Vorticity statistics based on velocity and density-weighted velocity in premixed reactive turbulence

The local and non-local statistics of vorticity (omega) over right arrow (i.e. curl of velocity vector (u) over right arrow) and pseudo-vorticity (omega) over right arrow* (i.e. curl of density-weighted velocity vector. rho(u) over right arrow/rho(0)) have been investigated in detail based on a direct numerical simulation (DNS) database of freely propagating statistically planar flames in different regimes of premixed turbulent combustion. It has been found that the relative orientation of (omega) over right arrow* can be significantly different to that of (omega) over right arrow. for small values of the Karlovitz number and large values of the Reynolds number. The vorticity (omega) over right arrow shows, depending on the case, considerable alignment with either the most extensive or compressive principal strain rate. In contrast, (omega) over right arrow* has been found to align with the intermediate principal strain rate for all cases. The transport statistics of Reynolds averaged enstrophy (i.e. (Omega) over bar = <(<(omega)over right arrow> . (omega) over right arrow )over bar>/2) and pseudo-enstrophy (i.e. (Omega) over bar* = <(<(omega)over right arrow>* . (omega) over right arrow*)over bar>/2) have been investigated in detail. The non-local vorticity statistics in turbulent premixed combustion have been investigated based on the vorticity line segment (VLS) structure, which is defined with respect to each grid point as the part of the (pseudo) vorticity line bounded by the two adjacent extremal points of the (pseudo) vorticity magnitude. VLS can be characterised by the segment length and the (pseudo) vorticity magnitude difference across the segment, i.e. (Delta omega*) Delta omega. Strong dilatation effects tend to increase VLS length, whereas turbulent convection disturbs the flow field resulting in shorter VLS. The joint PDFs between the segment length and (Delta omega) Delta omega* are found to be symmetric, whereas the joint PDFs between the segment length and the pseudo-vorticity magnitude difference across the VLS in the flame normal direction show significant asymmetry, which is primarily determined by density variation across the flame front and turbulence intensity.