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
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.
PACS: 47.27.Ak – Fundamentals / 47.27.Gs – Isotropic turbulence; homogeneous turbulence / 47.27.Qb – Turbulent diffusion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
