Scalar Intermittency

Anne Bourlioux
University of Montreal
Department of Mathematics

I will introduce elementary models involving advection diffusion
of a passive scalar with a mean gradient by a velocity field
consisting of a deterministic or random shear flow with a
transverse time-periodic cross-sweep. Despite the simplicity of
these models, the PDF's exhibit scalar intermittency,
i.e. a transition from a Gaussian PDF to a broader than Gaussian
PDF with large variance as the Peclet number increases with a
universal self-similar shape which is determined analytically
by explicit formulas. The intermittent PDF's resemble those that
have been found recently in numerical simulations of much more
complex models. Examples will be presented to demonstrate
unambiguously that neither velocity fields inducing chaotic
particle trajectories with positive Lyapunov exponents nor
strongly turbulent velocity fields are needed to produce scalar
intermittency with an imposed mean gradient.
(joint work with A.J.Majda)


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