Mean flow generation due to longitudinal librations of sidewalls of a rotating annulus

Abstract

Laboratory experiments with a rotating cylindrical annulus are reported that reveal a prograde jet, which is adjacent to a (longitudinally) librating inner straight cylindrical wall. Here, wall libration is realised as a time-harmonic modulation of the inner cylinder's rotation rate. The outer cylindrical wall and bottom and top lids rotate with constant angular velocity. The main purpose of our study is to contribute to a qualitative and quantitative understanding of non-linearities that are present in oscillating, but centrifugally stable, vertical boundary layers frequently encountered in rotating wall-bounded flows. We consider a problem that is in a sense complementary to that of previous works that focused on oscillating Ekman layers but neglected the vertical Stokes−Stewartson layers. A simple analytical model is proposed that is able to predict the magnitude and spatial structure of the emerging prograde near-wall jet in terms of nonlinearity inherent in the inner cylinder's boundary layer dynamics.

Keywords:

• Boundary layer structure
• geophysical and geological flows
• longitudinal libration

Acknowledgments

We further thank Abouzar Ghasemi V. for many helpful discussions, as well as Robin Stöbel and Ludwig Stapelfeld for technical support. Finally we thank Xiaomin Bi for help with respect to the measurements and data analysis and two anonymous reviewers for many helpful suggestions to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Michael V. Kurgansky https://orcid.org/0000-0001-9960-6093

Torsten Seelig https://orcid.org/0000-0002-6780-7437

Marten Klein https://orcid.org/0000-0003-0609-8961

Uwe Harlander https://orcid.org/0000-0002-3834-6248

Additional information

Funding

UH thanks the German Science Foundation (DFG) (Deutsche Forschungsgemeinschaft) for financial support via the projects HA 2937/8-2 (DFG research unit MS-GWaves) and the DFG core facility centre, HA 2937/10-1. TS, MK, AW, and UH have further benefited from the DFG project ‘Mixing and mean flow generation by propagating inertial waves (HA 2937/6-1)’.