Wave-Vortex mode coupling in astrophysical accretion disks under combined radial and vertical stratification
Résumé
We examine accretion disk flow under combined radial and vertical stratification utilizing a local Cartesian (or "shearing box") approximation. We investigate both axisymmetric and nonaxisymmetric disturbances with the Boussinesq approximation. Under axisymmetric disturbances, a new dispersion relation is derived. It reduces to the Solberg-Hoïland criterion in the case without vertical stratification. It shows that, asymptotically, stable radial and vertical stratification cannot induce any linear instability; Keplerian flow is accordingly stable. Previous investigations strongly suggest that the so-called bypass concept of turbulence (i.e., that fine-tuned disturbances of any inviscid smooth shear flow can reach arbitrarily large transient growth) can also be applied to Keplerian disks. We present an analysis of this process for three-dimensional plane-wave disturbances comoving with the shear flow of a general rotating shear flow under combined stable radial and vertical rotation. We demonstrate that large transient growth occurs for K 2/k 1 Gt 1 and k 3 = 0 or k 1 ~ k 3, where k 1, K 2, and k 3 are the azimuthal, radial, and vertical components of the initial wave vector, respectively. By using a generalized "wave-vortex" decomposition of the disturbance, we show that the large transient energy growth in a Keplerian disk is mainly generated by the transient dynamics of the vortex mode. The analysis of the power spectrum of total (kinetic+potential) energy in the azimuthal or vertical directions shows that the contribution coming from the vortex mode is dominant at large scales, while the contribution coming from the wave mode is important at small scales. These findings may be confirmed by appropriate numerical simulations in the high Reynolds number regime.
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