Turbulent horizontal convection under spatially periodic forcing: a regime governed by interior inertia
Turbulent horizontal convection under spatially periodic forcing: a regime governed by interior inertia
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空间周期性强迫下的湍流水平对流：由内部惯性控制的状态
DOI：
10.1017/jfm.2017.640
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发表时间：
2017
影响因子：
3.7
通讯作者：
R. W. Griffiths
中科院分区：
文献类型：
--
作者：
M. G. Rosevear;B. Gayen;R. W. Griffiths
在单个水平边界处施加的不同加热会产生“水平对流”，即使在没有净热通量通过边界时也是如此。然而，几乎所有关于水平对流的研究都局限于一类特殊的问题，在这些问题中，温度或热通量的差异只在一个方向上和在一个盒子的水平长度上应用（罗斯比问题；罗斯比，深海研究，1965年第12卷，第9-16页）。这些条件强烈地限制了流动。在这里，我们报告了实验室实验和直接数值模拟（DNS），扩展了Griffiths和Gayen（物理学家）的结果。启。在二维周期阵列中施加边界条件的水平对流，vol. 115, 2015, 204301)。实验在可渗透的基础上使用盐水和淡水通量，施加的边界盐度具有盒子宽度的四分之一的水平长度刻度。流动达到一种状态，在这种状态下，净边界浮力通量消失，流体的体积显示出湍流长度尺度的惯性范围。随着水深的增加，出现了一种状态转变，从强迫尺度上的单个连贯羽流阵列到由涌现的更大规模的倾覆主导的对流。DNS探讨了波数为n=4的正弦边界温度的类似热强迫情况，并用于研究浅水和深水情况下瑞利数（Ra）的依赖关系。对于浅水，随着Ra$的增加，流动从层流过渡到湍流边界层，这与罗斯比问题很熟悉，并且具有标准化的热传输标度为$Nu\sim Ra^{1/5}$和$Nu\sim (Ra\,Pr)^{1/5}$，其中$Nu$为努塞尔数，$Pr$为普朗特数，在这种情况下保持稳定的相干湍流羽流阵列。对于深水和大$Ra$，层流尺度转变为$Nu\sim (Ra\,Pr)^{1/4}$，湍流尺度扩展到盒子的尺寸。$1/4$幂律制度是根据内部对称的、无粘性的大尺度运动的动量来解释的，这些动量与通过边界层稳定部分的热扩散损失相耦合。湍流的产生主要是剪切不稳定而不是对流，粘性耗散分布在整个流体中。这些条件在罗斯比问题的高度不对称流动中看不到，即使在瑞利数比这里发现的过渡大6个数量级的情况下也是如此。新的惯性内区具有可用势能的供给速率和密度混合去除速率，随Ra^{5/4}$增加，比Rossby问题中的Ra^{6/5}$快。不可逆混合被限制在强迫边界附近，并且比粘滞耗散大得多，粘滞耗散与Ra成正比。
Differential heating applied at a single horizontal boundary forces ‘horizontal convection’, even when there is no net heat flux through the boundary. However, almost all studies of horizontal convection have been limited to a special class of problem in which temperature or heat flux differences were applied in only one direction and over the horizontal length of a box (the Rossby problem; Rossby, Deep-Sea Res., vol. 12, 1965, pp. 9–16). These conditions strongly constrain the flow. Here we report laboratory experiments and direct numerical simulations (DNS) extending the results of Griffiths & Gayen (Phys. Rev. Lett., vol. 115, 2015, 204301) for horizontal convection forced by boundary conditions imposed in a two-dimensional periodic array at a horizontal boundary. The experiments use saline and freshwater fluxes at a permeable base with the imposed boundary salinity having a horizontal length scale one quarter of the width of the box. The flow reaches a state in which the net boundary buoyancy flux vanishes and the bulk of the fluid shows an inertial range of turbulence length scales. A regime transition is seen for increasing water depth, from an array of individual coherent plumes on the forcing scale to convection dominated by emergent larger scales of overturning. The DNS explore the analogous thermally forced case with sinusoidal boundary temperature of wavenumber $n=4$ , and are used to examine the Rayleigh number ( $Ra$ ) dependence for shallow- and deep-water cases. For shallow water the flow transitions with increasing $Ra$ from laminar to turbulent boundary layer regimes that are familiar from the Rossby problem and which have normalised heat transport scaling as $Nu\sim Ra^{1/5}$ and $Nu\sim (Ra\,Pr)^{1/5}$ , with $Nu$ the Nusselt number and $Pr$ the Prandtl number, in this case maintaining a stable array of coherent turbulent plumes. For deep-water and large $Ra$ the laminar scaling transitions to $Nu\sim (Ra\,Pr)^{1/4}$ , with the scales of turbulence extending to the dimensions of the box. The $1/4$ power law regime is explained in terms of the momentum of symmetric, inviscid large scales of motion in the interior coupled to diffusive loss of heat through stabilised parts of the boundary layer. The turbulence production is predominantly by shear instability rather than convection, with viscous dissipation distributed throughout the bulk of the fluid. These conditions are not seen in the highly asymmetric flow in the Rossby problem even at Rayleigh numbers up to six orders of magnitude greater than the transition found here. The new inertial interior regime has the rate of supply of available potential energy, and its removal by mixing of density, increasing as $Ra^{5/4}$ , which is faster than $Ra^{6/5}$ in the Rossby problem. Irreversible mixing is confined close to the forcing boundary and is very much larger than the viscous dissipation, which is proportional to $Ra$ .
影响因子：
3.7
作者：
R. Barkan;K. Winters;Stefan G. Llewellyn Smith
通讯作者：
R. Barkan;K. Winters;Stefan G. Llewellyn Smith