Crosscorrelationaided transport in stochastically driven accretion flows
Abstract
The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such nonnormal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and coworkers [Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013), 10.1088/17518113/46/3/035501; Nath et al., Phys. Rev. E 88, 013010 (2013), 10.1103/PhysRevE.88.013010] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a "cold" accretion flow at 3000 K is too "hot" in the statistical parlance and is capable of inducing strong thermal modes) with the underlying TaylorCouette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing nonnormal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.
 Publication:

Physical Review E
 Pub Date:
 December 2014
 DOI:
 10.1103/PhysRevE.90.063014
 arXiv:
 arXiv:1412.1752
 Bibcode:
 2014PhRvE..90f3014N
 Keywords:

 47.35.Tv;
 05.20.Jj;
 95.30.Qd;
 98.62.Mw;
 Magnetohydrodynamic waves;
 Statistical mechanics of classical fluids;
 Magnetohydrodynamics and plasmas;
 Infall accretion and accretion disks;
 Astrophysics  High Energy Astrophysical Phenomena;
 Condensed Matter  Statistical Mechanics;
 Physics  Fluid Dynamics
 EPrint:
 13 figures in main tex, 8 figures in online supplemental, accepted in Physical Review E