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Corner universality in polygonal hydraulic jumps

S. I. Tamim1,2, T. Nichols2, J. Lundbek Hansen3, T. Bohr4, and J. B. Bostwick2,*

  • 1Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
  • 2Department of Mechanical Engineering, Clemson University, Clemson, South Carolina 29634, USA
  • 3SuperAI, Risk Analytics, Danske Bank, Laksegade 8, Copenhagen 1063, Denmark
  • 4Department of Physics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark

  • *jbostwi@clemson.edu
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Phys. Rev. Fluids 8, L032001 – Published 7 March, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.L032001

Abstract

Steady polygonal hydraulic jumps have a complex flow structure and are formed when a circular jump loses stability through an increase in the downstream liquid height beyond a critical value. We report the experimental observation of a universal corner shape in polygonal hydraulic jumps over a wide range of experimental conditions that include the flow rate, weir geometry, and flow history, as defined by the tip radius of curvature and the corner angle. The tip radius of curvature is nearly constant over all experimental conditions, whereas the corner angle weakly depends on gravitational effects. Knowledge of the corner angle allows one to determine the global jump shape, as defined by a dimensionless geometry number related to the isoperimetric inequality, thus giving a complete description of the jump shape.

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Phys. Rev. Fluids 8, L032001– Published 7 March, 2023
  • Received 18 August 2022
  • Accepted 3 February 2023
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