The competition between the hydrodynamic instability from noise and magnetorotational instability in the Keplerian disks

Abstract

We venture for the comparison between growth rates for magnetorotational instability (MRI) and hydrodynamics instability in the presence of an extra force in the local Keplerian accretion flow. The underlying model is described by the Orr-Sommerfeld and Squire equations in the presence of rotation, magnetic field and an extra force, plausibly noise with a nonzero mean. We obtain MRI using Wentzel-Kramers-Brillouin (WKB) approximation without extra force for purely vertical magnetic field and vertical wavevector of the perturbations. Expectedly, MRI is active within a range of magnetic field, which changes depending on the perturbation wavevector magnitude. Next, to check the effect of noise on the growth rates, a quartic dispersion relation has been obtained. Among those four solutions for growth rate, the one that reduces to MRI growth rate at the limit of vanishing mean of noise in the MRI active region of the magnetic field, is mostly dominated by MRI. However, in MRI inactive region, in the presence of noise the solution turns out to be unstable, which are almost independent of the magnetic field. Another growth rate, which is almost complementary to the previous one, leads to stability at the limit of vanishing noise. The remaining two growth rates, which correspond to the hydrodynamical growth rates at the limit of the vanishing magnetic field, are completely different from the MRI growth rate. More interestingly, the latter growth rates are larger than that of the MRI. If we consider viscosity, the growth rates decrease depending on the Reynolds number.

arXiv comment13 pages, 19 figures, published in AIP Advances

References in corpus (24)

• Wind-driven Accretion in Protoplanetary Disks. I: Suppression of the Magnetorotational Instability and Launching of the Magnetocentrifugal Wind
• Local Magnetohydrodynamical Models of Layered Accretion Disks
• Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks
• On the relevance of subcritical hydrodynamic turbulence to accretion disk transport
• Wind-driven Accretion in Protoplanetary Disks --- II: Radial Dependence and Global Picture
• Measurement of angular momentum transport in turbulent flow between independently rotating cylinders
• The Stability of Magnetized Rotating Plasmas with Superthermal Fields
• Stability and angular-momentum transport of fluid flows between corotating cylinders
• Transport and Accretion in Planet-Forming Disks
• Bypass to Turbulence in Hydrodynamic Accretion: Lagrangian Analysis of Energy Growth
• On hydrodynamic shear turbulence in Keplerian disks: via transient growth to bypass transition
• The Twente turbulent Taylor-Couette (T3C) facility: Strongly turbulent (multiphase) flow between two independently rotating cylinders
• Bypass to Turbulence in Hydrodynamic Accretion Disks: An Eigenvalue Approach
• Turbulence in differentially rotating flows What can be learned from the Couette-Taylor experiment
• Angular momentum transport and turbulence in laboratory models of Keplerian flows
• Instability in strongly magnetized accretion discs: A global perspective
• Hydrodynamic turbulence in quasi-Keplerian rotating flows
• Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows
• Stochastically driven instability in rotating shear flows
• Origin of nonlinearity and plausible turbulence by hydromagnetic transient growth in accretion disks: Faster growth rate than magnetorotational instability
• A pure hydrodynamic instability in shear flows and its application to astrophysical accretion disks
• Perturbations dynamics in Keplerian flow under external stochastic forcing
• Origin of hydrodynamic instability from noise: from laboratory flow to accretion disk
• Hydrodynamical instability with noise in the Keplerian accretion discs: Modified Landau equation