There has been a long debate in the turbulence community about the 3D structure of magnetohydrodynamic (MHD) turbulence. Particularly intriguing is the sub-Alfvenic regime since most interstellar medium and space plasma has small perturbation. Do the perturbations in large scale system behave like waves or turbulence?  Does turbulence self-organize from linear wave-like fluctuations to strong turbulence during the energy cascade? The Alfvénic weak-to-strong transition is the most critical, yet observationally unconfirmed, prediction of MHD turbulence theory in the last three decades.

I also have also encountered such controvercy frequently during my research since the turbulence statistics is crucial for particle transport, a topic that I have been doing since my PhD.  We adopted the critical balance model (Goldreich & Sridhar 1995) in our earlier study of cosmic ray diffusion. In the mean time, I also noticed that many studies, particularly in the field of space plasma, used 2D+slab model, meaning that the Alfvenic turbulence has only perpendicular cascade. On the other hand, turbulence is also predicted to become critically balanced (nonlinear time comparable to wave period) down to some smaller scales even with 2D weak perturbation on the injection scale initially. Only a few years ago, the numerical test  in realistic settings. i.e., compressible medium has been achieved by my former postdoc Kirit Makwana (assistant professor now at IIT Hyderabad in India), by employing a weaker forcing scheme compared to commonly adopted delta-correlated-in-time  forcing.

A couple of years later, Dr. Siqi Zhao joined our group as a postdoc. Since her expertise is in space plasma, I thought it would be really exciting if we could identify such transition from the real observational data, which has never been done before. It is even more challenging to the numerical tests, which are well controlled. It is exceptionally difficult because the three-dimensional sampling of turbulence fluctuations was not available yet. We had to develop new multi-spacecraft analysis methods in order to obtain three-dimensional information on velocity and magnetic field fluctuations. Employing the multi-spacecraft timing analysis combined with the SVD (Singular Value Decomposition) method allowed us to make direct comparisons between observations and theory.  The methods are applied then to the ESA’s Cluster mission – consisting of a constellation of four space probes orbiting the Earth, which explore how the Sun and Earth interact.  

Our analysis shows that the Alfvénic transition to strong turbulence with critical balance is bound to occur with increasing nonlinearity, regardless of the initial level of MHD perturbations, highlighting the universality of strong MHD turbulence. Moreover, the study demonstrates that turbulence can self-organize from 2D wave-like fluctuations to 3D strong turbulence during the energy cascade, thus verifying the unified theoretical framework for both weak and strong turbulence.  

Thus, the debate between two-dimensional turbulence and turbulence with critical balance can be settled with the discovery of the Alfvénic transition. As the result, those findings substantially deepen our knowledge of ubiquitous turbulence, and their implications extend beyond the study of turbulence itself to particle transport and acceleration, magnetic reconnection, star formation, and all other relevant physical processes from our earth to the remote Universe.