Eur. Phys. J. B 18, 353-361 (2000)
https://doi.org/10.1007/PL00011075

Persistency of material element deformation in isotropic flows and growth rate of lines and surfaces

¹ IUSTI, Technopôle de Château Goubert, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
² IRPHE, Centre de Saint Jérôme, Service 252, 13397 Marseille Cedex 20, France

Received: 10 November 1999
Revised: 14 August 2000
Published online: 15 November 2000

Abstract

We explore the consequence of isotropy on the growth of material lines and surfaces in complex flows. We show that the key parameter is the persistency , defined as the product of a typical stretching rate γ to its associated coherence time τ. In particular, we derive the dependence of the net growth rate of both lines and surfaces on . Their growth rates increase strongly with increasing persistencies for small , and then saturate for . Making use of measurements of Girimaji and Pope [1], we estimate the persistency to be of order 1 in isotropic turbulence. We then comment on the evolution of the shape of an initially spherical material blob. While its length increases, one of its tranverse dimension increases slowly and the other one decreases. This quasi-two-dimensional deformation leads a final ribbon-shape.