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Models of internal jumps and the fronts of gravity currents: unifying two-layer theories and deriving new results

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)654-685
Number of pages32
JournalJournal of Fluid Mechanics
Volume846
Early online date9 May 2018
DOIs
DateAccepted/In press - 6 Mar 2018
DateE-pub ahead of print - 9 May 2018
DatePublished (current) - 10 Jul 2018

Abstract

The steady speeds of the front of a gravity current and of an internal jump on a two layer stratification are often sought in terms of the heights of the relatively dense fluid both up- and down-stream from the front or jump, the height of the channel within which they flow, the densities of the two fluids and gravitational acceleration. In this study a unifying framework is presented for calculating the speeds by balancing mass and momentum fluxes across a control volume spanning the front or jump and by ensuring the assumed pressure field is single-valued, which is shown to be equivalent to forming a vorticity balance over the control volume. Previous models have assumed the velocity field is piecewise constant in each layer with a vortex sheet at their interface and invoked explicit or implicit closure assumptions about the dissipative effects to derive the speed. The new formulation yields all of the previously presented expressions and demonstrates that analysing the vorticity balance within the control volume is a useful means of constraining possible closure assumptions, which is arguably more effective than consideration of the flow energetics. However the new approach also reveals that a novel class of models may be developed in which there is shear in the velocity field in the wake downstream of the front or the jump, thus spreading the vorticity over a layer of non-vanishing thickness, rather than concentrating it into a vortex sheet. Mass, momentum and vorticity balances applied over the control volume allow the thickness of the wake and the speed of the front/jump to be evaluated. Results from this vortex-wake model are consistent with published numerical simulations and with data from laboratory experiments, and improve upon predictions from previous formulae. The results may be applied readily to Boussinesq and non-Boussinesq systems and because they arise as simple algebraic expressions, can be straightforwardly incorporated as jump conditions into spatially and temporally varying descriptions of the motion.

    Research areas

  • geophysical and geological flows, gravity currents, shallow water flows

Documents

Documents

  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Cambridge University Press at https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/models-of-internal-jumps-and-the-fronts-of-gravity-currents-unifying-twolayer-theories-and-deriving-new-results/8175C2AE4996C06853CD5826689DC26D . Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 461 KB, PDF-document

    Embargo ends: 9/11/18

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