A mixing-length model for shallow turbulent wakes

    Research output: Chapter in Book/Report/Conference proceedingConference contribution


    A three-dimensional boundary-layer model of shallow-water flows assuming hydrostatic pressure with negligible numerical diffusion and wave damping has been extended to turbulent flow. A standard two-layer mixing-length model determines vertical length scales. The horizontal mixing length is made a multiple β of the vertical value and β is determined from comparison with experiment. Eddy viscosity is of a general three-dimensional form where, for example, the horizontal mixing length and associated strain rates determine the magnitude of eddy viscosity and hence vertical mixing (and vice versa). Direct comparison is made with previous experiments for subcritical flow around a conical island of small side slope which exhibits the transition from a vigorous vortex-shedding wake to a steady recirculating wake as the stability parameter, St, is increased. The value of β influences wake structure, particularly for stability parameters close to the critical (the value at which the wake becomes steady or stable). The critical value in the experiments was 0.4 and this was reproduced in the model with β = 6. Vortex shedding patterns with St = 0.26 and 0.36 were qualitatively reproduced. The flows were subcritical with an onset Froude number of about 0.2, with values approaching 0.6-0.7 in areas where depth-averaged vorticity magnitude was also greatest, at a small distance from the wet/dry intersection. At this intersection, depth-averaged vorticity approached zero while potential vorticity (depth-averaged vorticity/depth) was at a maximum, indicating the importance of the intersection as an origin for vorticity.
    Original languageEnglish
    Title of host publicationJournal of Fluid Mechanics|J. Fluid Mech.
    Number of pages15
    Publication statusPublished - 25 Nov 2003
    EventIAHR Symposium on Shallow Flows, Delft (selected for publication in a special volume: Shallow Flows, Balkema, The Netherlands) -
    Duration: 1 Jan 1824 → …


    ConferenceIAHR Symposium on Shallow Flows, Delft (selected for publication in a special volume: Shallow Flows, Balkema, The Netherlands)
    Period1/01/24 → …


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