Bypass to Turbulence in Hydrodynamic Accretion Disks: An Eigenvalue Approach
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CitationMukhopadhyay, Banibrata, Niayesh Afshordi, and Ramesh Narayan. 2005. “Bypass to Turbulence in Hydrodynamic Accretion Disks: An Eigenvalue Approach.” The Astrophysical Journal 629 (1): 383–96. https://doi.org/10.1086/431419.
AbstractCold accretion disks with temperatures below similar to 3000 K are likely to be composed of highly neutral gas. The magnetorotational instability may cease to operate in such disks, so it is of interest to consider purely hydrodynamic mechanisms of generating turbulence and angular momentum transport. With this motivation, we investigate the growth of hydrodynamic perturbations in a linear shear flow sandwiched between two parallel walls. The unperturbed flow is similar to plane Couette flow, but with a Coriolis force included. Although there are no exponentially growing eigenmodes in this system, nevertheless, because of the nonnormal nature of the eigenmodes, it is possible to have a large transient growth in the energy of perturbations. For a constant angular momentum disk, we find that the perturbation with maximum growth is axisymmetric with vertical structure. The energy grows by more than a factor of 100 for a Reynolds number R = 300 and more than a factor of 1000 for R = 1000. Turbulence can be easily excited in such a disk, as found in previous numerical simulations. For a Keplerian disk, on the other hand, similar perturbations with vertical structure grow by no more than a factor of 4, explaining why the same simulations did not find turbulence in this system. However, certain other two-dimensional perturbations with no vertical structure do exhibit modest growth. For the optimum two-dimensional perturbation, the energy grows by a factor of similar to 100 for R similar to 10(4.5) and by a factor of 1000 for R similar to 10(6). Such large Reynolds numbers are hard to achieve in numerical simulations, and so the nonlinear development of these kinds of perturbations is only beginning to be investigated. It is conceivable that these nearly two-dimensional disturbances might lead to self-sustained three-dimensional turbulence, although this remains to be demonstrated. The Reynolds numbers of cold astrophysical disks are much larger even than 10(6); therefore, hydrodynamic turbulence may be possible in disks through transient growth.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:41384962
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