Postdoc opportunity!

Postdoc position: Scalar turbulence driven by multifractal random flows

Funding from the CNRS to fund a 12-month postdoc position to work on scalar turbulence. One constraint: the contract must start by the end of 2025. The postdoctoral researcher will join the nonlinear physics team at the institut de physique de Nice and benefit from a dynamic and collaborative environment focused on stochastic physics and turbulence.

Please contact me if interested! Applications will be considered on an ongoing basis.

Context

Spatiotemporal intermittency is a fundamental feature of turbulent environments, characterized in particular by multifractal scaling laws. Recent developments at the intersection of mathematics and statistical physics have extended the multifractal framework of turbulence toward a genuine statistical theory of random fields. The project aims to explore the physics of transport in multifractal environments following a recent extension of the theory of Kraichnan flows to a multifractal setting [1,2], using the Gaussian Multiplicative Chaos as a building block [3] and variants of the random flows constructed by [4].

Project

Analysis of pair separation in multifractal kraichnan flows revealed a regularization effect due to intermittency and connections with the theory of Liouville Brownian motion [2,5]. We propose here to extend the analysis to scalar transport, combining numerical simulations and theoretical analysis. Passive scalar fields are naturally multifractal, in the sense that it is multifractal even within the Gaussian framework of Kraichnan flows [1]. Passive scalars are defined via averages over Lagrangian trajectories, so their multifractal properties are partly determined by the zero modes associated with the backward propagator, which are strongly linked to statistical conservation laws involving the geometry of particle clusters. Characterizing these zero modes will enable a quantitative connection between scalar intermittency and the intermittency of the advecting field — beyond the Gaussian framework. A preliminary step to become familiar with the theory could involve working with multifractal generalizations of the transport model from [6].

Biblio

  • [1] Falkovich, Gawedzki & Vergassola (2001). Rev. Mod. Phys., 73(4); Gawędzki (2008). Non-Eq. Stat. Mech. Turb.4.; Bernard, Gawedzki & Kupiainen (1998). J. Stat. Phys., 90(3); Gawędzki & Vergassola (2000). Physica D, 138; Le Jan & Raimond (2002). Ann. Proba., 30(2), 826-873;
  • [2] Considera & Thalabard, Phys. Rev. Lett (2023), arXiv:2503.18851 (2025)
  • [3] Robert & Vargas (2010). Ann. Proba 38(2), 605-631 ; Rhodes & Vargas (2014). Probab. Surv., 11; Aru (2015). ENS Lyon; Rhodes (2016). arXiv:1602.07323;
  • [4] Pereira, Garban & Chevillard (2016). J. Fluid Mech., 794; Chevillard, Garban, Rhodes & Vargas (2019). Ann. H. Poincaré, 20; Reneuve & Chevillard (2020). Phys.Rev. Lett., 125(1)
  • [5] Berestycki (2015). Ann. H. Poincaré, 51(3); Garban, Rhodes, & Vargas, V. (2016); Jackson (2018). Ann. H. Poincaré, 54(1).
  • [6] Thalabard & Mailybaev, J. Stat. Phys (2024)