SURPRISING BEHAVIOUR AND SINGULARITY IN THE SAINT VENANT APPROXIMATION FOR A FLUID

P. Luchini
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引用次数: 1

Abstract

A research line is reviewed which, over a few years, led to a substantial change of perspective about the simplified models that underlie the description of quasi-onedimensional streams, their instabilities, and their effects upon sandy beds. Even when the flow is assumed to be laminar, the Saint-Venant equation of quasi-onedimensional fluid flow can be formulated in more than one manner; it will be shown that only one of these choices is consistent with the complete three-dimensional Navier- Stokes equations. When the flow is turbulent, an added complication is the presence of a turbulence model, most often of the eddy-viscosity type; it will be shown that such a model can be in strong contrast with a direct numerical simulation of the same phenomenon, even to the point of producing results of opposite sign. In addition, the complete numerical simulation of flow past an undulated bottom exhibits a non-monotonic approach to its long-wave, quasi-onedimensional limit, with a surprising resonance that has no laminar counterpart and must become the subject of future investigations.
流体圣维南近似中的奇异行为和奇点
本文回顾了几年来的一条研究路线,这条路线导致了关于准一维溪流、其不稳定性及其对砂床的影响的简化模型的观点的实质性变化。即使假定流体流动为层流,准一维流体流动的Saint-Venant方程也可以用多种方式表示;它将表明,这些选择中只有一个与完整的三维纳维-斯托克斯方程一致。当流动是湍流时,一个额外的复杂性是湍流模型的存在,最常见的是涡流粘度型;将表明,这种模型可以与对同一现象的直接数值模拟形成强烈的对比,甚至达到产生相反符号的结果的地步。此外,通过波动底部的完整数值模拟显示出非单调接近其长波,准一维极限,具有令人惊讶的共振,没有层流对应,必须成为未来研究的主题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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