### Research

The focus of Goldburg's work is turbulence and new probes for understanding it. Here are some problems on which he is working:

- In all turbulence, energy is injected at one spatial scale and dissipated at another. Thus there is a rate of flow of energy between the injection and dissipative scales. The flow is being studied in a large tank full of turbulent fluid (water). The transformation between energy input per sec to the rate of energy dissipation is called the energy cascade process.

- Particles that float on the surface of the water in the tank behave very differently than the water molecules in the bulk. The heart of the difference is that the floaters form a compressible system, whereas water is incompressible. The physics of compressible flows is entirely different from incompressible ones, and that difference is being studied.

- Because the floaters are compressible, one can define an entropy for them and invoke ideas of thermodynamics. Measurements are being made of the rate of change of entropy in the system. The goal here is to link ideas about turbulence (which refers to systems far from equilibrium) with those of equilibrium statistical mechanics.

- In most fluid dynamics studies, the driving power for the creation of turbulence is constant in time, though, of course, the response of the system fluctuates in time. Experiments are being conducted in which the turbulence generation rate is periodically modulated it time. The response of the system will reflect this modulation. More specifically the system's turbulent response provides information about the energy cascade process referred to above.

- As a fluid flows through a pipe, it experiences a frictional force with the wall, causing the dissipation of heat. As one might expect, the amount of heat dissipation depends on the roughness of the interior of pipe. It has been suggested that the frictional energy loss /f/ depends on the flow rate /F/ through the pipe roughness /R/ in the same way that the magnetization of a magnet depends in temperature T and on the strength of the magnetic field H in which the magnet is immersed. In both cases there is a transition as T is varied in one case and as /F/ is varied in the other. The connection between these two phenomena is being investigated in a flowing soap film. This work is a collaboration with G. Gioia and N. Goldenfeld at the U. of Illinois.

### Selected Publications

- "Eulerian and Lagrangian studies in surface flow turbulence," J. R. Cressman, J. Davoudi, W. I. Goldburg, and J. Schumacher, New Journal of Physics, 6, 53, (2004).
- "Compressible flow: turbulence at the surface," J. R. Cressman , W. I. Goldburg, and J. Schumacher, J. Stat. Phys, 113, 875 (2003).
- "Two-dimensional turbulence: a review of some recent experiments," H. Kellay and W. I. Goldburg, Repts. Prog. Physics, 65, 845, (2002).
- "Fluctuation and Dissipation in Liquid Crystal Electrconvection," W. I. Goldburg, Y. Y. Goldschmidt, H. Kellay, Phys. Rev. Lett., 87, 245502 (2001).
- "Energy flux fluctuations in a finite volume of turbulent flow," M. M. Bandi, W. I. Goldburg, J. T. Cressman Jr., and A. Pumir, Phys. Rev E, 73, (2006) in press.