A modelling study of transient, buoyancy-driven exchange flow over a descending barrier

Alan J.S. Cuthbertson, Peter A. Davies, Michael J. Coates, Yakun Guo

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    Results are presented from a series of model studies of the transient exchange flow resulting from the steady descent of an impermeable barrier separating initially-quiescent fresh and saline water bodies having density po and po +( ?p)o, respectively. A set of parametric laboratory experiments has been carried out (i) to determine the characteristic features of the time-dependent exchange flow over the barrier crest and (ii) to quantify the temporal increase in the thickness and spatial extent of the brackish water reservoir formed behind the barrier by the outflowing, partly-mixed saline water. The results of the laboratory experiments have been compared with the predictions of a theoretical model adapted from the steady, so-called maximal exchange flow case and good qualitative agreement between theory and experiment has been demonstrated. The comparisons indicate that head losses of between 7% and 3% are applicable to the flow over the ridge crest in the early and late stages, respectively, of the barrier descent phase, with these losses being attributed to mixing processes associated with the counterflowing layers of fresh and saline water in the vicinity of the ridge crest. The experimental data show ( and the theoretical model predictions confirm) that ( i) the dimensionless time of detection tdet (g'/ Hb)1/ 2 of the brackish water pool fed by the dense outflow increases ( at a given distance from the barrier) with increasing values of the descent rate parameter g'Hb/(dhb/dt)2 and (ii) the normalised thickness d(x, t)/H-b of the pool at a given reference station increases monotonically with increasing values of the modified time (t-tdet)/(Hb/g')1/2, with the rate of thickening decreasing with increasing values of the descent rate parameter g' Hb(dhb/dt)2. Here, g' = (g/po)(?p)0 is the modified gravitational acceleration, Hb is the mean depth of the water and dhb/dt denotes the rate of descent of the barrier height hb with elapsed time t after the two water bodies are first brought into contact.

    Original languageEnglish
    Pages (from-to)127-155
    Number of pages29
    JournalEnvironmental Fluid Mechanics
    Volume4
    Issue number2
    DOIs
    Publication statusPublished - Jun 2004

    Keywords

    • hydraulics
    • stratification
    • mixing
    • turbulence
    • exchange flow
    • buoyancy

    Cite this

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    title = "A modelling study of transient, buoyancy-driven exchange flow over a descending barrier",
    abstract = "Results are presented from a series of model studies of the transient exchange flow resulting from the steady descent of an impermeable barrier separating initially-quiescent fresh and saline water bodies having density po and po +( ?p)o, respectively. A set of parametric laboratory experiments has been carried out (i) to determine the characteristic features of the time-dependent exchange flow over the barrier crest and (ii) to quantify the temporal increase in the thickness and spatial extent of the brackish water reservoir formed behind the barrier by the outflowing, partly-mixed saline water. The results of the laboratory experiments have been compared with the predictions of a theoretical model adapted from the steady, so-called maximal exchange flow case and good qualitative agreement between theory and experiment has been demonstrated. The comparisons indicate that head losses of between 7{\%} and 3{\%} are applicable to the flow over the ridge crest in the early and late stages, respectively, of the barrier descent phase, with these losses being attributed to mixing processes associated with the counterflowing layers of fresh and saline water in the vicinity of the ridge crest. The experimental data show ( and the theoretical model predictions confirm) that ( i) the dimensionless time of detection tdet (g'/ Hb)1/ 2 of the brackish water pool fed by the dense outflow increases ( at a given distance from the barrier) with increasing values of the descent rate parameter g'Hb/(dhb/dt)2 and (ii) the normalised thickness d(x, t)/H-b of the pool at a given reference station increases monotonically with increasing values of the modified time (t-tdet)/(Hb/g')1/2, with the rate of thickening decreasing with increasing values of the descent rate parameter g' Hb(dhb/dt)2. Here, g' = (g/po)(?p)0 is the modified gravitational acceleration, Hb is the mean depth of the water and dhb/dt denotes the rate of descent of the barrier height hb with elapsed time t after the two water bodies are first brought into contact.",
    keywords = "hydraulics, stratification, mixing, turbulence, exchange flow, buoyancy",
    author = "Cuthbertson, {Alan J.S.} and Davies, {Peter A.} and Coates, {Michael J.} and Yakun Guo",
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    language = "English",
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    A modelling study of transient, buoyancy-driven exchange flow over a descending barrier. / Cuthbertson, Alan J.S.; Davies, Peter A.; Coates, Michael J.; Guo, Yakun.

    In: Environmental Fluid Mechanics, Vol. 4, No. 2, 06.2004, p. 127-155.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - A modelling study of transient, buoyancy-driven exchange flow over a descending barrier

    AU - Cuthbertson, Alan J.S.

    AU - Davies, Peter A.

    AU - Coates, Michael J.

    AU - Guo, Yakun

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    AB - Results are presented from a series of model studies of the transient exchange flow resulting from the steady descent of an impermeable barrier separating initially-quiescent fresh and saline water bodies having density po and po +( ?p)o, respectively. A set of parametric laboratory experiments has been carried out (i) to determine the characteristic features of the time-dependent exchange flow over the barrier crest and (ii) to quantify the temporal increase in the thickness and spatial extent of the brackish water reservoir formed behind the barrier by the outflowing, partly-mixed saline water. The results of the laboratory experiments have been compared with the predictions of a theoretical model adapted from the steady, so-called maximal exchange flow case and good qualitative agreement between theory and experiment has been demonstrated. The comparisons indicate that head losses of between 7% and 3% are applicable to the flow over the ridge crest in the early and late stages, respectively, of the barrier descent phase, with these losses being attributed to mixing processes associated with the counterflowing layers of fresh and saline water in the vicinity of the ridge crest. The experimental data show ( and the theoretical model predictions confirm) that ( i) the dimensionless time of detection tdet (g'/ Hb)1/ 2 of the brackish water pool fed by the dense outflow increases ( at a given distance from the barrier) with increasing values of the descent rate parameter g'Hb/(dhb/dt)2 and (ii) the normalised thickness d(x, t)/H-b of the pool at a given reference station increases monotonically with increasing values of the modified time (t-tdet)/(Hb/g')1/2, with the rate of thickening decreasing with increasing values of the descent rate parameter g' Hb(dhb/dt)2. Here, g' = (g/po)(?p)0 is the modified gravitational acceleration, Hb is the mean depth of the water and dhb/dt denotes the rate of descent of the barrier height hb with elapsed time t after the two water bodies are first brought into contact.

    KW - hydraulics

    KW - stratification

    KW - mixing

    KW - turbulence

    KW - exchange flow

    KW - buoyancy

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    DO - 10.1023/B:EFMC.0000016472.52867.eb

    M3 - Article

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    SP - 127

    EP - 155

    JO - Environmental Fluid Mechanics

    JF - Environmental Fluid Mechanics

    SN - 1567-7419

    IS - 2

    ER -