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. ${\it\Omega}_{o}/{\it\Omega}_{i}=(r_{i}/r_{o})^{3/2}$

, where

${\it\Omega}_{o}/{\it\Omega}_{i}$

is the angular velocity at the outer/inner boundary and

$r_{i}/r_{o}$

is the inner/outer radius), the presence of stratification can make the quasi-Keplerian flow susceptible to the stratorotational instability. Otherwise (e.g. for

${\it\Omega}_{o}/{\it\Omega}_{i}=(r_{i}/r_{o})^{1/2}$

), 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

$Re=O(10^{4})$

. This observation is consistent with most recent computational (Ostilla-Mónico, et al. J. Fluid Mech. , vol. 748, 2014, R3) and experimental results (Edlund & Ji, Phys. Rev.  E, vol. 89, 2014, 021004) at high

$Re$

, and reinforces the growing consensus that turbulence in cold accretion disks must rely on additional physics beyond that of incompressible hydrodynamics.