PI: Mattias Brynjell-Rahkola

Magnetic fields have a strong influence on the gas dynamics in accretion discs around stars and black holes. Through magnetohydrodynamic (MHD) instabilities, they may lead to turbulence in the disc that significantly increases the radial transport of angular momentum. In zero-net flux discs, large-scale magnetic fields are generated by dynamos. A common model for such processes involves a toroidal magnetic field that is created by differential rotation from a poloidal magnetic field, which in turn is maintained by an electromotive force that stems from the toroidal field. In the project DP395, such dynamo processes are addressed from a multidisciplinary dynamical systems perspective. Specifically, a better understanding of nonlinear disc dynamos is sought through study of self-sustaining states, which correspond to exact solutions of the MHD equations.

The project uses the open-source spectral code Dedalus on the DiRAC HPC resource CSD3 in Cambridge. Self-sustaining states are computed using the bisection method, which is a method for finding unstable nonlinear solutions. To perform stability analysis, matrix-free time-stepping methods are used. Studies of turbulence in discs frequently adopt a shearing box framework where the radial boundaries are assumed to be shear-periodic. However, results from the present study suggest that isolated dynamo processes can exist in unbounded shear flows irrespective of such artificial boundaries. As a first step towards a numerical proof of this, the existence of isolated self-sustaining states in unbounded non-rotating hydrodynamic shear layers has been shown (see figure), which is an important result for several astro- and geophysical flows.

Figure: Self-sustaining state in an unbounded hydrodynamic shear flow (x – streamwise, y – shearwise, z – spanwise direction). Plotted are positive and negative streamwise velocity streaks in orange and purple, contours of streamwise vorticity (white – negative, red – positive), 3D surfaces of the streamwise wave component (blue – negative, green – positive).