Institute of Mathematics for Industry


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Dynamics of unstable fluid interface: conservation laws and group theory

Hold Date 2011-12-15 15:30~2011-12-15 17:00

Place Seminar Room 3, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Snezhana I. Abarzhi (The University of Chicago)

We observe the development of the Rayleigh-Taylor instability (RTI)
whenever two fluids of different densities are accelerated against the
density gradients. RTI plays a key role in a broad variety of natural
phenomena spanning astrophysical to atomistic scales and in
technological applications. It influences the formation of ‘hot spot’ in
inertial confinement fusion, limits radial compression of imploding
Z-pinches, controls non-equilibrium heat transfer induced by ultra-fast
high-power lasers in solids, and governs the transports of mass,
momentum and energy in interstellar molecular clouds, flashes of
supernovae, ocean, atmosphere, flames and fires. RTI is essential to
occur under extreme conditions of high energy density, and one can still
observe it easily in everyday life when looking at how salted and fresh
water mix.

We developed the theoretical analysis to systematically study the
nonlinear evolution of Rayleigh-Taylor instability. Fluids may have
similar or contrasting densities, acceleration can be sustained or
time-dependent, the domain may have a finite size, and the flow is
periodic in the plane normal to direction of acceleration. The concepts
of theory of discrete groups are applied to capture properties of the
interfacial dynamics. Asymptotic nonlinear solutions are found, and
their structure and stability are investigated.

It is shown that isotropic coherent structures are stable. For
anisotropic structures, secondary instabilities develop with the
growth-rate determined by the density ratio. For stable structures, the
invariants of the dynamics, which are independent of the density ratio,
are identified. The influence of the height of the domain on diagnostic
parameters of the flow is studied. The results obtained show that the
large-scale coherent dynamics in the Rayleigh-Taylor instability has
essentially non-local and multi-scale character.