Origin of hydrodynamic instability from noise: From laboratory flow to accretion disk

We attempt to address the old problem of plane shear flows: the origin of turbulence and hence transport of angular momentum in accretion flows as well as laboratory flows, such as plane Couette flow. We undertake the problem by introducing 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 with 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 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. This helps us to compare the different timescales corresponding to the perturbations as well as 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. Repetition of the analysis throughout the disk explains the transport of angular momentum and matter along outward and inward directions, respectively.

Automated summary

The author addresses the old problem of turbulence in plane shear flows by introducing an extra force in the equations. By studying the dispersion relation for different wave vector combinations, they show that both Keplerian flow and plane Couette flow are unstable due to the presence of the extra force. The analysis of perturbation eigenmodes' Argand diagrams helps compare different timescales corresponding to perturbations and accretion.