Turbulent thermal convection in a rotating stratified fluid

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In: Journal of Fluid Mechanics, 467(2002), S. 19 - 40
Format: E-Artikel
Sprache: Englisch
veröffentlicht: Cambridge University Press (CUP)
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ISSN: 0022-1120
1469-7645
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Details: <jats:p>Turbulent convection induced by heating the bottom boundary of a horizontally homogeneous, linearly (temperature) stratified, rotating fluid layer is studied using a series of laboratory experiments. It is shown that the growth of the convective mixed layer is dynamically affected by background rotation (or Coriolis forces) when the parameter <jats:italic>R</jats:italic> = (<jats:italic>h</jats:italic><jats:sup>2</jats:sup><jats:italic>Ω</jats:italic><jats:sup>3</jats:sup>/<jats:italic>q</jats:italic><jats:sub>0</jats:sub>)<jats:sup>2/3</jats:sup> exceeds a critical value of <jats:italic>R</jats:italic><jats:sub><jats:italic>c</jats:italic></jats:sub> ≈ 275. Here <jats:italic>h</jats:italic> is the depth of the convective layer, <jats:italic>Ω</jats:italic> is the rate of rotation, and <jats:italic>q</jats:italic><jats:sub>0</jats:sub> is the buoyancy flux at the bottom boundary. At larger <jats:italic>R</jats:italic>, the buoyancy gradient in the mixed layer appears to scale as (d<jats:styled-content style="e14">b</jats:styled-content>/d<jats:italic>z</jats:italic>)<jats:sub><jats:italic>ml</jats:italic></jats:sub> = <jats:italic>CΩ</jats:italic><jats:sup>2</jats:sup>, where <jats:italic>C</jats:italic> ≈ 0.02. Conversely, when <jats:italic>R</jats:italic> &lt; <jats:italic>R</jats:italic><jats:sub><jats:italic>c</jats:italic></jats:sub>, the buoyancy gradient is independent of <jats:italic>Ω</jats:italic> and approaches that of the non-rotating case. The entrainment velocity, <jats:italic>u</jats:italic><jats:sub><jats:italic>e</jats:italic></jats:sub>, for <jats:italic>R</jats:italic> &gt; <jats:italic>R</jats:italic><jats:sub><jats:italic>c</jats:italic></jats:sub> was found to be dependent on <jats:italic>Ω</jats:italic> according to <jats:italic>E</jats:italic> = [<jats:italic>Ri</jats:italic>(1 + <jats:italic>CΩ</jats:italic><jats:sup>2</jats:sup>/<jats:italic>N</jats:italic><jats:sup>2</jats:sup>)]<jats:sup>−1</jats:sup>, where <jats:italic>E</jats:italic> is the entrainment coefficient based on the convective velocity <jats:italic>w</jats:italic>∗ = (<jats:italic>q</jats:italic><jats:sub>0</jats:sub><jats:italic>h</jats:italic>)<jats:sup>1/3</jats:sup>, <jats:italic>E</jats:italic> = <jats:italic>u</jats:italic><jats:sub><jats:italic>e</jats:italic></jats:sub>/<jats:italic>w</jats:italic>∗, <jats:italic>Ri</jats:italic> is the Richardson number <jats:italic>Ri</jats:italic> = <jats:italic>N</jats:italic><jats:sup>2</jats:sup><jats:italic>h</jats:italic><jats:sup>2</jats:sup>/<jats:italic>w</jats:italic><jats:sup>2</jats:sup>∗, and <jats:italic>N</jats:italic> is the buoyancy frequency of the overlying stratified layer. The results indicate that entrainment in this case is dominated by non-penetrative convection, although the convective plumes can penetrate the interface in the form of lenticular protrusions.</jats:p>
Beschreibung: 19-40