The importance of lateral boundary layer drag forces in rotating fluids

Scolan, H., Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, Verzicco, R. and Flór, J. B. (2026) The importance of lateral boundary layer drag forces in rotating fluids. Geophysical & Astrophysical Fluid Dynamics, 120 (1). pp. 45-70. ISSN 1029-0419 doi: 10.1080/03091929.2026.2655597

Abstract/Summary

The relative motion of fluids in rotating tanks is opposed by viscous boundary layers at the lateral and horizontal boundaries. The influence of drag at the lateral boundaries is often tacitly assumed to be much weaker than at the horizontal boundaries, allowing the former to be neglected in analytical and numerical models. In the present study, the rationale behind this assumption is scrutinised, analytically, numerically and experimentally. A simple equilibrium torque balance model applied to the one-layer and two-layer configurations of the rotating annulus, predicts that the drag torques at the lateral and horizontal boundaries may be comparable in magnitude (Williams et al., Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization. Nonlinear Process. Geophys. 2004a, 11, 127–135). The effect of lateral boundaries depends on geometrical aspect ratio, radii ratio and Ekman number and can be expected large for experimental configurations with high aspect ratios and low rotation giving larger Ekman number. In this torque model, the thickness of the Stewartson layer can be defined using either a horizontal or a vertical length scale, yielding two distinct models. The strong agreement between the numerical results and the model based on the horizontal length scale, implying an Ekman number based on the width of the container, contrasts with the poor agreement observed for the vertically based model. This discrepancy highlights the importance of lateral boundaries in the momentum balance. Experimental results obtained in the laboratory using both a one-layer cylinder configuration and a two-layer salt-stratified rotating annulus show results that are consistent with the model predictions only if lateral boundary layer drag is included, confirming that lateral boundary layers contribute critically to the equilibrium torque balance. The effect was found weaker in the one-layer configuration than in the two-layer annulus configuration. Insight is also gained from the annulus experiments into the vertical transfer of horizontal momentum across density interfaces, which is of great relevance to geophysical flows. The results are relevant for rotating laboratory experiments.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/129869
Identification Number/DOI	10.1080/03091929.2026.2655597
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	Taylor & Francis
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