Excitation of spiral density waves by convection in accretion discs

Abstract

Motivated by the recent results of \citet{Lesur_Ogilvie10} on the transport properties of incompressible convection in protoplanetary discs, in this paper we study the role of compressibility and hence of another basic mode -- spiral density waves -- in convective instability in discs. We analyse the linear dynamics of non-axisymmetric convection and spiral density waves in a Keplerian disc with superadiabatic vertical stratification using the local shearing box approach. It is demonstrated that the shear associated with Keplerian differential rotation introduces a novel phenomenon, it causes these two perturbation modes to become coupled: during evolution the convective mode generates (trailing) spiral density waves and can therefore be regarded as a new source of spiral density waves in discs. The wave generation process studied here owes its existence solely to shear of the disc's differential rotation, and is a special manifestation of a more general linear mode coupling phenomena universally taking place in flows with an inhomogeneous velocity profile. We quantify the efficiency of spiral density wave generation by convection as a function of azimuthal and vertical wavenumbers of these modes and find that it is maximal and most powerful when both these length-scales are comparable to the disc scale height. We also show that unlike the convective mode, which tends to transport angular momentum inwards in the linear regime, the spiral density waves transport angular momentum outwards. Based on these findings, we suggest that in the non-linear regime spiral density waves generated by convection may play a role in enhancing the transport of angular momentum due the convective mode alone, which is actually being changed to outward by non-linearity, as indicated by above-mentioned recent developments.

17 pages, 8 figures, accepted for publication in MNRAS

References in corpus (10)

• The subcritical baroclinic instability in local accretion disc models
• Baroclinic Vorticity Production in Protoplanetary Disks; Part II: Vortex Growth and Longevity
• Turbulent Torques on Protoplanets in a Dead Zone
• Vortices in Thin, Compressible, Unmagnetized Disks
• On the angular momentum transport due to vertical convection in accretion discs
• Hydrodynamic stability and mode coupling in Keplerian flows: local strato-rotational analysis
• Vortices in self-gravitating gaseous discs
• Transient growth and coupling of vortex and wave modes in self-gravitating gaseous discs
• Stability and nonlinear adjustment of vortices in Keplerian flows
• Angular momentum transport in convectively unstable shear flows

Cited by in corpus (5)

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• Revisiting linear dynamics of non-axisymmetric perturbations in weakly magnetized accretion discs
• Nonlinear hydrodynamical evolution of eccentric Keplerian discs in two dimensions: validation of secular theory
• On fragmentation of turbulent self-gravitating discs in the long cooling time regime
• Non-axisymmetric vertical shear and convective instabilities as a mechanism of angular momentum transport