July 1, 1998
Analyzing liquid helium using sound to understand the wild and erratic motions of a turbulent fluid is one of the major open problems in physics.
To help our understanding of order and disorder in hydrodynamic systems, we try to analyze turbulence in as many ways as possible. We studied turbulence in a tank of liquid helium colder than four degrees above absolute zero (it turns out that heating liquid helium produces especially strong turbulence, due to its weak viscosity and ability to attain high speeds of flow). In one study we displayed the differences in various magnitudes of turbulence (described below) using sound.
It was first necessary to produce turbulence in a sufficiently controlled environment. In most situations heating a fluid reduces its density, while cooling it has the opposite effect. When a fluid is heated from below and cooled from above, the bottom is lighter than the top: an unstable situation. This instability tends to produce swirling type motions in which hot material is moved from the bottom to the top of the container. The simplest motion, occuring for slight temperature differences (fractions of a degree), is one in which the fluid rolls around in a time-independent manner. As the difference increases, the motion gains in complexity and contains many swirls of various magnitudes. The heat in the fluid is only partially mixed, resulting in large variations in temperature.
The strength of turbulence induced by heating is measured by the "Rayleigh number", a number proportional to the temperature difference between the top and bottom of the container and involving the viscosity, etc (see HERE for details). When the Rayleigh number exceeds roughly 2000, the fluid begins to roll around. One can see the trace of the hotter regions by illuminating the fluid with the proper lighting. See the picture above. Rayleigh numbers of approximately 105 to 107 give so-called "soft" turbulence. Above Rayleigh numbers of 108 the turbulence takes on a different character denoted "hard" turbulence. Hard turbulence is "intermittent"; that is, gently flowing regions are punctuated by small regions of violent flow and wild temperature swings (listen to the "hard turbulence" below to experience this "intermittency" firsthand).
How do you think it will sound? Like the white noise of an FM radio tuned between stations? Like a passing freight train? Like a thunderclap? Like the Space shuttle taking off? Or like brushing your finger against a phonograph needle?
Capturing the Sound
We produced the sound files below by reading the temperature from a tiny region of the sample many times a second. The fluctuating temperature causes the pressure to fluctuate as well. Fluctuations in pressure are what are read by the human ear as sound. Thus the temperature sensor can be thought of as a pressure sensor---a tiny microphone. In the recordings below we treated the temperature signal as though it hadcome from a microphone. The sounds you hear are played back approximately 16 times faster than they were recorded. We sped up the playback (8,192 samples per second) to produce a sound in the audible range of frequencies.
- sine wave(6.2 seconds) of about 200 cycles per second, for comparison. It should sound like a pure tone pitched at about the G below middle C on a piano.
- random white noise(6.3 seconds), for comparison (watch out; it's loud). It should sound like an FM radio tuned between stations.
- Softest: Rayleigh number 2.1 times 10 to the 7.(10.2 seconds) This is near the upper limit of "soft turbulence".
- Marginal: Rayleigh number 6.0 times 10 to the 8.(51.2 seconds) This is approaching the regime of hard turbulence.
- Hard: Rayleigh number 7.3 times 10 to the 10.(76.8 seconds) This is well into the hard turbulence regime. Here one can clearly hear the phenomenon of intermittency. The fluid is mostly quiet, with occasional violent bursts of sound.
- Hardest: Rayleigh number 5.8 times 10 to the 14.(102.4 seconds) This is the most turbulent fluid we could obtain. The intermittency is noticeably increased.
- Wait till one sound is over before playing the next one. Playing two sounds simultaneously is confusing.
Jason South and T. Witten, with thanks to L. Kadanoff and E. Ching
approved for posting by T. Witten, 07/17/98
Reference:
- Probabilities for temperature differences in Rayleigh-Benard convection, Emily S.C. Ching, Phys. Rev. A.,44, 3622-3629, (1991).
- Scaling of Hard Thermal Turbulence in Rayleigh Benard Convection, B. Castaing, G. Gunaratne, F. Heslot, L.P. Kadanoff, A. Libchaber, S. Thomae, X.-Z. Wu, S. Zaleski and G. Zanetti, J. Fluid Mechanics, 209, 1 (1989). Permission to reproduce turbulence data from this experiment granted by Albert Libchaber, via email 7/17/98.
- Bubble, Bubble, Boil, and Trouble, D.H. Rothman and L.P. Kadanoff, Computations in Physics, 8, 199-204 (1994).
- Turbulence in a Box, L.P. Kadanoff, A. Libchaber, E. Moses and G. Zocchi, La Recherche, 22, 628 (1991).
- The temperature data was converted to sound by Emily Ching in collaboration with T. Witten.