Instability of the realizable k–ε turbulence model beneath surface waves

David R. Fuhrman*, Yuzhu Li

*Corresponding author for this work

    Research output: Contribution to journalJournal articleResearchpeer-review

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    Abstract

    Recent research has proved that most widely used two-equation turbulence closure models are unconditionally unstable in regions of nearly potential flow having finite strain, as commonly found beneath non-breaking surface waves. In this work, we extend such analysis to consider the popular realizable k–ε turbulence model. It is proved that this model, unlike all others thus far analyzed, is only conditionally unstable in such regions due to the addition of viscosity in the ε dissipation term. A method for formally stabilizing the model in the problematic regions is likewise developed. The results of the analysis, using both standard and stabilized turbulence closures, are confirmed via numerical simulations of progressive surface wave trains using a computational fluid dynamics model. Important qualitative differences are likewise demonstrated in simulations involving spilling breaking waves. (In the above, k is the turbulent kinetic energy density, and ε is the turbulence dissipation rate.)
    Original languageEnglish
    Article number115108
    JournalPhysics of Fluids
    Volume32
    Number of pages10
    ISSN1070-6631
    DOIs
    Publication statusPublished - 2020

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