Abstract
A structure function describing the geometrical properties of Lagrangian turbulence is proposed. This function yields the asymptotic mixing properties of inertial range turbulence. The form of the structure function is deduced from Richardson’s particle dispersion law. Scaling relationships for the mixing volume fraction, the surface area of boundaries between materials, and the chord lengths defined by the intersection points of a ray with material boundaries are obtained. Scaling laws are also deduced for the area fraction, perimeter length, and chord lengths in a two-dimensional section, and for the trajectory of a single particle. The predictions for the two-dimensional case have been verified in several examples of mixing, using data obtained from numerical integration of the Navier–Stokes equations.
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