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arXiv 1011.0887cond-mat.soft
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湍流悬浮体中的输运弛豫时间和长度尺度

Transport relaxation time and length scales in turbulent suspensions

P. Claudin, F. Charru, B. Andreotti

摘要:

结果表明,在紊流输沙条件下,非饱和输沙通量$q(x,t)$可用一阶松弛方程描述。从模式分析的对流扩散方程的颗粒浓度,松弛长度和时间尺度的主导模式被证明是沉积长度$H U/V_{\rm fall}$和沉积时间$H/V_{\rm fall}$,其中$H$是流的深度,$U$的平均流速和$V_{\rm fall}$的沉积物沉降速度。预计这一结果将特别适用于缓慢变化的水流中的泥沙输运情况,因为在这种情况下,流量永远不会远离饱和。预测被证明是在定量协议与水槽实验,净侵蚀和净沉积的情况。

英文摘要:

We show that in a turbulent flow transporting suspended sediment, the unsaturated sediment flux $q(x,t)$ can be described by a first-order relaxation equation. From a mode analysis of the advection-diffusion equation for the particle concentration, the relaxation length and time scales of the dominant mode are shown to be the deposition length $H U/V_{\rm fall}$ and deposition time $H/V_{\rm fall}$, where $H$ is the flow depth, $U$ the mean flow velocity and $V_{\rm fall}$ the sediment settling velocity. This result is expected to be particularly relevant for the case of sediment transport in slowly varying flows, where the flux is never far from saturation. Predictions are shown to be in quantitative agreement with flume experiments, for both net erosion and net deposition situations.

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