Issue |
A&A
Volume 427, Number 3, December I 2004
|
|
---|---|---|
Page(s) | 855 - 872 | |
Section | Interstellar and circumstellar matter | |
DOI | https://doi.org/10.1051/0004-6361:20040573 | |
Published online | 16 November 2004 |
Hydrodynamic stability of rotationally supported flows: Linear and nonlinear 2D shearing box results *
Department of Physics, Technion-Israel Institute of Technology, 32000 Haifa, Israel e-mail: mumurhan@physics.technion.ac.il
Received:
1
April
2004
Accepted:
2
August
2004
We present here both analytical and numerical results
of hydrodynamic stability investigations of rotationally supported
circumstellar flows using the shearing box formalism. Asymptotic
scaling arguments justifying the shearing box approximation are
systematically derived, showing that there exist two limits which
we call small shearing box (SSB) and large shearing box (LSB). The
physical meaning of these two limits and their relationship to
model equations implemented by previous investigators are
discussed briefly. Two dimensional (2D) dynamics of the SSB are
explored and shown to contain transiently growing (TG) linear
modes, whose nature is first discussed within the context of
linear theory. The fully nonlinear regime in 2D is investigated
numerically for very high Reynolds (Re) numbers. Solutions
exhibiting long-term dynamical activity are found and manifest episodic
but recurrent TG behavior and these are associated with the
formation and long-term survival of coherent vortices. The
life-time of this spatio-temporal complexity depends on the Re
number and the strength and nature of the initial disturbance.
The dynamical activity in finite Re solutions ultimately decays
with a characteristic time increasing with Re. However, for large
enough Re and appropriate initial perturbation, a large number of TG
episodes recur before any viscous decay begins to clearly manifest itself.
In cases where nominally (i.e. any dissipation resulting
only from numerical truncation errors),
the dynamical activity persists
for the entire duration of the simulation (hundreds of box
orbits).
Because the SSB
approximation used here is equivalent to a 2D incompressible flow,
the dynamics can not depend on the Coriolis force.
Therefore, three dimensional (3D) simulations are needed in order to decide if this
force indeed suppresses nonlinear hydrodynamical
instability in rotationally supported disks in the shearing box
approximation, and if recurrent TG behavior can still persist in three dimensions
as well – possibly giving rise to a subcritical transition to long-term
spatio-temporal complexity.
Key words: accretion, accretion disks / hydrodynamics / instabilities / stars: novae, cataclysmic variables / methods: numerical / stars: planetary systems: protoplanetary disks
© ESO, 2004
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