The flow generated in a continuously stratified rotating fluid by the differential rotation of a plane horizontal disc

R. J. Munro, P. A. Davies

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    Results are presented from a modelling investigation into the response of a rotating, linearly stratified fluid to local forcing induced by a differentially rotating smooth, horizontal disc. Attention was directed at cases in which the disc forcing is relatively strong, with Rossby number epsilon = omega/2 Omega of order 1 or greater; here omega and Omega are the disc and background rotation frequencies, respectively. The principal flow dynamics resulting in the mixing and deformation of the initially stable density distribution were identified as (i) shear-induced mixing due to the local increase in fluid vorticity above the disc and (ii) meridional circulations produced by Ekman processes and the constraint of the container sidewall. Laboratory experiments revealed the growth of a mixed layer adjacent to the disc and the subsequent development of layers within the mixed region. Furthermore, the experiments showed that, even at relatively large epsilon, Ekman processes associated with background rotation constituted the dominant mechanism controlling development and evolution of the primary interface between mixed and unmixed fluid regions. Theoretical, energy-based scalings are derived to describe the growth rate of the interfacial region for epsilon greater than or similar to O(1) which are consistent with the epsilon--> infinity limit corresponding to the Omega = 0 case. These scalings are shown to describe well the development of the density field within the forced flow. (C) 2006 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.

    Original languageEnglish
    Pages (from-to)522-538
    Number of pages17
    JournalFluid Dynamics Research
    Volume38
    Issue number8
    DOIs
    Publication statusPublished - Aug 2006

    Keywords

    • Driven
    • Turbulent entrainment
    • Ekman dynamics
    • Annulus
    • Density interface
    • stratified rotating flows
    • Gradient
    • Size
    • interfacial mixing
    • spin-up

    Cite this

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    title = "The flow generated in a continuously stratified rotating fluid by the differential rotation of a plane horizontal disc",
    abstract = "Results are presented from a modelling investigation into the response of a rotating, linearly stratified fluid to local forcing induced by a differentially rotating smooth, horizontal disc. Attention was directed at cases in which the disc forcing is relatively strong, with Rossby number epsilon = omega/2 Omega of order 1 or greater; here omega and Omega are the disc and background rotation frequencies, respectively. The principal flow dynamics resulting in the mixing and deformation of the initially stable density distribution were identified as (i) shear-induced mixing due to the local increase in fluid vorticity above the disc and (ii) meridional circulations produced by Ekman processes and the constraint of the container sidewall. Laboratory experiments revealed the growth of a mixed layer adjacent to the disc and the subsequent development of layers within the mixed region. Furthermore, the experiments showed that, even at relatively large epsilon, Ekman processes associated with background rotation constituted the dominant mechanism controlling development and evolution of the primary interface between mixed and unmixed fluid regions. Theoretical, energy-based scalings are derived to describe the growth rate of the interfacial region for epsilon greater than or similar to O(1) which are consistent with the epsilon--> infinity limit corresponding to the Omega = 0 case. These scalings are shown to describe well the development of the density field within the forced flow. (C) 2006 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.",
    keywords = "Driven, Turbulent entrainment, Ekman dynamics, Annulus, Density interface, stratified rotating flows, Gradient, Size, interfacial mixing, spin-up",
    author = "Munro, {R. J.} and Davies, {P. A.}",
    year = "2006",
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    The flow generated in a continuously stratified rotating fluid by the differential rotation of a plane horizontal disc. / Munro, R. J.; Davies, P. A.

    In: Fluid Dynamics Research, Vol. 38, No. 8, 08.2006, p. 522-538.

    Research output: Contribution to journalArticle

    TY - JOUR

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    AU - Munro, R. J.

    AU - Davies, P. A.

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    N2 - Results are presented from a modelling investigation into the response of a rotating, linearly stratified fluid to local forcing induced by a differentially rotating smooth, horizontal disc. Attention was directed at cases in which the disc forcing is relatively strong, with Rossby number epsilon = omega/2 Omega of order 1 or greater; here omega and Omega are the disc and background rotation frequencies, respectively. The principal flow dynamics resulting in the mixing and deformation of the initially stable density distribution were identified as (i) shear-induced mixing due to the local increase in fluid vorticity above the disc and (ii) meridional circulations produced by Ekman processes and the constraint of the container sidewall. Laboratory experiments revealed the growth of a mixed layer adjacent to the disc and the subsequent development of layers within the mixed region. Furthermore, the experiments showed that, even at relatively large epsilon, Ekman processes associated with background rotation constituted the dominant mechanism controlling development and evolution of the primary interface between mixed and unmixed fluid regions. Theoretical, energy-based scalings are derived to describe the growth rate of the interfacial region for epsilon greater than or similar to O(1) which are consistent with the epsilon--> infinity limit corresponding to the Omega = 0 case. These scalings are shown to describe well the development of the density field within the forced flow. (C) 2006 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.

    AB - Results are presented from a modelling investigation into the response of a rotating, linearly stratified fluid to local forcing induced by a differentially rotating smooth, horizontal disc. Attention was directed at cases in which the disc forcing is relatively strong, with Rossby number epsilon = omega/2 Omega of order 1 or greater; here omega and Omega are the disc and background rotation frequencies, respectively. The principal flow dynamics resulting in the mixing and deformation of the initially stable density distribution were identified as (i) shear-induced mixing due to the local increase in fluid vorticity above the disc and (ii) meridional circulations produced by Ekman processes and the constraint of the container sidewall. Laboratory experiments revealed the growth of a mixed layer adjacent to the disc and the subsequent development of layers within the mixed region. Furthermore, the experiments showed that, even at relatively large epsilon, Ekman processes associated with background rotation constituted the dominant mechanism controlling development and evolution of the primary interface between mixed and unmixed fluid regions. Theoretical, energy-based scalings are derived to describe the growth rate of the interfacial region for epsilon greater than or similar to O(1) which are consistent with the epsilon--> infinity limit corresponding to the Omega = 0 case. These scalings are shown to describe well the development of the density field within the forced flow. (C) 2006 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.

    KW - Driven

    KW - Turbulent entrainment

    KW - Ekman dynamics

    KW - Annulus

    KW - Density interface

    KW - stratified rotating flows

    KW - Gradient

    KW - Size

    KW - interfacial mixing

    KW - spin-up

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