Transition to disordered front propagation

过渡到无序前传播

• 批准号: EP/P026044/1
• 负责人: Anne Juel
• 金额: $ 61.04万
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Research Grant
• 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=EP%2FP026044%2F1
• 关键词: Transition; disordered; front; propagation

The transition to turbulence in pressure-driven pipe flow has remained the greatest unsolved problem in fluid mechanics since Reynolds' pioneering experiments in the late nineteenth century. Although Poiseuille flow in a cylindrical pipe is linearly stable for all values of the Reynolds number - the ratio of inertial to viscous forces - turbulence can appear for Re > 2000 in the form of localised puffs advected down the pipe, if perturbations exceed a finite-amplitude threshold. In the last twenty years, significant progress in the understanding of the transition to turbulence in pipe flow, and more generally shear flows, has been achieved by focusing on the nonlinear dynamics of these flows. The central question underlying this proposal is whether the complex transition scenario uncovered for shear flows may arise in other fluid mechanical systems.We focus on a canonical flow, Saffman-Taylor fingering in a confined channel - parallel plates separated by a narrow gap so that the width to depth aspect ratio is very large - which is an archetype for front propagation and pattern formation. The displacement of a more viscous fluid (oil) by a less viscous fluid (air) under constant volume-flux (or pressure head) yields patterns ranging from to the steady propagation of a single air finger to unsteady front propagation - highly branched patterns which arise through repeated tip-splitting events and finger competition. This transition exhibits striking similarities with shear flow transition in that (a) the single propagating finger solution of a depth-averaged model is known to be linearly stable up to very large values of the driving parameter, and (b) the threshold value of the driving parameter for transition was found experimentally to be very sensitive to the level of perturbations in the system.In shear flow turbulence, a key theoretical concept is the interpretation of localised turbulent puffs as edge states - weakly unstable states with a stable manifold that determines the basin boundary separating initial conditions decaying to laminar flow from those growing to turbulence. The fundamental hypothesis to be investigated in the proposed research is that unstable solutions of the Saffman-Taylor flow are edge states that underlie both the transition from the steadily propagating Saffman-Taylor finger to the experimentally observed complex patterns, and the dynamics of the patterns themselves. This hypothesis stems from preliminary experimental observations and time-dependent numerical simulations of a depth averaged model, which indicates destabilisation of a bubble through the transient exploration of weakly unstable solutions of the Saffman-Taylor problem, when a large value of parameter is applied from rest.The shear flow transition also exhibits excitable dynamics, in that below threshold a turbulent puff excited by a localised perturbation is a transient excursion from laminar flow, which eventually decays on long time scales. Beyond threshold, a turbulent fixed point appears that enables localised patches of turbulence to grow. We will investigate whether excitable dynamics underlie transition in the Saffman-Taylor problem. We will apply a range of localised or spatially-distributed topographical perturbations of known amplitude in order to probe the dynamical response of the interface and establish the transition threshold as a function of perturbation and driving parameter.Finally, a yet unproven hypothesis of shear flow transition is that turbulence can be characterised by a chaotic meandering between unstable solutions. The Saffman-Taylor fingering problem exhibits a much simpler spatial structure partly because nonlinearities only occur within interfacial conditions. Hence, we will attempt to to characterise disordered front propagation and assess the above hypothesis for the Saffman-Taylor transition scenario.

在压力驱动的管道流动中向湍流的过渡一直是流体力学中最大的未解决的问题，因为雷诺在19世纪后期的开创性实验。尽管圆柱形管道中的泊泽维尔流对于所有雷诺数值（惯性力与粘性力之比）都是线性稳定的，但如果扰动超过有限振幅阈值，Re > 2000中的湍流可能以沿管道平流的局部泡波的形式出现。在过去的二十年中，通过关注这些流动的非线性动力学，在理解管道流动和更普遍的剪切流动向湍流过渡方面取得了重大进展。这一提议的核心问题是，在其他流体力学系统中，剪切流所揭示的复杂过渡情景是否也会出现。我们关注的是一个典型的流动，即封闭通道中的Saffman-Taylor指动——平行的板块被一个狭窄的间隙隔开，因此宽度与深度的纵横比非常大——这是锋面传播和图案形成的原型。在恒定的体积通量（或压头）下，粘性较强的流体（油）被粘性较弱的流体（空气）置换产生的模式从单个空气指的稳定传播到非定常锋传播——通过反复的尖端分裂事件和指的竞争产生的高度分支模式。这种过渡表现出与剪切流过渡惊人的相似之处：(a)已知深度平均模型的单传播手指解在驱动参数的很大值之前是线性稳定的，并且(b)在实验中发现过渡的驱动参数的阈值对系统中的扰动水平非常敏感。在剪切流湍流中，一个关键的理论概念是将局部湍流泡波解释为边缘状态-具有稳定流形的弱不稳定状态，该流形决定了将初始条件从增长到湍流的层流分离开来的盆地边界。本研究提出的基本假设是，Saffman-Taylor流的不稳定解是边缘状态，它是稳定传播的Saffman-Taylor指向实验观察到的复杂模式转变的基础，也是模式本身动力学的基础。这一假设源于深度平均模型的初步实验观察和随时间变化的数值模拟，该模型表明，当从静止应用大参数值时，通过对Saffman-Taylor问题弱不稳定解的瞬态探索，气泡不稳定。剪切流转变也表现出可激发的动力学，在阈值以下，由局部扰动激发的湍流泡发是层流的短暂偏移，最终在长时间尺度上衰减。超过阈值，湍流固定点就会出现，使得局部湍流块能够增长。我们将研究在Saffman-Taylor问题中是否存在可激发动力学。我们将应用一系列已知振幅的局部或空间分布的地形扰动，以探测界面的动态响应，并建立过渡阈值作为扰动和驱动参数的函数。最后，一个尚未证实的切变流过渡假设是，湍流可以通过不稳定解之间的混沌蜿蜒来表征。Saffman-Taylor指法问题表现出更简单的空间结构，部分原因是非线性只发生在界面条件下。因此，我们将尝试描述无序锋面传播的特征，并评估上述假说对Saffman-Taylor过渡情景的影响。

项目成果

Peeling fingers in an elastic Hele-Shaw channel

手指在弹性 Hele-Shaw 通道中脱皮

• DOI: 10.48550/arxiv.2310.12940
• 发表时间: 2023
• 作者: Fontana J

Bubble propagation in Hele-Shaw channels with centred constrictions

• DOI: 10.1088/1873-7005/aaa5cf
• 发表时间: 2018-04-01
• 期刊: FLUID DYNAMICS RESEARCH
• 影响因子: 1.5
• 作者: Franco-Gomez, Andres;Thompson, Alice B.;Juel, Anne
• 通讯作者: Juel, Anne

The life and fate of a bubble in a geometrically perturbed Hele-Shaw channel

• DOI: 10.1017/jfm.2020.844
• 发表时间: 2021-03-05
• 期刊: JOURNAL OF FLUID MECHANICS
• 影响因子: 3.7
• 作者: Gaillard, Antoine;Keeler, Jack S.;Juel, Anne
• 通讯作者: Juel, Anne

The engulfment of aqueous droplets on perfectly wetting oil layers

• DOI: 10.1017/jfm.2021.90
• 发表时间: 2020-09
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Callum Cuttle;A. Thompson;D. Pihler-Puzović;A. Juel

Modelling finger propagation in elasto-rigid channels

模拟弹性刚性通道中的手指传播

• DOI: 10.1017/jfm.2021.219
• 发表时间: 2021
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Fontana J