Particle pair separation in kinematic simulations

Abstract

The separation of pairs of particles within turbulent flow fields constructed using the ‘kinematic simulation’ method is explored. A consequence of the way the flow is constructed is that, in contrast to real turbulence, there is no ‘sweeping’ of the smaller eddies by the larger eddies. The implications of this are investigated. A simple phenoenological argument is presented which predicts that the mean-square separation of the particle pairs should grow like $t^6$ in kinematic simulation. Simulations support this result for the case where a large mean velocity is added to the flow to exaggerate the sweeping problem and the inertial subrange is sufficiently long. In the absence of a large mean velocity, the situation is more complex with the simple phenomenological argument failing in the parts of the flow where the velocity is much smaller than the r.m.s. velocity and where there is no sweeping problem. The separation process then follows $t^6$ in the bulk of the flow but follows Richardson's classical $t^3$ law in regions where the velocity is much smaller than the r.m.s. velocity. Because of the way the size of these regions varies in time, the resulting mean-square separation grows like $t^{9/2}$. Both the $t^6$ and $t^{9/2}$ behaviours contrast with the classical Richardson $t^3$ law, which is believed to hold in reality, and raise questions about the applicability of the kinematic simulation approach to the separation of pairs in real turbulent flows.