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Turbulent flows beyond the Kolmogorov barrier through small scale 4D-PTV measurements

Contact: Cheminet Adam, , adam.cheminet@cea.fr, +33 1 69 08 70 39
Summary:
The goal of this internship is to develop, test and assess particle detection methods specifically designed for the optical measurement of sub-Kolmogorov small scale structures of turbulence, in a new experimental facility : Giant Von Karman (GVK).
Possibility of continuation in PhD: Oui
Deadline for application:31/03/2023

Full description:
Viscous flows are ubiquitous in nature and impact many areas of physics, engineering sciences, astrophysics, geophysics, or aeronautics. If you stir strongly enough a viscous flow, it becomes turbulent and displays vortices and coherent structures of various sizes. Typical sizes and organization of such structures can be described by a power-law energy spectrum characteristic of a scale-to-scale energy transfer, by which all the energy injected at large scale is transferred and dissipated at small scale.

The typical scale for energy dissipation is called the Kolmogorov scale and marks the transition between the power law behavior and a steep exponential decay in the wavenumber range. Therefore, scales smaller than the Kolmogorov scale contain a negligible fraction of the kinetic energy. Because of that, it is often thought that scales below are irrelevant and that “nothing interesting is happening below the Kolmogorov scale”. For a long time, a direct numerical simulation of a viscous fluid was thought to be “well resolved” if its minimal grid spacing is Kolmogorov scale. Recent theoretical and experimental advances however suggest that many interesting phenomena do happen below the Kolmogorov scale [1] and this may impact the validity of Navier-Stokes equations (NSE) as model for the dynamics of industrial, geophysical or astrophysical fluids.

Indeed, below the Kolmogorov scale, energy fluxes can still happen and could create a non-viscous dissipation totally independent of the fluid viscosity. This would constitute genuine dissipative singularities which existence could be the origin of the well-known dissipative anomaly in turbulent flows. Existence of dissipative NSE singularities may have profound implications on the validity of NSE as a model of fluid, as differentiability is lost at this point. Furthermore, following [2,3] and confirmed by numerical simulations [4], thermal noise from the molecular agitation of the fluid could compete with macroscopic motions at scales below the Kolmogorov scale. More generally, we may think that the whole structure of small-scale turbulence is affected by thermal fluctuations that may impact or impede the development of quasi-singularities.

In the BANG project funded by the French National Research Agency, we explore the validity of the Navier-Stokes equation as a fluid model by studying the phenomena occurring below the Kolmogorov scale, using multi-scale tools and advanced visualization techniques, ie 4D Particle Tracking Velocimetry (4D-PTV), in a dedicated large turbulent experiment called Giant Von Karman (GVK) built at CEA (see Figure 1). By the sheer size of the experiment, it is perfectly tailored for the exploration of small scales as the Kolmogorov scale is of the order of 1 mm. To access small scales, we plan to carry out several 4D-PTV measurement campaigns in GVK, using high particle densities as well as unconventional optical conditions with telecentric lenses allowing for a magnification of 2 tested at LMFL. Under such optical conditions, the most difficult step 4D-PTV algorithms have to face resides in the image particle detection. Identifying particles in dense images is indeed the cornerstone of the 4D-PTV method. It is a challenging chicken-and-egg problem, where overlapping particle images generate biased particle localizations, missed particles and false positives (also known as “ghost particles”). As seeking for smaller turbulent scales can only be done by increasing the particle density, this particle image overlapping is thus identified as one of the main challenges that has to be tackled in the perspective of breaking the Kolmogorov barrier.

This internship’s aim is to develop, test and assess such a particle detection method for the problem of thermal noise characterization in order to increase the spatial resolution. The intern will build on the different algorithms and tools developed at ONERA for multiview particle detection and localisation [5] in order to process and analyze the experimental image data from GVK. At first, she/he will be in charge of creating the preliminary benchmark scenario and datasets that mimics the main features of the experimental setup. This scenario will be the basis for preliminary tuning of the processing tools before the intern handles experimental data processing and analysis from the GVK facility. The internship is the first step toward a full PHD position devoted to the discovery of sub Kolmogorov phenomena.

[1] [D19] Dubrulle B. Beyond Kolmogorov, J. Fluid Mech. Perspectives (2019).
[2] R. Betchov On the fine structure of turbulent flows, JFM 3 205-216 (1957); https://doi.org/10.1017/S0022112057000579
[3] R. Betchov Measure of the Intricacy of Turbulence The Physics of Fluids 7, 1160 (1964); https://doi.org/10.1063/1.1711356
[4] Eyink et al Dissipation-Range Fluid Turbulence and Thermal Noise (2021). https://arxiv.org/abs/2107.13954
[5] Cornic et al Double‑frame tomographic PTV at high seeding densities Experiments in Fluids,61:23 (2020).
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