Lagrangian multi-particle statistics

Combined measurements of the Lagrangian evolution of particle constellations and the coarse-grained velocity derivative tensor. partial derivative(u) over tilde (i) /partial derivative x(j) are presented. The data are obtained from three-dimensional particle tracking measurements in a quasi isotropic turbulent flow at an intermediate Reynolds number.

Particle constellations are followed for as long as one integral time and for several Batchelor times. We suggest a method to obtain. partial derivative(u) over tilde (i) /partial derivative x(j) from velocity measurements at discrete points. Based on an analytical result and on a sensitivity analysis, both presented here, we estimate the accuracy for filtered strain, (s) over tilde (2), and enstrophy, (omega) over tilde (2), at around 30%.

The accuracy improves with higher tracer seeding density and with smaller filter scale Delta. We obtain good scaling with t* = root 2r(2)/15S(2)(r) for filtered strain and vorticity and present filtered R-Q invariant maps with the typical 'tear drop' shape that is known from velocity gradients at viscous scales.

Lagrangian results are given for the growth of particle pairs, triangles and tetrahedra. Their principal axes are preferentially oriented with the eigenframe of coarse-grained strain, just like constellations with infinitesimal separations are known to do. The compensated separation rate is found to be close to its viscous counterpart as 1/2 . t*/root 2 approximate to 0.12.

It appears that the contribution from the coarse-grained strain field, r(i)r(j)(s) over tilde (ij) filtered at scale Delta = r, is responsible for roughly 2/3 of the separation rate, while 1/3 stems from scales Delta