Transient growth of perturbations on scales beyond the accretion disc thickness

Abstract

Turbulent state of spectrally stable shear flows may be developed and sustained according to the bypass scenario of transition. If it works in non-magnetised boundless and homogeneous quasi-Keplerian flow, transiently growing shearing vortices should supply turbulence with energy. Employing the large shearing box approximation, as well as a set of global disc models, we study the optimal growth of the shearing vortices in such a flow in the whole range of azimuthal length-scales, ${\lambda }_y$, as compared to the flow scale-height, $H$. It is shown that with the account of the viscosity the highest possible amplification of shearing vortices, $G_{max}$, attains maximum at ${\lambda }_y\lesssim H$ and declines towards both the large scales ${\lambda }_y\gg H$ and the small scales ${\lambda }_y\ll H$ in a good agreement with analytical estimations based on balanced solutions. We pay main attention to the large-scale vortices ${\lambda }_y\gg H$, which produce $G_{max}\propto (\Omega /\kappa {)}^4$, where $\Omega$ and $\kappa$ denote local rotational and epicyclic frequencies, respectively. It is demonstrated that the large-scale vortices acquire high density perturbation as they approach the instant of swing. At the same time, their growth is not affected by bulk viscosity. We check that $G_{max}$ obtained globally is comparable to its local counterpart and the shape and localisation of global optimal vortices can be explained in terms of the local approach. The obtained results allow us to suggest that the critical Reynolds number of subcritical transition to turbulence in quasi-Keplerian flow, as well as the corresponding turbulent effective azimuthal stress should substantially depend on shear rate.

Accepted for publication in MNRAS

References in corpus (12)

• On the Stability of Elliptical Vortices in Accretion Discs
• On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks
• Conservative GRMHD Simulations of Moderately Thin, Tilted Accretion Disks
• Nonlinear Evolution of Hydrodynamical Shear Flows in Two Dimensions
• Formation, Survival, and Destruction of Vortices in Accretion Disks
• Hydrodynamic stability and mode coupling in Keplerian flows: local strato-rotational analysis
• Subcritical dynamos in shear flows
• Nonmodal growth of the magnetorotational instability
• Nonlinear transverse cascade and two-dimensional magnetohydrodynamic subcritical turbulence in plane shear flows
• Magnetorotational instability: nonmodal growth and the relationship of global modes to the shearing box
• Nonmodal energy growth and optimal perturbations in compressible plane Couette flow
• A study of transient dynamics of perturbations in Keplerian discs using a variational approach

Cited by in corpus (2)

• Nonlinear transverse cascade and sustenance of MRI-turbulence in Keplerian disks with an azimuthal magnetic field
• Analytic construction of baroclinic tori by non-linear summation