  Randomization of the Lagrangian chaos in fluid dynamics has been analyzed
using results of direct numerical simulations, laboratory measurements, and
oceanic observations. The notion of distributed chaos has been used in order to
quantify this phenomenon (the main dimensionless parameter of distributed chaos
has been used as a measure of randomization). The analysis includes isotropic
homogeneous fluid motion, buoyancy-driven flows, particle-laden flows,
magnetohydrodynamic flows, and subsurface oceanic mixing. The role of the
dissipative Birkhoff-Saffman and Loitsyanskii invariants as well as the
invariants related to the spontaneous breaking of the local reflectional
symmetry (in particular, the Levich-Tsinober invariant) in the randomization
phenomenon has been also investigated.
