β-plane magnetohydrodynamic instability in the Kolmogorov flow

Planar Kolmogorov flow (a pure sinusoidal velocity field restricted to one direction) has various applications in geophysics, astrophysics, and stability theory. This flow can generate large-scale instabilities, which are similar to the jet formation found in many models of fluid flows with a random forcing (known as zonostrophic instability). An important extension of the Kolmogorov flow is the inclusion of a background vorticity gradient at an angle to the flow (known as the β-effect). In this article, we consider the Kolmogorov flow influenced by a β-effect and coupled with a horizontal magnetic field, finding initial suppression of instability in the weak field branch and appearance of a range of instabilities and jet-like structures in the strong field branch. For weak fields, there is suppression of the pure hydrodynamic instability, but another instability branch appears as the field strength is increased. Alfvén waves interact with Rossby waves to generate magnetohydrodynamic Rossby waves, which have no hydrodynamic analogue. For high magnetic field strengths, these waves return to being Alfvén waves. Numerical results were found to compare well with results obtained using matrix eigenvalue perturbation theory. Although the flow we study is laminar, our results are relevant for a better understanding of instabilities for a wide class of turbulent magnetohydrodynamic flows.