1 Risø National Laboratory for Sustainable Energy, Technical University of Denmark2 IT Service Department, Risø National Laboratory for Sustainable Energy, Technical University of Denmark3 Department of Wind Energy, Technical University of Denmark4 IT Service, Administration, Technical University of Denmark
On the basis of Corrsin’s independence hypothesis, in conjunction with specific assumptions about the form of the distance-neighbour function, an equation is derived for twoparticle dispersion in isotropic turbulence with no mean motion. It is formulated in terms of the mean-square difference between the particle positions r 1(t1) and r2(t2) at arbitrary times t1 and t2 after the release of the particles with a given initial separation. Eddy removal and eddy decay are included with wave-number dependent time scales. The equation, which in general must be solved numerically, has been considered for the scale free k−5/3 energy spectrum as well as for the von K´arm´an spectrum. The model implies that only when the outer scale is infinite, i.e. in the limit where the energy spectrum is of the form k−5/3, will there be a Cεt 3 range of the mean-square separation between the two particles. In this limiting case it is possible to estimate the dimensionless Richardson- Obukhov constant C as a function of a dimensionless eddy-decay parameter. A reasonable choice of this parameter leads to a C-value of the order 1.