Synthetic Models in Turbulence

Purpose and focus of SIG

Synthetic models were developed in turbulence as an alternative to stochastic methods or direct numerical methods for Lagrangian applications.

SIG 42 was set up after it was realised that many research teams in Europe were using "synthetic turbulence models" and that there was a need form more interaction and unification between the different groups.

Most teams working on synthetic turbulence will be using Kinematic Simulation (KS).  KS is a unified Lagrangian model of one- and two- and indeed multi-particle turbulent dispersion where incompressibility is enforced by construction in the generation of every particle trajectory, the energy spectrum is prescribed according to the type of turbulence considered and where the effects of small-scale flow structure on Lagrangian statistics are taken into account.

As such, KS should be contrasted with Lagrangian stochastic models of turbulent diffusion which do not incorporate small-scale flow structure effects and which are by construction different models for one- and two-particle statistics.

KS is widely used in various domains, including Lagrangian aspects in turbulence mixing/stirring, particle dispersion/clustering, aeroacoustics.

Flow realisations with complete spatial, and sometime spatio-temporal, dependence, are generated via superposition of random modes (mostly  spatial, and sometime spatial and temporal, Fourier modes), with prescribed constraints such as: strict incompressibility (divergence-free velocity field at each point), high Reynolds energy spectrum, ...

Recent improvements consisted in incorporating linear dynamics, for instance in rotating and/or stably-stratified flows, with possible easy generalisation to MHD flows, and perhaps to plasmas. On the other hand, the absence of "sweeping effects" in present conventional KS versions is identified as a major drawback in very different applications: inertial particle clustering as well as in aeroacoustics.

Though most of the work involved in SIG 42 is done using KS, the SIG is open to other `synthetic turbulence'. People using other approaches to study particle dispersion or also welcome to participate in SIG 42's activities in particular to contribute to the different workshops.

A non-exhaustive list of topics the group is interested in:

• Improvement of the modelling of small scales advection by largest scales (sweeping).
• Introduction of strongly anisotropic energy spectra with better randomization of the wave-vector.
• Analogy with initialisation of DNS/LES and with "Particle
  Representation Models".
• Use of specific modes consistent with geometric constraints, e.g. solid walls, instead of 3D spatial Fourier modes.
• Improvement of KS as a subgrid model for LES : Lagrangian diffusion and aeroacoustics.
• Competition between "wavy" (really spatio-temporal, propagating) and "vortical" structures of the velocity field for organising Lagrangian turbulence diffusion, from fluid to plasma turbulence.
• Other "synthetic" models, e.g. to afford intermittency, possibly very different from conventional KS.