A viscous-convective instability in laminar Keplerian thin discs. II. Anelastic approximation

Abstract

Using the anelastic approximation of linearised hydrodynamic equations, we investigate the development of axially symmetric small perturbations in thin Keplerian discs. The sixth-order dispersion equation is derived and numerically solved for different values of relevant physical parameters (viscosity, heat conductivity, disc semi-thickness and vertical structure). The analysis reveals the appearance of two overstable modes which split out from the classical Rayleigh inertial modes in a wide range of the parameters in both ionized and neutral gases. These modes have a viscous-convective nature and can serve as a seed for turbulence in astrophysical discs even in the absence of magnetic fields.

arXiv comment10 pages, 5 figures, accepted for publication in MNRAS, Main Journal

References in corpus (2)

• Energy conservation and gravity waves in sound-proof treatments of stellar interiors: Part II Lagrangian constrained analysis
• A viscous instability in axially symmetric laminar shear flows

Cited by in corpus (4)

• Evolution of a Viscous Protoplanetary Disk with Convectively Unstable Regions
• Convection in axially symmetric accretion discs with microscopic transport coefficients
• On the appearance of non-local MRI in Keplerian accretion discs
• Evolution of a Viscous Protoplanetary Disk with Convectively Unstable Regions. II. Accretion Regimes and Long-Term Dynamics