Dynamics of threads and polymers in turbulence: power-law distributions andsynchronization

Abstract

We study the behavior of threads and polymers in a turbulent flow. These objects havefinite spatial extension, so the flow along them differs slightly. The corresponding dragforces produce a finite average stretching and the thread is stretched most of the time.Nevertheless, the probability of shrinking fluctuations is significant and is known to decayonly as a power law. We show that the exponent of the power law is a universal numberindependent of the statistics of the flow. For polymers the coil–stretch transition exists: theflow must have a sufficiently large Lyapunov exponent to overcome the elastic resistanceand stretch the polymer from the coiled state it takes otherwise. The probability ofshrinking from the stretched state above the transition again obeys a power law but with anon-universal exponent. We show that well above the transition the exponent becomesuniversal and derive the corresponding expression. Furthermore, we demonstratesynchronization: the end-to-end distances of threads or polymers above the transition aresynchronized by the flow and become identical. Thus, the transition from Newtonian tonon-Newtonian behavior in dilute polymer solutions can be seen as an orderingtransition.