# Quasi-viscous accretion flow -- I: Equilibrium conditions and asymptotic behaviour Source: [Quasi-viscous accretion flow -- I: Equilibrium conditions and asymptotic behaviour]() Collection index: [llms.txt]() Data updated: 2025-10-28T13:53:30.913Z Authors: Jayanta K. Bhattacharjee, Atri Bhattacharya, Tapas K. Das, Arnab K. Ray Published: 2008-12-28T05:10:56.000Z ## 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 $\\alpha$-viscosity parameter. This method reduces the problem of solving a second-order nonlinear 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. A linearised and radially propagating time-dependent perturbation gives rise to secular instability on large spatial scales of the disc. Further, on these same length scales, the velocity evolution equation of the quasi-viscous flow has been transformed to bear a formal closeness with Schr\\"odinger'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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()