9,626 research outputs found
Global instability of low-density jets
The global stability of laminar axisymmetric low-density jets is investigated
in the low Mach number approximation. The linear modal dynamics is found to be
characterised by two features: a stable arc branch of eigenmodes and an
isolated eigenmode. Both features are studied in detail, revealing that,
whereas the former is highly sensitive to numerical domain size and its
existence can be linked to spurious feedback from the outflow boundary, the
latter is the physical eigenmode that is responsible for the appearance of
self-sustained oscillations in low-density jets observed in experiments at low
Mach numbers. In contrast to previous local spatio-temporal stability analyses,
the present global analysis permits, for the first time, the determination of
the critical conditions for the onset of global instability, as well the
frequency of the associated oscillations, without additional hypotheses,
yielding predictions in fair agreement with previous experimental observations.
It is shown that under the conditions of those experiments, viscosity variation
with composition, as well as buoyancy, only have a small effect on the onset of
instability
A class of Hamilton-Jacobi equations on Banach-Finsler manifolds
The concept of subdifferentiability is studied in the context of
Finsler manifolds (modeled on a Banach space with a Lipschitz bump
function). A class of Hamilton-Jacobi equations defined on Finsler
manifolds is studied and several results related to the existence and
uniqueness of viscosity solutions are obtained.Comment: 24 page
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