Quasi-viscous accretion flow - I. Equilibrium conditions and asymptotic behaviour

Abstract

In a novel approach to studying viscous accretion flows, viscosity has been introduced as a perturbative effect, involving a first‐order correction in the α‐viscosity parameter. This method reduces the problem of solving a second‐order non‐linear differential equation (Navier–Stokes equation) to that of an effective first‐order equation. Viscosity breaks down the invariance of the equilibrium conditions for stationary inflow and outflow solutions, and distinguishes accretion from wind. Under a dynamical systems classification, the only feasible critical points of this ‘quasi‐viscous’ flow are saddle points and spirals. On large spatial scales of the disc, where a linearized and radially propagating time‐dependent perturbation is known to cause a secular instability, the velocity evolution equation of the quasi‐viscous flow has been transformed to bear a formal closeness with Schrödinger's equation with a repulsive potential. Compatible with the transport of angular momentum to the outer regions of the disc, a viscosity‐limited length‐scale has been defined for the full spatial extent over which the accretion process would be viable.

Dissipation and acoustic tunnelling about the sonic horizon of Bondi accretion

“…Both phenomena are consistent with each other, when we recall the possibility of the evaporation of black holes (Unruh 1981;Jacobson 1991;Unruh 1995). Since viscosity appears to be instrumental in the Hawking radiation, which is fundamentally a quantum effect, we mention a study where viscosity in the Navier-Stokes equation was shown to be equivalent to Planck's constant in Schrödinger's equation (Bhattacharjee et al 2009).…”

Multi-criticality and related bifurcation in accretion discs around non-rotating black holes -- an analytical study

“…Recent studies have concluded that, low angular momentum axially symmetric sub-Keplarian accretion flow shows multi-transonicity as well [1]. Apart from this multi-transonic behaviour, we can demonstrate this whole accretion as a dynamical system and can draw a phase portrait where the transonic points are realized mathematically as the critical points of phase flow [2,3,4,5,6,7,8,9,10,11,12,13]. For certain astrophysically relevant boundary conditions, the flow can have a maximum of three critical points, of which two are saddletype critical points and the third one is a centre-type critical point, which is attenuated between the previous two.…”

Nonlinear variations in axisymmetric accretion

“…Fluid flows are affected both by nonlinearity and viscosity, occasionally as competing effects. In models of accretion discs, viscous dissipation usually brings about stability, but in one of the models of axisymmetric accretion, namely, the quasi-viscous accretion disc, viscosity actually destabilizes the flow under linear perturbations [41,45]. In this model, kinematic viscosity is constrained as a vanishingly small first-order perturbative effect about a background inviscid flow.…”