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Boundary layer beneath a tornado-like vortex

Leven Davies, P. A. Davidson, and John K. Harvey

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Phys. Rev. Fluids 11, 094703 – Published 21 September, 2026

DOI: https://doi.org/10.1103/28pj-lw6x

Abstract

We examine experimentally the boundary layer beneath a Rankine vortex, which consists of a central vortex tube surrounded by an irrotational free vortex. We do this by setting up a tornado-like vortex in a large water tank, and then we examine the resulting boundary layer using particle image velocimetry. The boundary layer beneath a Rankine vortex has attracted considerable attention in the past, as it is thought to play an important role in the dynamics of a tornado R. Rotunno [Annu. Rev. Fluid. Mech. 45, 59 (2013)]. In particular, Burggraf [Phys. Fluids 14, 1821 (1971)] have performed an approximate asymptotic analysis of the steady, laminar boundary layer beneath a free vortex, predicting a complex, two-layer structure for the boundary layer. Their predictions have been found to be in qualitative agreement with experiments on the flow surrounding a tornado-like vortex, but to date there is no detailed, quantitative comparison. We provide such a comparison here. We find that the analysis of Burggraf et al. is in good agreement with our measurements when the boundary layer is steady, but discrepancies start to arise as the Reynolds number increases and the flow becomes unsteady.

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References (8)

  1. R. Rotunno, The fluid dynamics of tornadoes, Annu. Rev. Fluid. Mech. 45, 59 (2013).
  2. O. R. Burggraf, K. Stewartson, and R. Belcher, Boundary layer induced by a potential vortex, Phys. Fluids 14, 1821 (1971).
  3. U. T. Bödewadt, Die Drehströmung über festem Grunde, Z. Angew Math. Mech. 20, 241 (1940).
  4. W. R. C. Phillips, On vortex boundary layers, Proc. R. Soc. London, Ser. A 400, 253 (1985).
  5. W. R. C. Phillips and B. C. Khoo, The boundary layer beneath a Rankine-like vortex, Proc. R. Soc. London, Ser. A 411, 177 (1987).
  6. S. J. Ying and C. C. Chang, Exploratory model study of tornado-like vortex dynamics, J. Atmos. Sci. 27, 3 (1970).
  7. P. A. Davidson, The Dynamics of Rotating Fluids (Oxford University Press, Oxford, 2024).
  8. H. P. Greenspan, Theory of Rotating Fluids (Cambridge University Press, Cambridge, 1968).

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Phys. Rev. Fluids 11, 094703– Published 21 September, 2026
  • Received 15 December 2025
  • Accepted 6 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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