Magnetorotational instability and nonmodal stability
The non-axisymmetric modes of the MRI are very nicely analyzed in terms of nonmodal stability theory. This theory recognizes that a non-self-adjoint linear operator may not be best described by eigenmodes, since other perturbations can grow much faster over finite time-scales. For the MRI this approach is very fruitful and helps to clarify how modes in local “shearing box” theories related to eigenmodes of the global eigenmodes. (Collaborators: Amitava Bhattacharjee)
Accretion disk dynamos and statistical simulation
Statistical simulation is the idea of numerically solving for the statistics of turbulence, rather than an individual realization. This is very useful for studying the dynamo in MRI turbulence, relating this to the “magnetic shear-current effect” described in Turbulence and Dynamos. (Collaborators: Amitava Bhattacharjee)
Hydrodynamic Keplerian turbulence
With all this talk of magnetized turbulence, there’s an interesting theoretical question that remains unsolved, concerning whether hydrodynamic Keplerian flows are nonlinearly unstable when the viscosity is low enough. While all simulations and experiments up to now have seen that they are stable, it is hard to know for sure that this holds for the very low dissipation environments in astrophysics. We’ve been attempting to address this using direct numerical simulation and statistical simulation. (Collaborators: Jeremy Goodman).
MRI in collisionless plasmas
The plasmas in hot accretion disks are effectively collisionless. The MRI still exists in collisionless plasmas, but it can be significantly modified by the developing pressure anisotropies (see also Turbulence and Dynamos). We’ve been thinking about how this might modify the nonlinear development and turbulence in such systems. (Collaborators: Eliot Quataert).