42.1 Basic properties

Consider a mixing process governed by a tensor ${\bf J}$. This tensor in general contains both symmetric and anti-symmetric components^42.1 given by

$$J^{m n} = {1 \over 2}(J^{m n} + J^{n m}) + {1 \over 2}(J^{m n} - J^{n m}) \equiv K^{m n} + A^{m n},$$ (42.3)

where the symmetric part of the tensor is written K^{m n} and the anti-symmetric part as A^{m n} = - A^{n m}. For diffusive or dissipative mixing, K^{m n} is symmetric and positive semi-definite. Note that anti-symmetry implies the diagonal terms in A^{m n}vanish. Additionally, anti-symmetry is a frame invariant property of a tensor.