Spiral velocity, vortex flow, is quite a bit more difficult to study and understand than either Linear or Rotational velocities due to the dynamics required to maintain it, and the relatively brief time that any particular particle is experiencing the flow. To be sure, we have much less experience with it in our everyday lives. We see it when the water drains down a hole, but that’s about all. We don’t use the vortex principles on machines (excepting maybe vane pumps or cams) and it’s not so easy to set up a constantly operating system in order to study it. And since Spiral velocity includes such a wide variety of phenomena, it is difficult to make generalizations. That being said, we’ll make a few, and then talk more specifically about the special case of the Phi based logarithmic spiral.
In the preceding chapters, we’ve shown how Linear velocity is indeed line-like, that as a velocity it really has neither width or depth (although the acceleration created by it is basically planar). Rotation, as long as the subject under consideration has an appreciable diameter, is basically a planar function. Indeed, a circle defines a plane, and only one plane.
But a Spiral velocity is, by its very nature, volumetric (in the old vernacular, 3-D), and must always be volumetric to exist. Although much of the spiral activity can be basically planar; since the flow in a vortex must proceed either away from or in to the center of the rotation, the source (or drain) surrounded by the spiral activity, must be out of that plane of rotation. This necessitates a ‘counter’ flow in the only possible direction, which is perpendicular to that plane. By definition, Spiral velocity is a spatial phenomenon.
Also, by definition, Spiral flow must be either a concentrator or a disburser, that is, a spiral can never have a complete steady state all across its ‘field’ like a projectile in space or a gyroscope can. Even if the particles within the spirally moving system are moving at a constant rate (as they are if they are traveling in a logarithmic spiral), they must be moving from a state of either lesser or greater concentration, to the other state. This means that Spiral systems, in and of themselves, must have a varying energy density within the boundary of the system.
For the velocity to remain constant in the Spiral Dimension, the energy density must vary across the system.
Of course, you could create a spiral motion in which the energy contained by every equal partition of the system had the same energy density, but typically, that’s not the case, otherwise, you know, the toilet would never empty.
And a water drain provides an excellent example of how a naturally occurring vortex looks and works. It’s not exactly a logarithmic spiral, since there is a lot of complex flow going on within the overall structure, but it’s pretty close. A drain vortex is driven by the (downward) force of gravity, and therefore, it has a directional character. And since it is not a closed flow system (like a hurricane, which we’ll discuss later) it’s free to take on a shape that has much to do with the physical geometry of the system (the depth of the water, the size of the drain opening, etc.) but it definitely has the characteristics that we’re talking about here.
Go fill up your tub (or sink) and pull the drain plug, and watch the vortex formed; pictures just won’t do this example justice.
First off, did you notice how a vortex was formed every time you opened the drain? Not like, once and a while or most of the time. Every time.
Did you see the flow lines on the surface of the water, at the boundary of the system? They show long and lazy rotation about the center of the vortex, an almost pure rotation, whose rotational aspects change dramatically as they approach the center.
In fact, the rate of rotation increases so much that in the center of the vortex, the water actually defies gravity and opens the center column to air, all of the way down to the drain!
Think about this. If Linear velocity were the dominant feature of this system, why, the water would just fill the entire drain pipe and flow out the hole like sugar through a funnel. But it doesn’t. Every time that you open the drain, the system starts its own rotating (vortex) system.
What is even more odd and counter intuitive is that most of the water going down the drain comes from the top of the reservoir. Put a small wood chip in the water and watch it. The water at the bottom of the vessel is at a higher pressure than that at the top, right? And systems want to flow from areas of higher pressure to lower pressure, right? So wouldn’t it make sense for the water at the bottom to be more likely to enter the drain before the water at the top?
And then there’s that whole gravity thing. The whirling motion of the fluid creates a gyroscopic effect on itself, and the molecules are drawn away from the center, creating an open column that extends (in most cases) to the limit of the system, in this case, the opening of the drain. And it creates so much suction that it even makes noise. Think about that. This is not a normal water noise like waves or gurgling streams in which the water makes noise by impacting itself in a linear fashion. Water in a vortex creates a suction that causes the system to vibrate sufficiently to create sound without impact (and at a whole different frequency, I might add).
So while this system is being driven by gravity, it is simultaneously defying it, or at least creating force that is opposing it, in a plane that is perpendicular to the line of action of the applied force.
You can see a similar interaction with gravity by twirling a straight sided bucket with water in it. Although this example has more to do with the effects of pure rotation than with spiral motion, the reaction to gravity is similar.
Do this (outside, preferably). Get a straight sided bucket and attach a rope to the handle. Fill the bucket about one quarter full with water. Now, hold the bucket out in from of you by the rope and using both hands so that you can really spin up the bucket, start to twirl it. What happens? Regardless of the material from which the bucket is made, the water climbed up the side, didn’t it? If you had used a tapered bucket, the water would climb completely up and over the top, since as the diameter increases, so does the rotational velocity and hence, the internal gravity. The water thinks that by running up to the top of the tapered bucket that it is going ‘down hill’. Viola! You’ve created antigravity!
Of course, even though you have actually created antigravity (that is, a force system that is opposed to gravity, instead of one that truly nullifies its effects), the force created only effects the small, closed system. The bucket doesn’t get any heavier or lighter in relation to the Earth, unless the water spins out over the sides.
But the larger point here is that the spinning aspects of the vortex whether a concentrating or dissociating flow (the tapered bucket is a dissociating flow) creates a gravity opposing field that is inherent to the system under study, and that field is not diametrically homogeneous, that is, across any given diameter, the field strength created by the vortex is not uniform, but gets stronger or weaker depending on the rotational aspect of the velocity.
We’re going to leave our discussion of vortices for the time being, and move on to talk about closed system spiral flow after making this last point:
All vortexes have a core, a minimum center diameter (given sufficient velocity), that does not participate in the overall flow of the system, and that has characteristics that are completely at odds with the more general system. Which is the perfect segue to talk some more about…..