Fully conservative hydraulic jumps and solibores in two-layer Boussinesq fluids

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We consider a special type of hydraulic jumps (internal bores) which, in the vertically bounded system of two immiscible fluids with slightly different densities, conserve not only the mass and impulse but also the circulation and energy. This is possible only at specific combinations of the upstream and downstream states. Two such combinations are identified with arbitrary upstream and downstream interface heights. The first has a cross-symmetry between the interface height and shear on both sides of the jump. This symmetry, which is due to the invariance of the two-layer shallow-water system with swapping the interface height and shear, ensures the automatic conservation of the impulse and energy as well as the continuity of characteristic velocities across the jump. The speed at which such jumps propagate is defined uniquely by the conservation of the mass and circulation. The other possibility is a marginally stable shear flow that can have fully conservative jumps with discontinuous characteristic velocities. Both types of conservative jumps are shown to represent a long-wave approximation to the so-called solibores that appear as smooth permanent-shape solutions in a weakly non-hydrostatic model. A new analytical solution for solibores is obtained and found to agree very well with the previous DNS results for partial-depth lock release flow. The finding that certain large-amplitude hydraulic jumps can be fully conservative, while most are not such even in the inviscid approximation, points towards the wave dispersion as a primary mechanism behind the lossy nature of internal bores
Original languageEnglish
Article numberA36
Number of pages14
JournalJournal of Fluid Mechanics
Early online date22 May 2023
Publication statusPublished - 25 May 2023

Bibliographical note

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.


  • hydraulics
  • internal waves
  • stratified flows

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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