  Nonlinear phenomena and turbulence are central to our understanding and
modeling the dynamics of fluids and plasmas, and yet they still resist
analytical resolutions in many instances. However, progress has been made
recently, displaying a richness of phenomena which was somewhat unexpected a
few years back, such as the double constant-flux cascades of a same invariant
to both the large and to the small scales, or the presence of non-Gaussian
wings in the large-scale fields, for fluids and plasmas. Here, I will
concentrate on the direct measurement of the magnitude of dissipation and an
evaluation of intermittency in a turbulent plasma using exact laws stemming
from invariance principles and involving cross-correlation tensors with both
the velocity and the magnetic fields. I will illustrate these points through
scaling laws, together with data analysis from existing experiments,
observations and numerical simulations. Finally, I will also briefly explore
the possible implications for validity and use of several modeling strategies.
To appear, Plasma Physics and Controlled Fusion, 2023.
