Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996apj...460..855l&link_type=abstract
Astrophysical Journal v.460, p.855
Astronomy and Astrophysics
Astronomy
19
Stars: Circumstellar Matter, Hydrodynamics, Instabilities, Solar System: Formation
Scientific paper
Single-armed spiral instabilities may play an important role in self-gravitating disks. However, past studies have indicated that disks which are less massive than an embedded central star are in general linearly stable to m = 1 perturbations. In this paper, we outline how the nonlinear interaction of two growing modes with azimuthal mode numbers m = n and m = n + 1 can excite the development of a one-armed disturbance which grows exponentially at a rate equal to the sum of the growth rates of the two linearly unstable modes. Within the context of a second order, semianalytic analysis, we discuss the special case of a unique nonwinding, exponentially growing solution, and then we consider further solutions based on physically relevant initial conditions. We find that the nonwinding solution describes the general dynamics of the mode at later times. We then compare the results of our nonlinear analysis with hydrodynamic simulations, illustrating that the process we have considered is indeed an important effect.
Korchagin Vladimir
Laughlin Gregory
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