A note on the angular dispersion of a fluid line element in isotropic turbulence

The mean-square angular displacement of a fluid material line element is expressed as an integral of the corresponding angular velocity in material coordinates, with forms like those in Taylor's (1921) linear displacement analysis. Measurements using a hydrogen-bubble tracer in isotropic turbulence show that the mean-square angular velocity of a line is of the same order of magnitude as the mean-square vorticity, and that its ‘Lagrangian’ integral time scale is of the order of the inverse of the r.m.s. vorticity. The angular velocity of a line element is also formulated in spatial co-ordinates. Finally, the connexion between angular dispersion and the approach toward isotropy is pointed out.