Using stratification to mitigate end-effects in quasi-Keplerian Taylor-Couette flow

Abstract

Efforts to model accretion disks in the laboratory using Taylor–Couette flow apparatus are plagued with problems due to the substantial impact the end-plates have on the flow. We explore the possibility of mitigating the influence of these end-plates by imposing stable stratification in their vicinity. Numerical computations and experiments confirm the effectiveness of this strategy for restoring the axially-homogeneous quasi-Keplerian solution in the unstratified equatorial part of the flow for sufficiently strong stratification and moderate layer thickness. If the rotation ratio is too large, however, (e.g. Ωₒ/Ωᵢ = (rᵢ/rₒ) ^(3/2) where Ωₒ/Ωᵢ is the angular velocity at the outer/inner boundary and ri/ro is the inner/outer radius) the presence of stratification can make the quasi-Keplerian flow susceptible to the stratorotational instability. Otherwise (e.g. for Ωₒ/Ωᵢ = (rᵢ/rₒ) ^(1/2) ) our control strategy is successful in reinstating a linearly-stable quasi-Keplerian flow away from the end-plates. Experiments probing the nonlinear stability of this flow show only decay of initial finite-amplitude disturbances at a Reynolds number Re = O(10⁴). This observation is consistent with most recent computational (Ostilla-Mónico et al. 2014) and experimental results (Edlund & Ji 2014) at high Re, and reinforces the growing consensus that turbulence in cold accretion disks must rely on additional physics beyond that of incompressible hydrodynamics.