Global transient dynamics of three-dimensional hydrodynamical disturbances in a thin viscous accretion disk

Abstract

Thin viscous Keplerian accretion disks are considered asymptotically stable, even though they can show significant dynamic activity on short timescales. In this paper the dynamics of nonaxisymmetric hydrodynamical disturbances of disks are investigated analytically building upon the steady state three-dimensional structure and evolution of axisymmetric perturbations explored in previous work. Assuming a polytropic equation of state solutions are found by means of an asymptotic expansion in the small parameter measuring the ratio of the disk thickness to characteristic radius. In-depth analysis shows that every perturbation that disturbs the radial velocity induces significant transient growth in the (acoustic) energy of the evolving disturbance. This effect is most evident in the density and vertical velocity. The transient growth observed is tied to the nonseparable nature of the solutions where, in particular, pattern evolution is controlled by a similarity variable composed of the radial coordinate and time. This leads to growing winding perturbations that display successive radial peaks and troughs. We argue that these transient non-axisymmetric structures may precipitate secondary instabilities which, consequently, may be a critical element for a new alternative picture of turbulence arousal in non-magnetized astrophysical disks.

Non-exponential hydrodynamical growth in density-stratified thin Keplerian discs

“…Thus, rendering the linear operator non‐normal, the flow shear may give rise to transiently growing perturbations (Gustavsson 1991; Butler & Farrel 1992; Reddy & Henningson 1993; Trefethen et al 1993; Criminale et al 1997), and the recent review by Schmid (2007) whose energy is eventually redistributed among different length‐scales due to non‐linear effects. Indeed, recent calculations in real thin disc geometry have demonstrated the efficiency of such processes to significantly amplify initially small perturbations, and thus to generate intensive hydrodynamical activity in the otherwise centrifugally stable Keplerian discs (Umurhan et al 2006; Rebusco et al 2009). Such non‐modal growth of perturbations has also been obtained for ballooning modes in magnetized rotating plasmas in tokamaks (Chun & Hameiri 1990).…”

Collisionless kinetic regimes for quasi-stationary axisymmetric accretion disc plasmas

“…We now analyze whether these requirements can be satisfied in the various kinetic regimes indicated above by a KDF of the form given by Eq. (11). It follows immediately that this can be achieved for all magnetic field-based configurations belonging to either the SEPE or WEPE regimes.…”

“…Within this framework, each plasma species is described by a KDF which satisfies the Vlasov kinetic equation d dt f s ðy; tÞ ¼ 0, with the velocity moments determining the system fluid fields and the sources of the EM self-fields fE self ; B self g. In particular, ignoring possible weakly dissipative effects (Coulomb collisions and turbulence) and instabilities (see for example Refs. [10][11][12], this paper focuses on regimes which are purely collisionless.…”

Kinetic description of quasi-stationary axisymmetric collisionless accretion disk plasmas with arbitrary magnetic field configurations

“…They are observed in a wide range of astrophysical contexts [1] and consist of plasma orbiting a central object with the velocities of the inward accretion flow usually being much smaller than the rotational velocities. In order for the accretion to happen, there needs to be a net outward transport of angular momentum and there are several conceivable mechanisms for producing this (see for example [17,18]). The most obvious one is fluid viscosity, but this would need to be an "anomalous"viscosity, driven by some type of turbulence, rather than a standard viscosity connected with Coulomb collisions (Spitzer viscosity) which would be much too small to explain the observed accretion rates under the conditions actually found in accretion disks (see [19] for a review of turbulence mechanisms).…”