La Jolla

La Jolla California

La Jolla is fun, its a bit more uptown than Mission Beach. Here the surf is about perfect for learners, all day long the waves run two to three feet, with a nice break all up and down the beach. A few hundred yards north of here is the Scripps Oceanography Institute. They take in a lot of ocean water all the time for their laboratory experiments and there is an outfall up there that dumps their used water onto the beach, 24 hours a day. If you go up on the cliff and look, you can see the different colored water from the outfall trailing away out to sea, drifting south and west until it gets beyond sight down near LaJolla point.

There are a few interesting stories about how some rivers and streams do not mingle their waters when they meet a tributary, and this is similar to that. I have sometimes wondered if the Scripps water floating on the surface somehow makes the surfing waves more stable and consistent. I suppose that the Scripps water is warmer, from being in their buildings, but maybe it also has a lighter density from less salt, or ionic differences or something.

One thing is clear from looking at the ocean and that is that an offshore kelp bed can make the water more glassy when it gets to breaking on the beach, and maybe the Scripps water helps do this too. Its an interesting question, and as I sometimes say, there might be some small value in looking for the answer, but I am not going to look for it today. But the thing to do if you look at waves is do some Fourier transforms in your head, and try to identify how many wavelengths you can see in the waves. The highest frequency is the ripples caused by the wind, generally when talking about wind you have to include turbulent eddys or "breezes". So there are probably two frequencies of ripples in the water caused by wind.

Then there are the big ripples caused by the surfers or by sea lions, take your pick. These are quite a bit slower than the wind ripples, but are single point sources, and the waves are dampened out by viscosity after only a few inches. Say these are one tenth the frequency of the ripples. Then you have your chop from the ocean, little garbage waves created due to constructive or destructive interference from a multitude of waves. These things must chop along at some natural frequency of the water since by definition they never got dampened. It might be right to assign them a frequency another order of magnitude slower than the sea lion waves. Another order of magnitude gets you to the swell that causes the breaker, and swells come in sets of 4 to 6 waves in between lulls of 4 to 6 non-waves, so sets have a frequency that is another order of magnitude less. Then you have an occasional swell that comes in from another direction. The swell itself has a frequency equal to what the surfers are using, but it disappears for long periods, another order of magnitude slower.

Summing up the Fourier parts, assigning each a frequency that is an order of magnitude different:
ripples caused by breezes,
normal wind ripples,
mammal ripples
chop,
swell,
set,
cross set

The timing between swells is available from the lifeguards, and so from there you can make a pretty nice model of the waves in the ocean. Then you can try to predict what a kelp bed will do, or what different quality water will do, or the Scripps outfall, to make things glassy. If you want glassy. Note that this is not a surf predictor model. There are plenty of those, and they work pretty good, mostly depending on surf measurement and reporting stations in order to keep themselves calibrated.

And I am at the beach now, and as a segue into what I wanted to talk about, let me tell you that when someone says "have a good day" what that means to me is involuntary memories of long summer days in the blue Pacific, whitewater waves falling down, the back pull of the ocean just before a wave picks you up and sends you ashore, boogie board surfing with my friends, and laughter and a little bit of yahoo yelling. I once heard a hardboard stand up surfer describe what it's like to be in a tube of water with the tube closing in, and water spraying all around you and a deafening noise. Have a good day really means something to me. I try not to think about getting tumbled over while out of breath and underwater or getting my skin thrashed against the broken seashells on the beach when a wave threw me up there before I was ready to go.

What I wanted to talk about instead was imperfect gases and something important that a brilliant scientist named Kantrowitz found during the war. It was classified at the time, so it never made headlines, and if you think about it, even Einstein did not really get famous for about 40 years after his two most important papers. I like the other one the most, the one about magnetism.

Anyway Kantrowitz was trying to get the most combustion out of turbines, and what he found was that nitrogen was a little slow in expanding, compared to the rest of the air, the rest is mostly oxygen, but nitrogen was slow. I say nitrogen is "stubborn" and what Kantrowitz measured was that different shaped nozzles helped the nitrogen expand faster or slower which affects the amount of combustion, more or less of it. He was trying to find an extra ten percent of engine power that the math models predicted would be there, but was not actually there when they built the first jet turbines.

But the critical result was the simple observation that under his conditions the air was not an ideal gas. The nitrogen behaved differently than the theoretical models and it affected the observable performance of the turbine system he was working on. You would think there is other evidence of observable differences in air that show it is not an ideal gas. One of these instances of non-ideal behavior might occur near Mach 1. Pilots report an increase in buffeting starting around .94 Mach, or within 6 percent of the speed of sound.

This buffeting could very well be the result of something that is common to all gaseous fluids, but that seems unlikely. It seems more likely that the buffeting is caused by the variations in the gases in the air, some effect that is similar to the Kantrowitz observation that nitrogen is stubborn when pushed under pressure through a nozzle.

It seems like Kantrowitz observed an imperfect behavior of expansion, and the test pilots observed an imperfect behavior of incompressibility. Are these the result of the same imperfect properties in the air? In the nitrogen? One approach to that question would be to ask what kind of observable imperfect behaviors can there be? And to look at that you would start to look at phase changes for each gas, and look at parametric charts of the gas phase behavior under different pressures and temperatures. Langmuir had his people doing things like this, notably Kurt Vonnegut's brother, who identified twelve or eighteen different types of ice, with the ninth type being wholly theoretical and unable to create in the laboratory.

Parametric phase charts would be a productive way to look at the problem, but another approach is whether there are some fundamental properties of the individual molecules that makes a gas behave in an imperfect way. This approach appeals to me a great deal, frankly my attitude has a lot to do with why I never finished my engineering degree, but it appeals to me and that is what I want to talk about today.

I've spent the last couple of years thinking about this, after reading Kantrowitz' paper back in about 2000 or 2001. After about two years I wrote a paper on smartgroups.com/hilsch about how the Kantrowitz behavior is probably responsible for devices that create a temperature difference in air. My position is that the temperature difference is created during the time the nitrogen is too stubborn to expand. During this time the oxygen has to do all the expanding, absorbing all the heat, and making its surroundings colder, the same way the coolant in your air conditioner keeps you cool.

Anyway the oxygen gets hot, and so the nitrogen gets cold, and according to Kantrowitz you have up to about 5 milliseconds to separate them and get a cold flow and a hot flow. After 5 ms all things reach equilibrium - the temperature difference is gone. One way to separate them is with a centrifuge, or spinning them inside a tube, and another way seems to be to vibrate them with sound.

Two or three of my contributions to the smartgroups/hilsch forum are worth reading, and there are a number of interesting papers describing the centrifuge technique which has been known for ninety years or longer. I can never keep it straight in my head but it seems to me that the heavier oxygen molecules (the warm ones) get forced to the outer layer, and the lighter nitrogen (the colder ones) stay in the center of the vortex. It could be wrong, maybe the low density hot oxygen molecules stay in the center. Maybe there is a critical speed where the system flip-flops. I don't care today.

The question I want to know is why the nitrogen is stubborn. Why is it that Kantrowitz found that water vapor or dust made the nitrogen more willing to play ball? Which gas causes the buffeting at .94 Mach? Why?

To answer these questions I think you should ask questions like what shape is the molecule, what is the weight, how does the molecule behave under pressure or temperature changes. You need to consider atomic weights and theory of s p f electron shells, think about ionic potential, electric conductivity or resistance, whether there is gravity or weightlessness, and always remember that the magnetic moment of an electron is 1000 times greater than the magnetic moment of a proton. Heavy things have higher magnetic fields. There are other things to think about too, that are probably outside the environment that normal air works in, such as oxidation, or fission, and others I have never dreamed of. But at some point I am going to want to talk about what happens at hypersonic speeds like Mach 5 or 6, which is dissociation, and at about Mach 8 which is the ionization of molecules.

For now let's stick to gases behaving in the sonic and transonic regions. What I want to consider first is the bi-atomic molecules N2 and O2. Both of them are molecules made up of two atoms, and the theory says that the molecules are probably symmetrical with respect to electric/magnetic fields, and symmetrical when expressing their observable energy through vibrating or translating. In fact you can work out a table showing the different ways a two atom molecule can translate while vibrating, either along the axis, or against the axis. And curiously this makes you wonder if the two atoms are rotating around each other, and if they are is that something that we can measure.

My thoughts on this are that rotation is something that we can not measure, we can't observe it. I suppose that rotation is not something that is expressed by the PV=kRT equation, and wonder where that takes me. The first thing I do is assume that the molecules all rotate at some equal energy level, and that they also vibrate and translate while the neutrons orbit each other. If you look at the periodic table the oxygen atom is heavier, so the oxygen molecule will spin slower and wider, following Kepler, and the nitrogen molecule will be smaller and spinning faster. The angular momentum is the same, but the kinetic energy of the nitrogen is much greater, proportional to the square of the velocity.

So what happens if you picture a chain-link-fence like lattice of nitrogen and oxygen molecules spinning against one another? The big slow oxygen molecules are like 3 foot windmills getting bombarded by tennis balls. Four tennis balls for every windmill. Pretty soon the oxygen stops spinning. The little nitrogen guys are spinning around like crazy bumping into each other, and every so often clobbering up against some big dumb oxygen molecule. When they hit they might roll off, or they might skid up against it depending on their rotation, or they might hit along their axis and just bump off. But the result after a suitable time delay for equilibrium is a gas where the oxygen gets bumped around all day long by energetically spinning nitrogen molecules, nitrogen molecules spinning more or less energetically depending on their last few collisions with other molecules. Quite an exciting game of molecular billiards.

Does the imagined system match the observed performance? Yes. First, what about the case of rapid expansion in a nozzle? Can this model predict what Kantrowitz observed? Yes. Under expansion our model predicts that the oxygen has a very low angular momentum and can easily change its vibration rate to expand rapidly. The nitrogen has a comparatively large angular momentum and cannot readily change its vibrational energy. Its stubborn.

Kantrowitz observation about water and dust could possibly be due to the irregular shapes of these molecules (dust being a suspended solid molecule). The irregular shapes knock the spin out of the nitrogen so that it is not stubborn.

Second, what about the case of Mach .94 buffeting? Does this model handle that? Yes. It could be that starting at about .94 Mach we have reached the sonic speed of some or all of the nitrogen. It can no longer accept vibration as an input to its molecular energy. It behaves like an incompressible gas while the oxygen is still able to absorb energy. Six percent faster and the oxygen is also no longer able to accept the vibration as an input. This is Mach 1. The nitrogen sonic speed, for the spinning nitrogen molecules, has already been reached. At Mach 1, both gases pass along the momentous push of the aircraft like a liquid would, as sound, a sonic boom.

Now oddly, as a final question. Take the familiar curved shape of a Bernoulli wing as perfected by Wilber and Orville and imagine the airflow across it. This wing compresses and then expands the flow across it, creating a boundary layer and a smooth transition in air velocity until the boundary layer separates above or behind the wing. Behind the wing the fast moving low pressure air joins with the slower moving higher pressure air from below the wing, combining turbulently and creating wake vortices and wingtip vortices whose equations were worked out by von Karman.

What do you see? I see the wing as half a nozzle. If you took another wing, inverted it and placed it above the boundary layer, you would have two wings forming one nozzle. The wing and the nozzle are equivalent. The effect observed by Kantrowitz should be observable in wings. It turns out that it is. While working for Langmuir, Schaefer and Vonnegut tested the wing ice found on airplanes. There are gas molecules embedded in wing ice, proving that the air over the wing was cold, colder than the wing itself. It was the air that froze. The converse question is whether the .94 Mach buffeting of an aircraft is observable in a nozzle.

But you can prove the cooling thing for yourself. Drive down the highway on a warm summmer evening. Put your hand out the window just so! The flow from under the side mirror hits your wrist. The fastest part of the flow is cold, colder than the surrounding air. The blood coursing through your hand will get cool, in a few minutes it will be cooling off your whole body. Turn off your A/C! Save on gas! Breathe in the air.