Formation of accretion disk by hydrodynamic subcritical transition

Abstract

This work employs input-output analysis that is computationally efficient to provide insight into the dominant length scale the transition mechanism in rotating plane Couette flow that is relevant to the accretion disk. We also incorporate componentwise analysis to isolate the effect of different input body forces and different output velocity responses. We compared results associated with three different Reynolds numbers and rotation numbers considering both the overall effect and the effect under isolated input and output directions. We observe different patterns in which the maximum energy amplification strength changes as Reynolds number and rotation number change. We also derive the scaling law of the largest input-output gain over Reynolds number and rotation number, which suggests a higher rotation rate is playing a stabilizing role. We observe that the maximum amplification at rotation number equal to one shows symmetry against the lift-up mechanism in non-rotating plane Couette flow. As the stabilizing effect of rotation is further increased, we observe the most amplified flow structures are more elongated in the spanwise direction reminiscent of the Taylor-Proudman effect.