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Temporal behaviour of global perturbations in compressible axisymmetric flows with free boundaries | V.V. Zhuravlev
; N.I. Shakura
; | Date: |
26 Aug 2008 | Abstract: | The dynamics of small global perturbations in the form of linear combination
of a finite number of non-axisymmetric eigenmodes is studied in two-dimensional
approximation. The background flow is assumed to be an axisymmetric perfect
fluid with the adiabatic index $gamma=5/3$ rotating with power law angular
velocity distribution $Omega propto r^{-q}$, $1.5<q<2.0$, confined by free
boundaries in the radial direction. The substantial transient growth of
acoustic energy of optimized perturbations is discovered. An optimal energy
growth $G$ is calculated numerically for a variety of parameters. Its value
depends essentially on the perturbation azimuthal wavenumber $m$ and increases
for higher values of $m$. The closer the rotation profile to the Keplerian law,
the larger growth factors can be obtained but over a longer time. The highest
acoustic energy increase found numerically is of order $sim 10^2$ over $sim
6$ typical Keplerian periods. Slow neutral eigenmodes with corotation radius
beyond the outer boundary mostly contribute to the transient growth. The
revealed linear temporal behaviour of perturbations may play an important role
in angular momentum transfer in toroidal flows near compact relativistic
objects. | Source: | arXiv, 0808.3480 | Services: | Forum | Review | PDF | Favorites |
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