On the Breaking of Mirror Symmetry in Homogeneous Isotropic Turbulence-Helicity Effect

In homogeneous isotropic turbulence when reflexional (or mirror) symmetry breaks down, it becomes necessary to take accounts of the additional fundamental invariants in constructing forms for correlation tensors of different orders that characterize the flow. It is helicity which plays its role in such a situation. Attention is paid here, in particular to the construction of appropriate invariant forms for the several two-point second and third order correlation tensors that arise out of fluctuating pressure, velocity and external force fields of such a turbulent flow. Utilizing these forms of second and third order tensors, the two-point vorticity-vorticity and acceleration-acceleration correlations are determined, separately illustrating the effects of helicity on them. Mathematics Subject Classification: 76F05, 76D05