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# Lagrangian structure-function using stationarised fluid trajectories in the wake of a smooth cylinder

Ali Rahimi Khojasteh, Dominique Heitz, Sylvain Laizet

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Ali Rahimi Khojasteh, Dominique Heitz, Sylvain Laizet. Lagrangian structure-function using stationarised fluid trajectories in the wake of a smooth cylinder. 14th European Fluid Mechanics Conference (EFMC14), European Mechanics Society, Sep 2022, Athens, Greece. 1 p. [hal-03861633](https://hal.inrae.fr/hal-03861633)

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https://hal.inrae.fr/hal-03861633

Submitted on 20 Nov 2022

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# Lagrangian structure-function using stationarised fluid trajectories in the wake of a smooth cylinder

Ali Rahimi Khojasteh<sup>a</sup>, Dominique Heitz<sup>b</sup> and Sylvain Laizet<sup>c</sup>

We present here a statistical study to determine the Lagrangian structure function in the anisotropic and inhomogeneous wake behind a smooth cylinder. Based on the extension of the stationary Lagrangian diffusion theory to self-similar flows, we stationarise velocity components in order to obtain Lagrangian statistics. Viggiano et al. (2011)<sup>1</sup> have shown how to obtain fundamental Lagrangian statistics from the anisotropic and inhomogeneous dynamics of a jet flow by normalizing the trajectories based on local Eulerian scales. In particular, computing the Lagrangian structure-function scaling constant $C_0$ is a crucial parameter in modelling turbulent transport. A similar role is played by the $C_0$ constant in the Lagrangian framework as a Kolmogorov constant in the Eulerian framework. We performed direct numerical simulations (DNS) and time-resolved particle tracking velocimetry (4D-PTV) experimental analyses in the wake behind a smooth cylinder for Reynolds numbers between 300 to 3900. Details of the tracking algorithm used in the present study are addressed in Khojasteh et al. (2021)<sup>2</sup>. Preliminary results of the experiments indicated reasonable agreement between the stationarised Lagrangian trajectories of the wake flow and the hypothesis of Lagrangian self-similarity at inertial scales (see Fig. 1).

<figure><img src="image_2.png" /><figcaption>Figure 1: Lagrangian second order structure function of the streamwise direction at four downstream locations. (a) As a function of non-dimensional timescale. (b) Re-dimensionalised structure function representing the $C_0$ constant.</figcaption></figure>

<footnote><sup>a</sup> INRAE, OPAALE, 35044 Rennes, France</footnote>

<footnote><sup>b</sup> Department of Aeronautics, Imperial College London, London, United Kingdom</footnote>

<footnote n="1">1 Viggiano et al., J. Fluid Mech. **918**, 25 (2021).</footnote>

<footnote n="2"><sup>2</sup> Khojasteh et al., *Phys. Fluids* **33**, 095113 (2021).</footnote>