Lorenzo Manfredini successfully defended his doctoral thesis on reduced models of turbulent cascades in fluids and plasmas
27 Oct. 2026
- Congratulations to Lorenzo Manfredini, who successfully defended his thesis entitled "Reduced Models for turbulent cascades in fluid and plasma turbulence".
- Abstract
High-Reynolds-number turbulent flows span many decades in scale, posing a challenge for direct numerical simulations. This limitation has motivated the development of reduced cascade models designed to achieve large separation of scales with a small number of degrees of freedom. The archetypical example of such reduction is shell models, which decimate Fourier space via a one-dimensional sequence of logarithmically spaced modes, reducing the complexity of triadic couplings. Shell models reproduce nontrivial features of turbulent cascades, such as power-law spectra, and exhibit intermittency, manifested as bursts of dissipation associated with extreme energy transfer events.
- The first part of this thesis characterizes the statistical properties of those events. The connection between intermittency and phase synchronization within the triads governing nonlinear energy transfer is investigated, showing that stronger triadic phase alignment enhances intermittency. A Kuramoto order parameter is introduced to quantify the phase synchronization of triads in wave-number space, connecting it to extreme energy transfer events, and opening a route toward studying intermittency in Fourier space.
- The second part of this thesis is devoted to Hybrid Lattices (HLs), a novel framework for investigating turbulent cascades in Fourier space, combining regular grids with cascade models based on logarithmic discretizations. The logarithmic spacing factor of these models, e.g. the golden ratio, being irrational, typically prevents interactions between a regular grid and a self-similar model. HLs are constructed by expanding a regular region in Fourier space through recurrence relations (e.g. the Fibonacci recurrence relation), generating an asymptotically logarithmic lattice in which Cartesian components remain integers. The resulting grid preserves triadic interactions linking regular and recurrent regions. The recurrence-sequence approach is first tested on shell models; the HL framework is then developed by proposing a numerical algorithm to compute convolutions on these grids, and by investigating the Burgers equation and two-dimensional turbulence on these lattices, which can be seen as Fourier-decimated grids.
- Date and venue of the Defense
- Friday, 2 October 2026 at 14:00
- Amphithéâtre Astier (bâtiment Esclangon), Jussieu (Campus Pierre & Marie Curie).
- Examination Committee
- Franck Plunian, Professor, ISTerre, Grenoble, Reviewer
- Wouter Bos, Research Director, LMFA, Lyon, Reviewer
- Berengere Dubrulle, Research Director, SPEC, CNRS, CEA, Saclay, Examiner
- Benjamin Favier, Research Scientist, IRPHE, Marseille, Examiner
- Steve Tobias, Professor, Institute for Condensed Matter and Complex Systems, Institute for Astronomy, Edinburgh, Examiner
- Yanick Sarazin, Research Director, IRFM, CEA, Cadarache, Examiner
- Sebastien Galtier, Professor, LPP, Palaiseau, Examiner
- Özgür Gürcan, Research Scientist, CNRS (LPP), Thesis Supervisor