# Title: The critical point for pipe flow

**Dwight Barkley**

**Short Abstract**

More than 125 years ago Osborne Reynolds launched the quantitative study of turbulent transition as he sought to understand the conditions under which fluid flowing through a pipe would be laminar or turbulent. Since laminar and turbulent flow have vastly different drag laws, this question is as important now as it was in Reynolds' day. Reynolds understood how one should define ``the real critical value'' for the fluid velocity beyond which turbulence can persist indefinitely. He also appreciated the difficulty in obtaining this value. For years this critical Reynolds number, as we now call it, has been the subject of study, controversy, and uncertainty. Now, more than a century after Reynolds pioneering work, we know that the onset of turbulence in shear flows is properly understood as a statistical phase transition. How turbulence first develops in these flows is more closely related to the onset of an infectious disease than to, for example, the onset of oscillation in the flow past a body or the onset of motion in a fluid layer heated from below. Through the statistical analysis of large samples of individual decay and proliferation events, we at last have an accurate estimate of the real critical Reynolds number for the onset of turbulence in pipe flow, and with it, an understanding of the nature of transitional turbulence.

This work is joint with: K. Avila, D. Moxey, M. Avila, A. de Lozar, and B. Hof.

### SPONSORS

#### University of Michigan Sponsors

- Horace H. Rackham School of Graduate Studies at the University of Michigan, Ann Arbor
- Michigan Center for Theoretical Physics
- Center for Studies of Complex Systems
- Medical School
- Department of Mathematics
- Department of Physics
- Biophysics Program