| dc.description.abstract | Accretion disks are astrophysical objects formed around a denser object, mainly in the form of a disk. In an accretion disk, matter spirals in and falls onto the central object. To match the observations, the underlying flow has to be turbulent. Nevertheless, the
accretion flow model is stable against the infinitesimal perturbations according to Rayleigh criterion. A similar kind of discrepancy
between theory and experiments prevails there in the case of some laboratory flows, i.e., plane Couette flow and plane Poiseuille
flow. However, the presence of a weak magnetic field in the hot enough accretion flow could plausibly explain the onset of turbulence
through magnetorotational instability (MRI). Nonetheless, among its many caveats, MRI operates when the ionization is significant.
We, therefore, look for hydrodynamic instability as it is a generic case in all kinds of flows. We consider and extra force of stochastic
nature with a nonzero mean to be present in the local flow. The plausible origins of the force could be the small thermal fluctuation
present in the systems, the disturbances of arbitrary origins, etc. However, in the context of an accretion disk, the extra force could
originate from the interaction between the dust grains and fluid parcel in protoplanetary disks; back reactions of outflow/jet to accretion
disks; external forcing of the disk, i.e. tidal forcing, shock wave debris, outburst, or internal forcing by nonlinear terms.
We start by undertaking the problem with the introduction of an extra force in Orr-Sommerfeld and Squire equations along with the
Coriolis force mimicking the local region of the accretion disk. For plane Couette flow, the Coriolis term drops. Subsequently, we solve
the equations by the WKB approximation method. We investigate the dispersion relation for the Keplerian flow and plane Couette flow
for all possible combinations of wave vectors. Due to the very presence of extra force, we show that both the flows are unstable for a
certain range of wave vectors. However, the nature of instability between the flows is different. We also study the Argand diagrams
of the perturbation eigenmodes. It helps us compare the different time scales corresponding to the perturbations and accretion. We
ultimately conclude with this formalism that fluid gets enough time to be unstable and hence plausibly turbulent, particularly in the local
regime of the Keplerian accretion disks.
We, then, provide one of the plausible models of the extra stochastic force rigorously in the context of the accretion flow. In the
presence of the extra force and Coriolis force, we eventually establish the evolution of nonlinear perturbation by numerical solutions.
We show that even in the linear regime, under suitable forcing and Reynolds number, the otherwise least stable perturbation evolves to a
very large saturated amplitude, leading to nonlinearity and plausible turbulence. Hence, forcing essentially leads a linear stable mode to
unstable. We further show that nonlinear perturbation diverges at a shorter timescale in the presence of force, leading to a fast transition
to turbulence. Interestingly, the emergence of nonlinearity depends only on the force but not on the initial amplitude of perturbation.
Next, we explore the effect of forcing on the linear shear flow or plane Couette flow, which is also the background flow in the
very small region of the Keplerian accretion disk. We show that depending on the strength of forcing and boundary conditions suitable
for the systems under consideration, the background plane shear flow and, hence, accretion disk velocity profile modifies to parabolic
flow, which is plane Poiseuille flow or Couette-Poiseuille flow, depending on the frame of reference. In the presence of rotation, plane
Poiseuille flow becomes unstable at a smaller Reynolds number under pure vertical as well as three-dimensional perturbations compared
to their non-rotating two-dimensional counterpart. Hence, while rotation stabilizes plane Couette flow, the same destabilizes plane
Poiseuille flow faster and forced-local accretion disk. Depending on the various factors, when local linear shear flow becomes Poiseuille
flow in the shearing box due to the presence of extra force, the flow becomes unstable even for the Keplerian rotation, and hence
turbulence will pop in there.
In the end, we venture for the comparison between growth rates for 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 WKB approximation
without extra force for purely vertical magnetic field and vertical wavevector of the perturbations. Expectedly, MRI is active within a
range of the 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 the 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 is 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.
Hence, we have established that the presence of an extra stochastic force with a nonzero mean makes the linearly stable flow
effectively unstable. Once the instability and, therefore, turbulence kicks in inside the shearing box, we consider the shearing box
repeatedly throughout the radial extension of the accretion disk. Hence, the angular momentum transport can be interpreted in the
Keplerian accretion disk. | en_US |
