Effect of split endcaps on the flow dynamics in a tall Taylor-Couette setup

The effects of axial boundaries or endcaps are of fundamental interest in many Taylor-Couette (TC) flow experiments. A main challenge in those experiments has been to minimize these effects, which can substantially alter the flow structure compared to the axially unbounded idealized case. Therefore, understanding and disentangling the influence of endcaps on the TC flow dynamics is essential for the unambiguous interpretation of experimental results, particularly when other dynamical processes (instabilities) in TC flows are involved. In this paper, we study the hydrodynamic evolution of a quasi-Keplerian TC flow in the presence of split endcaps for experimentally relevant high Reynolds numbers, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mtext>Re</a:mtext> </a:math> , up to <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mn>2</b:mn> <b:mo>×</b:mo> <b:msup> <b:mn>10</b:mn> <b:mn>5</b:mn> </b:msup> </b:mrow> </b:math> , which are larger than those considered in related previous studies. At these <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mtext>Re</c:mtext> </c:math> , the flow deviates from the ideal TC flow profile without endcaps, resulting in about <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mn>15</d:mn> <d:mo>%</d:mo> </d:mrow> </d:math> deviation in angular velocity at the midheight of the cylinder. Aside from turbulent fluctuations caused by shearing instability near the endcaps, the bulk flow remains nearly axially independent and exhibits overall Rayleigh stability. We characterize the scalings of the Ekman and Stewartson layer sizes with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mtext>Re</e:mtext> </e:math> as well as examine the effect of the ratio of the outer to inner cylinders' angular velocities on the flow. The implications of these findings for ongoing magnetorotational instability (MRI) experiments based on the similar axially bounded TC setup are also discussed. Specifically, it is shown that when imposing a constant axial magnetic field in all the considered configurations, the flow profile modified by the endcaps lowers the critical threshold for the onset of MRI that in turn can facilitate its emergence and detection in those experiments.