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Abstract
We study the possible origin of hydrodynamic turbulence in cold accretion disks such as those in star-forming systems and quiescent cataclysmic variables. As these systems are expected to have neutral gas, the turbulent viscosity is likely to be hydrodynamic in origin, not magnetohydrodynamic. Therefore, MRI will be sluggish or even absent in such disks. Although there are no exponentially growing eigenmodes in a hydrodynamic disk because of the non-normal nature of the eigenmodes, a large transient growth in the energy is still possible, which may enable the system to switch to a turbulent state. For a Keplerian disk, we estimate that the energy will grow by a factor of 1000 for a Reynolds number close to a million.
Highlights
In the context of Keplerian disks, while hydrodynamic simulations seem to confirm the absence of turbulence in the non-linear limit [1], the MagnetoRotational Instability [2], discovered by Balbus and Hawley [3] within ionized accretion flows, confirms the existence of MHD turbulence
A suitably tuned linear combination of modes can show an arbitrarily large transient energy growth 1. This transient growth may possibly lead to sustained hydrodynamic turbulence for large enough Reynolds numbers
We have shown that significant transient growth of perturbations is possible in a Keplerian flow
Summary
In the context of Keplerian disks, while hydrodynamic simulations seem to confirm the absence of turbulence in the non-linear limit [1], the MagnetoRotational Instability [2], discovered by Balbus and Hawley [3] within ionized accretion flows, confirms the existence of MHD turbulence. This helps to understand the origin of shear stress or “viscosity”. A suitably tuned linear combination of modes can show an arbitrarily large transient energy growth 1 This transient growth may possibly lead to sustained hydrodynamic turbulence for large enough Reynolds numbers. We present the set of scaling relations for the transient growth as a function of the Reynolds number
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