The subtle intermittency of elastic turbulence

ADIW04 - Anti-Diffusion in Multiphase and Active Flows

Turbulence is a state of irregular, chaotic and unpredictable fluid motion at very high Reynolds numbers (Re), which is the ratio of typical inertial forces over typical viscous forces in a fluid.  Conceptually, the fundamental problem of turbulence shows up in the simplest setting of statistically stationary, homogeneous and isotropic turbulent (HIT) flows: What are the statistical properties of velocity fluctuations?  In other words, what is the probability distribution function of velocity differences (PDF) across a length scale? Experiments and numerical simulations over the last seventy years have shown that this PDF  is non-Gaussian, not only because it has non-zero odd moments but also because  moments of all orders are important in determining the nature of the PDF . This is a phenomena called intermittency. A systematic theory of intermittency starting from the Navier-Stokes equation is the goal of turbulence research. Turbulent flows, both in nature and industry, are often multiphase, i.e. they are laden with particles, may comprise of fluid mixtures, or contain additives such as polymers. Of these, polymeric flows are probably the most curious and intriguing: the addition of high molecular weight (about 107) polymers in 10–100 parts per million (ppm) concentration to a turbulent pipe flow reduces the friction factor (or the drag) up to 5–6 times (depending on concentration). A straightforward parameterization of the importance of elastic effects is the Deborah number, De , which is the ratio of the characteristic scale of the polymer over some typical time scale of the flow.  Research in polymeric flows turned into a novel direction when it was realized that even otherwise laminar flows may become unstable due to the instabilities driven by the elasticity of polymers. Even more dramatic is the phenomena of elastic turbulence (ET), where polymeric flows at low Reynolds but high Deborah numbers are chaotic and mixing.  We, for the first time, show that such flows are also intermittent but unlike the usual turbulence, they are intermittent in a subtle way. The velocity field is smooth, i.e., the velocity difference across a length scale r, is proportional to r but, crucially, with a non-trivial sub-leading contribution r^(3/2) which we extract by using the second difference of velocity. The structure functions of second difference of velocity  show clear evidence of intermittency.

This talk is part of the Isaac Newton Institute Seminar Series series.