New work shows fluid in a curved pipe can undergo discontinuous transition

Turbulence is everywhere, yet much about the nature of turbulence remains unknown. During the last decade, physicists have discovered how fluids in a pipe or similar geometry transition from a smooth, laminar state to a turbulent state as their speed increases.

Surprisingly, in the newly emerging consensus, the process could be understood using statistical mechanics, not fluid mechanics, and was mathematically equivalent to the way in which water percolates down through a coffee filter.

In a new twist, UC San Diego researchers Guru K. Jayasingh and Nigel Goldenfeld have now predicted that if the pipe is sufficiently curved, the transition can become discontinuous, with the turbulent fraction undergoing a jump beyond a critical flow velocity. This jump is mathematically similar to the way in which water can suddenly and discontinuously turn into ice if cooled below the freezing temperature.

The new framework—so-called tricritical directed percolation—encompasses both the emerging consensus and very recent experiments, as well as making new predictions.

The study is published in Physical Review Letters.

Their work shows that the whole apparatus of phase transitions, originally developed for thermodynamics, and now foundational in materials science, chemistry and physics, can be applied to certain transitional phenomena in fluid mechanics.

“Our work is, once again, a striking example of the way in which multidisciplinary approaches can yield unexpected solutions to hard scientific problems—in this case one going back over a century,” says Goldenfeld, Chancellor’s Distinguished Professor of Physics.