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arXiv 0806.0064physics.flu-dyn
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第一个$R_{cr}$作为二维定常尾流中卷吸长度的可能量度

The first $R_{cr}$ as a possible measure of the entrainment length in a 2D steady wake

Tordella Daniela, Scarsoglio Stefania

摘要:

在距产生尾流的物体固定距离处,只有当距离接近20个物体尺度时,才能看到卷吸随雷诺数($R$)增加。这种增加水平高达雷诺数接近临界值的第一不稳定性的发病。在所考虑的$R$范围内(即[20 - 100]),对于所有定常尾流,在几乎相同的距离处观察到夹带几乎消失,这表明超临界定常尾流具有与亚临界尾流相同的夹带长度。据观察,该距离等于等于临界雷诺数($\sim 47$)的值的物体长度的数量,如大量的实验结果汇编所示。{\it A fortiori}这些发现,我们建议解释非定常分岔作为一个过程,允许一个平滑的增加-重新分布的卷吸沿尾流根据对流的重量在扩散。已使用Navier-Stokes速度场的匹配渐近展开[Tordella和Belan,{\it Physics of Fluids},15(2003)]确定了沿稳定尾流的卷吸变化,该展开建立在包括卷吸过程产生的横向速度匹配的标准上。

英文摘要:

At a fixed distance from the body which creates the wake, entrainment is only seen to increase with the Reynolds number ($R$) up to a distance of almost 20 body scales. This increase levels up to a Reynolds number close to the critical value for the onset of the first instability. The entrainment is observed to be almost extinguished at a distance which is nearly the same for all the steady wakes within the $R$ range here considered, i.e. [20-100], which indicates that supercritical steady wakes have the same entrainment length as the subcritical ones. It is observed that this distance is equal to a number of body lengths that is equal to the value of the critical Reynolds number ($\sim 47$), as indicated by a large compilation of experimental results. {\it A fortiori} of these findings, we propose to interpret the unsteady bifurcation as a process that allows a smooth increase-redistribution of the entrainment along the wake according to the weight of the convection over the diffusion. The entrainment variation along the steady wake has been determined using a matched asymptotic expansion of the Navier-Stokes velocity field [Tordella and Belan, {\it Physics of Fluids}, 15(2003)] built on criteria that include the matching of the transversal velocity produced by the entrainment process.

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