ABSTRACT
We discuss the significance of the law of conservation of angular momentum for freely evolving, homogeneous turbulence. We start by noting that Loitsyansky’s integral can be interpreted as the mean square angular momentum of a large cloud of isotropic turbulence. As noted by Landau, the near invariance of this integral is a direct consequence of the law of conservation of angular momentum. We show that these ideas may be generalized to any homogeneous system which preserves one or more components of angular momentum, such as MHD or stratified turbulence. We focus on the case of MHD turbulence where we derive a Loitsyansky-like invariant and show that a fully nonlinear decay model based on this invariant produces results compatible with the experimental data. The invariant exists for highly conducting and weakly conducting fluids (i.e., high and low Rm) and for any value of the imposed mean magnetic field, including zero field. The chapter concludes with a brief discussion of how these ideas extend to stratified turbulence.
