A new model of turbulent relative dispersion: a self-similar telegraph equation based on persistently separating motions

Abstract

Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity, which are crucial for real turbulence, are implemented to a master equation by multiple-scale consideration. A telegraph equation with scale-dependent coefficients is derived in the continuous limit. Unlike the conventional case, the telegraph equation has a similarity solution bounded by the maximum separation. The evolution is characterized by two parameters: the strength of persistency of separating motions and the coefficient of the drift term. These parameters are connected to Richardson's constant and, thus, expected to be universal. The relationship between the drift term and coherent structures is discussed for two 2-D turbulences.