Waking up to a new law

I once woke up to discover that the Philippines was under a new law – it was called Martial Law – in 1972. Luckily, I was in New York and insulated from any imagined repercussion. With that law, I simply protested.

Many years later, in 2004, in Geneva, I woke up to a new law, which for lack of any name I will simply call A Scaling Law. It happened this way. I was looking at the data observed by my colleague Luke Hinkle. The data simply described the flow of argon gas through a capillary tube, of the type used by chemists to transfer liquids from one beaker to another. I think it is called a pipette.

The gas was impelled to flow through the tube by pressure from a tiny tank. The gas exited out to the atmosphere. However, the pressure was accurately controlled to be at the critical pressure when the gas flowed from laminar or regular or smooth to turbulent. With complete control of the critical pressure, the gas could not make up its mind whether it was laminar or turbulent. When the flow was laminar, it flowed more. When it was turbulent, it flowed less. Not being able to make up its mind, the gas periodically became laminar or turbulent, a flow which I called oscillatory, but which Luke called vacillation. His description was actually more appropriate, if the gas had a mind. This intermittent behavior was known to exist in some random fashion, but we were first to show it could be periodic, not intermittent. Furthermore, the transition to turbulence was always accompanied by sound, that was also known, except we were again first to discover that each gas had its characteristic sound. For argon, it was a frequency of 210 Herz, or 210 cycles per second. Each gas had its own characteristic sound.

With the data, I decided to build a theory, using elementary quantum mechanics. The result was very simple, and could be explained using a simple example.

Instead of our carefully controlled apparatus, let us use a balloon at high pressure. If we open the mouth of the balloon, argon gas, say, will rush out, surely in turbulent fashion. If the flow rate fo (say gallons per minute) at pressure Po is measured, what would be the new flow rate f at a new higher pressure P? My first theoretical calculation, using quantum mechanics – never mind what that is – was simple:. Then I went back from CERN (Centre Europeen de Recherche Nucleare) to my studio where I met my guest Sergei to eat dinner.

Next day, Saturday, at 5 a.m., I realized that I had the data to test the equation. I took a cold shower – our boiler gave up two weeks earlier – took the 35-minute bus trip to CERN, and worked all day to see if the data fitted. It did, and at 5 p.m., I met again with Sergei, who was fast asleep when I left 12 hours earlier. By then he had already jumped into the lake, as he missed a cold lake in Siberia.

He asked me, "Where have you been? I looked for you in your living room, and could not find you." The living room, I may explain, is Place Bourg de Four, the square next to my tiny studio, which I call that because that’s where I meet everybody. My studio has a simple bed that falls out of the wall; there is no place to entertain.

I went to the kitchen whiteboard (Rule: every dwelling I have has a whiteboard) and wrote the law, and I exclaimed that we have discovered a new scaling law. He said, if true, it was significant, and I said that it had to be true because it was so simple and cute. Furthermore, the discovery of any scaling law for fully developed turbulence is a minor cause of celebration in research circles. To celebrate, I offered to jump into the lake with Sergei.

When he went back to Russia, he tested the exponent, which was not 1/3, but varied from one gas to another. My first version of the scaling law was wrong, but we did discover more accurate scaling laws where instead of the exponent 1/3, or index 1/3, we discovered mass-dependent indices. And the law could be written as is a function of mass. Theoretically, I must now challenge students and myself to derive that index. But already, engineering tables could be prepared for indices for various pure gases and mixtures, my gift to the engineering world that I entered as a freshman in the UP College of Engineering before I was seduced by physics. To vex your physics teacher whom you never liked anyway, ask the teacher what the index should be for smooth laminar flow – it is _ .

And that’s how we discovered an empirical law for fully developed turbulence. Except that I had to be wrong first and thoroughly enamored with simplicity and beauty.

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Amador Muriel, a proponent of the molecular theory of turbulence, is a corresponding member of the Philippine National Academy of Science and Technology. He owns whiteboards in three places, in Greenbelt, Makati, in New York and in Geneva, where he threatened to jump into the lake. This is the second of this column for The Philippine STAR. He may be reached at [email protected].