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

Abstract

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 by 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 to compare the different time scales 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 direction respectively.