In the present theoretical work, spatially locked, predominantly one-dimensional (1D) turbulent eddies hosting n fluid parcels that exchange chaotically their positions are approached as discretized, one-dimensional, “generic” rearrangements (permutations) that comprise assemblages, gn=mk1mk2mkl, of minor, “mixing” rearrangements, mki, satisfying three topological–kinematical criteria that outline their mixing extent. In turn, the criteria lead to the derivation of two theorems of mixing that help count the number of all possible mixing rearrangements. The “universal” set of all generic rearrangements, gn, is organized into subsets characterized by the same domain structure, gn=gnkmk+lgnl, that determines the size and location of a characteristic, minor mixing eddy mk+l within the major, generic one, gn. Under the guidance of the first of the two aforementioned theorems of mixing, there can be gathered all pairwise disjoint, domain-structured subsets that add up to the universal set. Then, a class of “independent degrees of freedom of turbulent mixing” has been assembled, a new functional tool in the probability theory of one-dimensional turbulent mixing. The theorem-dictated condition for making up a class of independent degrees of freedom of turbulent mixing is that the characteristic, minor, mixing domains mk+l of the participating subsets are all sharing one at least common point of the generic domain.

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