The role of exponentially-small terms in transition to turbulence.

指数小项在向湍流过渡中的作用。

• 批准号: 1936270
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1936270
• 关键词: role; exponentially; small; terms; transition

In a conventional asymptotic analysis of high-Reynolds-number flows, only one or two terms of the asymptotic expansions are calculated. It is assumed that the asymptotic expansion converges to the Navier-Stokes solution as the Reynolds number increases. However, over the last decade or so, examples have been furnished where this is not the case, e.g. in the case of high-Reynolds-number unsteady flows that are susceptible to Rayleigh instabilities. The aim of this project is to place the understanding of this phenomenon on a firmer mathematical basis. In particular, it is speculated that this is a Stokes phenomenon arising from the turn-on of exponentially-small terms. The first part of the project will be to demonstrate that this is the case for a one-dimensional model problem that captures the essentials, before extending the analysis to more realistic flows.

在高雷诺数流动的传统渐近分析中，只计算一项或两项渐近展开式。假设渐近展开式随着雷诺数的增加而收敛到Navier-Stokes解。然而，在过去十年左右的时间里，已经提供了不是这种情况的例子，例如，在易受瑞利不稳定性影响的高雷诺数非定常流的情况下。该项目的目的是将对这一现象的理解置于更坚实的数学基础上。特别是，据推测，这是一个斯托克斯现象所产生的开启指数小的条款。该项目的第一部分将证明，这是一个一维模型的问题，捕捉的要点，在扩展到更现实的流动分析。

项目成果

Inherent Instabilities and Discontinuities: The Kuramoto-Sivashinsky Equation and a Suspension Flow as Exemplars

固有的不稳定性和不连续性：Kuramoto-Sivashinsky 方程和悬浮流为例

• DOI: 10.17863/cam.88678
• 发表时间: 2021
• 作者: Sear C