139 research outputs found
Linear dynamics of the solar convection zone: excitation of waves in unstably stratified shear flows
In this paper we report on the nonresonant conversion of convectively
unstable linear gravity modes into acoustic oscillation modes in shear flows.
The convectively unstable linear gravity modes can excite acoustic modes with
similar wave-numbers. The frequencies of the excited oscillations may be
qualitatively higher than the temporal variation scales of the source flow,
while the frequency spectra of the generated oscillations should be
intrinsically correlated to the velocity field of the source flow. We
anticipate that this nonresonant phenomenon can significantly contribute to the
production of sound waves in the solar convection zone.Comment: 8 pages. To appear in the proceedings of the conference "Waves in
Dusty, Solar and Space Plasmas", Leuven, Belgium 21-26 May 200
A shallow-water theory for annular sections of Keplerian Disks
A scaling argument is presented that leads to a shallow water theory of
non-axisymmetric disturbances in annular sections of thin Keplerian disks. To
develop a theoretical construction that will aid in physically understanding
the relationship of known two-dimensional vortex dynamics to their
three-dimensional counterparts in Keplerian disks. Using asymptotic scaling
arguments varicose disturbances of a Keplerian disk are considered on radial
and vertical scales consistent with the height of the disk while the azimuthal
scales are the full angular extent of the disk. The scalings lead to
dynamics which are radially geostrophic and vertically hydrostatic. It follows
that a potential vorticity quantity emerges and is shown to be conserved in a
Lagrangian sense. Uniform potential vorticity linear solutions are explored and
the theory is shown to contain an incarnation of the strato-rotational
instability under channel flow conditions. Linearized solutions of a single
defect on an infinite domain is developed and is shown to support a propagating
Rossby edgewave. Linear non-uniform potential vorticity solutions are also
developed and are shown to be similar in some respects to the dynamics of
strictly two-dimensional inviscid flows. Based on the framework of this theory,
arguments based on geophysical notions are presented to support the assertion
that the strato-rotational instability is in a generic class of
barotropic/baroclinic potential vorticity instabilities. Extensions of this
formalism are also proposed. The shallow water formulation achieved by the
asymptotic theory developed here opens a new approach to studying disk
dynamics.Comment: Accepted (July 21, 2008), now in final for
Non-exponential hydrodynamical growth in density-stratified thin Keplerian discs
The short time evolution of three dimensional small perturbations is studied.
Exhibiting spectral asymptotic stability, thin discs are nonetheless shown to
host intensive hydrodynamical activity in the shape of non modal growth of
initial small perturbations. Two mechanisms that lead to such behavior are
identified and studied, namely, non-resonant excitation of vertically confined
sound waves by stable planar inertia-coriolis modes that results in linear
growth with time, as well as resonant coupling of those two modes that leads to
a quadratic growth of the initial perturbations. It is further speculated that
the non modal growth can give rise to secondary strato-rotational instabilities
and thus lead to a new route to turbulence generation in thin discs
On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples
We show a concise extension of the monotone stability approach to backward
stochastic differential equations (BSDEs) that are jointly driven by a Brownian
motion and a random measure for jumps, which could be of infinite activity with
a non-deterministic and time inhomogeneous compensator. The BSDE generator
function can be non convex and needs not to satisfy global Lipschitz conditions
in the jump integrand. We contribute concrete criteria, that are easy to
verify, for results on existence and uniqueness of bounded solutions to BSDEs
with jumps, and on comparison and a-priori -bounds. Several
examples and counter examples are discussed to shed light on the scope and
applicability of different assumptions, and we provide an overview of major
applications in finance and optimal control.Comment: 28 pages. Added DOI
https://link.springer.com/chapter/10.1007%2F978-3-030-22285-7_1 for final
publication, corrected typo (missing gamma) in example 4.1
Linear dynamics of weakly viscous accretion disks: A disk analog of Tollmien-Schlichting waves
This paper discusses new perspectives and approaches to the problem of disk
dynamics where, in this study, we focus on the effects of viscous instabilities
influenced by boundary effects. The Boussinesq approximation of the viscous
large shearing box equations is analyzed in which the azimuthal length scale of
the disturbance is much larger than the radial and vertical scales. We examine
the stability of a non-axisymmetric potential vorticity mode, i.e. a
PV-anomaly. in a configuration in which buoyant convection and the
strato-rotational instability do not to operate. We consider a series of
boundary conditions which show the PV-anomaly to be unstable both on a finite
and semi-infinite radial domains. We find these conditions leading to an
instability which is the disk analog of Tollmien-Schlichting waves. When the
viscosity is weak, evidence of the instability is most pronounced by the
emergence of a vortex sheet at the critical layer located away from the
boundary where the instability is generated. For some boundary conditions a
necessary criterion for the onset of instability for vertical wavelengths that
are a sizable fraction of the layer's thickness and when the viscosity is small
is that the appropriate Froude number of the flow be greater than one. This
instability persists if more realistic boundary conditions are applied,
although the criterion on the Froude number is more complicated. The unstable
waves studied here share qualitative features to the instability seen in
rotating Blasius boundary layers. The implications of these results are
discussed. An overall new strategy for exploring and interpreting disk
instability mechanisms is also suggested.Comment: Accepted for publication in Astronomy and Astrophysics. 18 pages.
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