in the microsetae and nanogrooves, forming a cushion at the leg–water interface. This cushion prevents the legs from being wetted."
"The strider looks as if he has only four legs, forming a giant X pattern on the water. But all insects have six legs and the water strider has two shorter additional legs that are folded up front for grabbing prey. The insect's claws or feet are not at the ends of its legs, but are located farther back so as not to interfere with its delicately balanced water ballet.
The ends of the legs that touch the water are covered with tiny hairs that increase the surface area of contact but are small enough not to break the surface tension of the water. So, in reality, the waft is in the hair! Shaving the legs of a water strider would be a disaster of titanic proportions. The gentle pressure of the hairy legs creates a dimple in the water surface. If seen in direct sunlight, these four dimples cast an enlarged, rounded shadow onto the river bottom if the river is shallow. To the observer, each rounded shadow may appear as a foot pad."
I'm fascinated by the shadows that are cast by the water-strider - that looks like a human skull grinning back from the river-bed, doesn't it? I realise that these shadows are produced by the dimples on the surface of the water, and that they are not made by the dipolar vortices of the horseshoe vortex, as such. However, looking at the shadows we can see they are very dark - it's as if they convey something which is almost material, something which has DENSITY. It's hard to believe that these shadows are made by dimples on the surface of the water and not by something solid like an object. Is the shadow being produced because the dimple has greater density than the surrounding body of water?
This photograph was taken on April, 29, 2000 At Montcalm Community College with a Sony FD-91 Digital Camera.~~ Published by the... Physics and Chemistry Departments
Carson City-Crystal High School
The dimples are being produced on the surface of the water by the gentle pressure of the water-strider's leg, and a very simple comparison to make is that it's something like pushing your finger down into the centre of a marshmallow. The marshmallow, or the molecules that make it up, are going to be squished together underneath your finger. In the same way, is it possible that the water-strider's leg is squashing molecules together on the surface of the water? If this was the case, then the dimple would be an area of increasing density, essentially making it a high pressure area.
At the moment, I don't have a confident model for the way that water looks atomically, but I do have some my ideas which differ from mainstream convention (who'd have guessed?). Modern science tends to think of water molecules as constantly vibrating, and running around bouncing off one another - here's an example of the typical explanation:
The molecules of a liquid move around a lot. They bounce off each other and spin around, and slide around from one side of the container to the other. They're always moving relative to each other.
However, I don't really envision it this way. I think water molecules are made up by donutoms of some description, and that these donutoms are pretty much stationary, except for the spin of their dipolar vortices, and are immersed in the fluid of the aether like cheerios in a bowl of milk; that is, until they are induced to flow from areas of high pressure to areas of low pressure - and for all I know, the molecules in an ordinary glass of water could be stagnant, or in a constant state of flux.
If we return to our dimple, then we have water molecules that are being condensed into a high pressure area. If you look round the periphery of the shadows made by the dimple, you can see that they are surrounded by a rim of bright light. This bright rim surrounds the shadow like a wall, and it appears to have a property that is the exact opposite to the darkness of the dimple's interior - the rim allows light to pass through, and even seems to enhance it. What is the rim of bright light describing in terms of density? One might make the assumption that the rim represents the exact opposite to the increased density that we see inside the dimple, and is thereby an area of low density - an area of low pressure.
Thus, we have an area of high pressure surrounded by a wall of low pressure. We've seen this somewhere before, right? Quite dramatically, the dimple beneath the water-strider's leg seems to echo one of the most famous anticyclone's in the solar system - Jupiter's Great Red Spot. I wonder if the GRS could be used to describe what's happening in the dimple? Another post, perhaps.
Observing the shadows also seems to reveal something interesting about surface tension. Having seen the darkness produced by the interior of the dimple, and the light produced by the rim, then it might be supposed that the surrounding surface water has a density that is somewhere between the two. What we appear to be witnessing is the fabric of the water being stretched like it's made of spandex or something. Assuming that it's not the molecules of water that are being stretched (I know, I know, I'm supposed to hate assumptions!), but the spaces between them, then it stands to reason that we are not only seeing pressure changes in terms of molecular density, but also pressure changes in the aether field.
All fluids are compressible - even water - their density will change as pressure changes, their density increases under increasing pressure. Throughout physics, it is always found that an increase in pressure will increase the density of a material. However, the fluid of the aether is a perfect fluid, and is notoriously incompressible, so any changes in its density must arise from changes in pressure as it passes through the atomic landscape. In much the same way that the diameter of a pipeline affects the pressure experienced by the water. If the diameter of a pipeline is reduced then the velocity of the water in the line must increase to allow the same amount of water to pass through.
As fluid moves from a wider pipe to a narrower one, the volume of that fluid that moves a given distance in a given time period does not change. But since the width of the narrower pipe is smaller, the fluid must move faster (that is, with greater dynamic pressure) in order to move the same amount of fluid the same distance in the same amount of time. One way to illustrate this is to observe the behavior of a river: in a wide, unconstricted region, it flows slowly, but if its flow is narrowed by canyon walls, then it speeds up dramatically.
If we have molecules tightened together in a high pressure area, then the fluid of the aether shall have less space to move, as it were. Under the constant applied pressure of the Universe, the same volume of aether fluid needs to pass between the molecules, and now that the gaps are smaller, the aether has to speed it up a bit. This is similar to what happens to water coming out of the end of a hose-pipe; if you put your finger over the end you get a jet of water - it's the same volume of water that you had previous to your finger being there, but now in order to get past you, it has to come out faster.
According to Bernoulli's Principle, a fast-moving fluid exerts less static pressure than a slow-moving fluid. The flow between narrow canyon walls is faster moving, and has a greater velocity than the water flowing in the wide river. The faster a fluid moves, the greater its velocity pressure, or dynamic pressure, then the smaller the static pressure it exerts on the sides. The pressure in a static fluid arises from the weight of the fluid. A fast moving fluid exerts less pressure than a slower moving fluid.
Total pressure is the sum of dynamic and static pressures. A fluid at rest in a pipe exerts static pressure on the walls. The pressure in a static fluid arises from the weight of the fluid. Dynamic pressure arises from the motion of the fluid, and is not really a pressure at all, but merely represents the decrease in pressure due to the velocity of the fluid. The faster a fluid moves, the greater its dynamic pressure and the smaller the static pressure it exerts on the sides.
Thus, the fluid of the aether in the dimple's interior is moving under high dynamic pressure, and thereby imparts less static pressure. However, in the rim surrounding the dimple, there are fewer molecules present, meaning that this area has less density, giving the aether fluid plenty more room to manoeuvre, and we now see courses which are wide and shallow, where the aether exerts less dynamic pressure, and greater static pressure. If the aether fluid has a greater static pressure, it then has greater density, and shall act upon the molecules by pushing them apart (just think of Chewbacca holding out his arms and pushing against the sides of the compactor). I think that is this "push" which could prove to be highly relevant to surface tension.
The density of water increases with depth. For example, if we look at a glass of water - the molecules on the surface of the water are not as squished as the molecules of water at the bottom of the glass. With increasing density the molecules are getting squeezed tighter together, while those on the water's surface are enjoying relatively greater freedom - they are not packed so closely together. This means that the fluid of the aether is under greater static pressure on the surface of the water. I wonder if this increased static pressure in the aether field is revealing something about the tension described by the water's surface?