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Register a new userLong time correlations in Lagrangian dynamics: a key to intermittency in turbulence
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Jean-Francois Pinton
Publication date
2002
fields
Physics
and research's language is
English
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New aspects of turbulence are uncovered if one considers flow motion from the perspective of a fluid particle (known as the Lagrangian approach) rather than in terms of a velocity field (the Eulerian viewpoint). Using a new experimental technique, based on the scattering of ultrasounds, we have obtained a direct measurement of particle velocities, resolved at all scales, in a fully turbulent flow. It enables us to approach intermittency in turbulence from a dynamical point of view and to analyze the Lagrangian velocity fluctuations in the framework of random walks. We find experimentally that the elementary steps in the walk have random uncorrelated directions but a magnitude that is extremely long-range correlated in time. Theoretically, we study a Langevin equation that incorporates these features and we show that the resulting dynamics accounts for the observed one- and two-point statistical properties of the Lagrangian velocity fluctuations. Our approach connects the intermittent statistical nature of turbulence to the dynamics of the flow.
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Intermittency is a hallmark of turbulence, which exists not only in turbulent flows of classical viscous fluids but also in flows of quantum fluids such as superfluid $^4$He. Despite the established similarity between turbulence in classical fluids and quasi-classical turbulence in superfluid $^4$He, it has been predicted that intermittency in superfluid $^4$He is temperature dependent and enhanced for certain temperatures, which strikingly contrasts the nearly flow-independent intermittency in classical turbulence. Experimental verification of this theoretical prediction is challenging since it requires well-controlled generation of quantum turbulence in $^4$He and flow measurement tools with high spatial and temporal resolution. Here, we report an experimental study of quantum turbulence generated by towing a grid through a stationary sample of superfluid $^4$He. The decaying turbulent quantum flow is probed by combining a recently developed He$^*_2$ molecular tracer-line tagging velocimetry technique and a traditional second sound attenuation method. We observe quasi-classical decays of turbulent kinetic energy in the normal fluid and of vortex line density in the superfluid component. For several time instants during the decay, we calculate the transverse velocity structure functions. Their scaling exponents, deduced using the extended self-similarity hypothesis, display non-monotonic temperature-dependent intermittency enhancement, in excellent agreement with recent theoretical/numerical study of Biferale et al. [Phys. Rev. Fluids 3, 024605 (2018)].
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