Pair dispersion over an inertial range spanning many decades

Abstract

New numerical results on scalar pair dispersion through an inertial range spanning many decades are presented here. These results are achieved through a new Monte Carlo algorithm for synthetic turbulent velocity fields, which has been developed and validated recently by the authors [J. Comput. Phys. 117, 146 (1995)]; this algorithm is capable of accurate simulation of a Gaussian incompressible random field with the Kolmogoroff spectrum over 12–15 decades of scaling behavior with low variance. The numerical results for pair dispersion reported here are within the context of random velocity fields satisfying Taylor’s hypothesis for two-dimensional incompressible flow fields. For the Kolmogoroff spectrum, Richardson’s t3 scaling law is confirmed over a range of pair separation distances spanning eight decades with a Richardson constant with the value 0.031±0.004 over nearly eight decades of pair separation, provided that the longitudinal component of the velocity structure tensor is normalized to unity. Remarkably, in appropriate units this constant agrees with the one calculated by Tatarski’s experiment from 1960 within the stated error bars. Other effects on pair dispersion of varying the energy spectrum of the velocity field and the degree of isotropy, as well as the importance of rare events in pair separation statistics, are also developed here within the context of synthetic turbulence satisfying Taylor’s hypothesis.