Dynamical and statistical properties of the large scales in turbulence – DYSTURB

Turbulence occurs in most astrophysical and geophysical flows, as well as in many industrial processes. In most situations, turbulence transfers energy from large to small scales. For three-dimensional flows, energy is injected at the forcing scale and nonlinear interactions transfer it to shorter spatial scales where it is efficiently dissipated by viscosity. The small scales of turbulent flows are supposed to be universal and have been studied in great details in various contexts. In contrast less is known for the large scales. The aim of this project is to study the properties of the large scales in turbulence, here defined as the scales larger than the forcing scale.

We propose to study experimentally and numerically two canonical systems to determine the behavior of large scale turbulent fluctuations under different circumstances. The first system is three dimensional homogeneous isotropic turbulence (3DT) and the second system is gravity wave turbulence (GWT) on the surface of a fluid.

We will develop two large scale experiments in which we will create a flow or an ensemble of waves at small scale compared to the largest scale of the system. The technical barrier is to create intense enough turbulence in a controlled manner to be able to generate larger scales. Our program contains back-up solutions to make sure that these experiments will be successful.

These two systems have different large scale properties. In 3D homogeneous turbulence no cascade to the large scales is expected while an inverse cascade of wave action towards the large scales is predicted for surface gravity wave turbulence. The purpose of our project is thus to perform a detailed study of the large scales with the largest possible scale separation in order to better understand the two possible situations: with inverse cascade (GWT) or without inverse cascade (3DT).

We want to understand and quantify the relation between the large scales and the fluxes of energy or wave action. Beyond the mean properties we will also focus on dynamical ones. To wit, we plan to perform accurate measurements of the instantaneous injected power and to develop and implement a new optical method to measure the instantaneous dissipation rate using Diffusing Wave Spectroscopy.

In the case of 3D turbulence, as there is no mean energy flux towards the larger scales, it is expected that these scales are in statistical equilibrium, i.e. all the modes have the same energy. An expected result is to observe and characterize this regime experimentally. This would provide a new way to model the large scales using the tools of equilibrium statistical mechanics.

In particular, our project will give a path to define for a turbulent system the effective temperature of a large scale flow or to predict the properties of rare events or the ones of the fluctuations of injected power. Such concepts are likely to be valid in the 3D turbulent system and we will investigate to what extent they also apply in the system of waves for which an inverse cascade exists.

We shall test these concepts in the experiments and compare them with numerical simulations. Despite being limited in the accessible parameter range, the simulations will be useful as they provide access to quantities difficult to measure in the experiments.