Disentangling eddy turbulence and wave turbulence: the challenge of rotating and stratified fluids – DisET

Turbulence, defined generically as an out-of-equilibrium state of systems with a large number of degrees of freedom, is not a concept restricted to fluid dynamics. An ensemble of dispersive waves in nonlinear interaction is indeed also said to be in a turbulent state, called Wave Turbulence, which is expected in a wide spectrum of systems from quantum mechanics to astrophysics. A theoretical framework for this “other kind” of turbulence has been developed starting with the work of Zakharov in the 1960’s focused on the weakly nonlinear limit. During the last two decades, this Weak Turbulence Theory (WTT) has been increasingly successful in describing the “turbulence of waves” in 2D mechanical systems such as surface water waves or bending waves in elastic plates.
In fluid mechanics, the situation is more complex when bulk waves are present since the system is prone to entangle strong hydrodynamic turbulence and weak wave turbulence. Turbulence in stratified or rotating fluids, enabling the propagation of internal gravity and inertial waves respectively, are typical examples of this situation which is still poorly understood. Rotation and stratification are moreover central ingredients of Earth atmospheric and oceanic dynamics. In comparison with 2D systems, the assessment of WTT in these systems raises the difficulty of dealing with 3D anisotropic velocity fields. This makes this dawning research area technically more challenging. Independently, approaching wave turbulence regimes in these systems, i.e. a turbulence dominated by weakly nonlinear waves, is in itself a challenge, which has rarely been realized. The relevance of WTT for rotating and/or stratified turbulence remains consequently an open question.
The primary goal of our project is to achieve wave turbulence regimes in experimental and numerical rotating and/or stratified turbulent flows. For this, we will set up original turbulence experiments and direct numerical simulations, promoting weak nonlinearity and injection of energy in waves. This strategy aims at exploring regimes significantly different from those of past studies in which energy was most often injected in eddy structures. The coordinated effort of the 4 partners, exploring different systems expected to develop similar behaviors, is a cornerstone of our project.
Experiments in water using stratified fluid channels and/or precision rotating platforms will be designed at LPENSL and FAST. These setups will allow us to install sophisticated wave generators injecting energy in weakly nonlinear waves. Experiments will also be conducted in the cryostat dedicated to turbulence at Institut Néel settled on a rotating platform in 2016. Taking advantage of the low viscosity of liquid helium, this technically extremely challenging experiment, which allows image-based velocimetry, aims at reaching unprecedented regimes of weak nonlinearity with respect to rotation (keeping nonlinearity strong with respect to viscous effects). Besides, high-resolution long-term direct numerical simulations will be performed at LMFA.
In order to access the high spatio-temporal resolution necessary to uncover the dynamics of the turbulent flows, we will use multiple camera velocimetry systems in experiments and high-performance computing facilities in numerics. The final objective is to implement a systematic spatio-temporal statistical analysis of the data gathered during the project, with the aim of disentangling waves from strongly nonlinear structures and, for the first time, to thoroughly test the relevance of WTT and its strongly nonlinear extensions in flows dominated by weakly nonlinear 3D waves.
The DisET project aims at producing a breakthrough in the understanding of bulk wave turbulence which is a key ingredient of large-scale geophysical flows and therefore fundamental regarding weather and climate forecast.