Unsteady turbulent plume models

M. M. Scase, R. E. Hewitt

    Research output: Contribution to journalArticlepeer-review


    Four existing integral models of unsteady turbulent plumes are revisited. We demonstrate that none of these published models is ideal for general descriptions of unsteady behaviour and put forward a modified model. We show that the most recent (top-hat) plume model (Scase et al. J. Fluid Mech., vol. 563, 2006, p. 443), and the earlier (Gaussian) plume models (Delichatsios J. Fluid Mech., vol. 93, 1979, p. 241; Yu Trans. ASME, vol. 112, 1990, p.186), are all ill-posed. This ill-posedness arises from the downstream growth of short-scale waves, which have an unbounded downstream growth rate. We show that both the top-hat and the Gaussian (Yu) models can be regularized, rendering them well-posed, by the inclusion of a velocity diffusion term. The effect of including this diffusive mechanism is to include a vertical structure in the model that can be interpreted as representing the vertical extent of an eddy. The effects of this additional mechanism are small for steady applications, and cases where the plume forcing can be considered to follow a power law (both of which have been studied extensively). However, the inclusion of diffusion is shown to be crucial to the general initial-value problem for unsteady models. © 2012 Cambridge University Press.
    Original languageEnglish
    Pages (from-to)455-480
    Number of pages25
    JournalJournal of Fluid Mechanics
    Publication statusPublished - 25 Apr 2012


    • plumes/thermals


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