Effects of symmetry breaking in the viscous pumping of an oscillating plate in the intermediate Reynolds numbers

A numerical investigation was conducted into the different flow states, and bifurcations leading to changes of state, found in open cylinders of medium to moderate depth driven by a constant rotation of the vessel base. A combination of linear stability analysis, for cylinders of numerous height-to-radius aspect ratios (H/R), and nonlinear stability analysis and three-dimensional simulations for a cylinder of aspect ratio 1.5, has been employed. Attention is focused on the breaking of SO(2) symmetry. A comprehensive map of transition Reynolds numbers as a function of aspect ratio is presented by combining a detailed stability analysis with the limited existing data from the literature. For all aspect ratios considered, the primary instabilities are identified as symmetry-breaking Hopf bifurcations, occurring at Reynolds numbers well below those of the previously reported axisymmetric Hopf transitions. It is revealed that instability modes with azimuthal wavenumbers m = 1, 3 and 4 are the most unstable in the range 1.0 < H/R < 4, and that numerous double Hopf bifurcation points exist. Critical Reynolds numbers generally increase with cylinder aspect ratio, though a decrease in stability occurs between aspect ratios 1.5 and 2.0, where a local minimum in critical Reynolds number occurs. For H/R = 1.5, a detailed characterisation of instability modes is given. It is hypothesized that the primary instability leading to transition from steady axisymmetric flow to unsteady three-dimensional flow is related to deformation of shear layers that are present in the flow, in particular at the interfacial region between the vortex breakdown bubble and the primary recirculation.

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Surfactant-loaded capsules as Marangoni microswimmers at the air–water interface: Symmetry breaking and spontaneous propulsion by surfactant diffusion and advection

The European Physical Journal E ◽

10.1140/epje/s10189-021-00035-8 ◽

2021 ◽

Vol 44 (2) ◽

Author(s):

Hendrik Ender ◽

Ann-Kathrin Froin ◽

Heinz Rehage ◽

Jan Kierfeld

Keyword(s):

Symmetry Breaking ◽

Peclet Number ◽

Reynolds Numbers ◽

Water Soluble ◽

Swimming Velocity ◽

Water Interface ◽

Péclet Number ◽

Air Interface ◽

Alginate Capsules ◽

Air Water Interface

Abstract We present a realization of a fast interfacial Marangoni microswimmer by a half-spherical alginate capsule at the air–water interface, which diffusively releases water-soluble spreading molecules (weak surfactants such as polyethylene glycol (PEG)), which act as “fuel” by modulating the air–water interfacial tension. For a number of different fuels, we can observe symmetry breaking and spontaneous propulsion although the alginate particle and emission are isotropic. The propulsion mechanism is similar to soap or camphor boats, which are, however, typically asymmetric in shape or emission to select a swimming direction. We develop a theory of Marangoni boat propulsion starting from low Reynolds numbers by analyzing the coupled problems of surfactant diffusion and advection and fluid flow, which includes surfactant-induced fluid Marangoni flow, and surfactant adsorption at the air–water interface; we also include a possible evaporation of surfactant. The swimming velocity is determined by the balance of drag and Marangoni forces. We show that spontaneous symmetry breaking resulting in propulsion is possible above a critical dimensionless surfactant emission rate (Peclet number). We derive the relation between Peclet number and swimming speed and generalize to higher Reynolds numbers utilizing the concept of the Nusselt number. The theory explains the observed swimming speeds for PEG–alginate capsules, and we unravel the differences to other Marangoni boat systems based on camphor, which are mainly caused by surfactant evaporation from the liquid–air interface. The capsule Marangoni microswimmers also exhibit surfactant-mediated repulsive interactions with walls, which can be qualitatively explained by surfactant accumulation at the wall. Graphic Abstract

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Simulation and feedback control of the Ahmed body flow exhibiting symmetry breaking behaviour

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.118 ◽

2017 ◽

Vol 817 ◽

Cited By ~ 16

Author(s):

O. Evstafyeva ◽

A. S. Morgans ◽

L. Dalla Longa

Keyword(s):

Reynolds Number ◽

Feedback Control ◽

Symmetry Breaking ◽

Numerical Simulations ◽

Control Strategy ◽

Low Reynolds Number ◽

Reynolds Numbers ◽

Low Reynolds ◽

Feedback Control Strategy ◽

Ahmed Body

The present work considers the low-Reynolds-number wake flow behind a squareback Ahmed body, in close proximity to a ground. At low Reynolds numbers such wakes are known to undergo a series of bifurcations to a state that breaks reflectional symmetry. The symmetry breaking of the wake also persists at turbulent high Reynolds numbers, where it manifests as bi-modal behaviour with random switching between the asymmetric states. Thus far, it has only been possible to study the low-Reynolds-number sequence of bifurcations experimentally and mathematically. The present work presents the first numerical simulations capturing the sequence of symmetry breaking bifurcations that occur. A study of how the wake topology changes throughout suggests that interaction between the closer top/bottom pair of parallel shear layers can only dominate once there is sufficient underbody flow. When this occurs, the two main vortex structures in the wake switch from being horizontally to vertically aligned. A linear feedback control strategy, designed to attenuate base pressure force fluctuations, is then implemented. This causes an accompanying reduction in drag and re-symmetrisation of the wake. Analysis using the dynamic mode decomposition confirms that the wake shedding mode is re-symmetrised. This work motivates future attempts to capture wake symmetry breaking and bi-modality in numerical simulations, and application of a promising feedback control strategy at higher, turbulent Reynolds numbers.

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Heat Transfer Enhancement for Blocks in a Channel Using a Rotationally Oscillating Plate

Journal of Electronic Packaging ◽

10.1115/1.4027090 ◽

2014 ◽

Vol 136 (3) ◽

Author(s):

Esam M. Alawadhi

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Heat Transfer Enhancement ◽

Dissipation Rate ◽

Thermal Characteristics ◽

Reynolds Numbers ◽

Thermal Dissipation ◽

Transfer Enhancement ◽

Maximum Angle ◽

Oscillating Plate

Heat transfer enhancement using a rotationally oscillating plate in a channel containing heated blocks is numerically studied. The blocks simulate electronic chips with a high thermal dissipation rate. The model consists of a channel formed by two plates with heated blocks attached to bottom walls and a plate installed at the centerline of the channel. The rotationally oscillating plate enhances heat transfer from the blocks through the flow accelerating above the blocks. The effect of the frequency and maximum angle of attack of the plate on the Nusselt number is investigated for different Reynolds numbers. Heat transfer enhancement of the blocks with the plate is evaluated by comparing their thermal characteristics to a channel without plate. The results show that the oscillating plate enhances overall heat flow out of the blocks by 21.72% but with significant pressure drop of 300%.

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Nonlinear flow phenomena in a symmetric sudden expansion

Journal of Fluid Mechanics ◽

10.1017/s0022112090001707 ◽

1990 ◽

Vol 211 ◽

pp. 595-608 ◽

Cited By ~ 225

Author(s):

R. M. Fearn ◽

T. Mullin ◽

K. A. Cliffe

Keyword(s):

Symmetry Breaking ◽

Three Dimensional ◽

Reynolds Numbers ◽

Time Dependent ◽

Nonlinear Flow ◽

Sudden Expansion ◽

Numerical Techniques ◽

Flow Phenomena ◽

Asymmetric Flows ◽

Good Agreement

The origin of steady asymmetric flows in a symmetric sudden expansion is studied using experimental and numerical techniques. We show that the asymmetry arises at a symmetry-breaking bifurcation and good agreement between the experiments and numerical calculations is obtained. At higher Reynolds numbers the flow becomes time-dependent and there is experimental evidence that this is associated with three-dimensional effects.

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Flow past a sphere up to a Reynolds number of 300

Journal of Fluid Mechanics ◽

10.1017/s0022112098003206 ◽

1999 ◽

Vol 378 ◽

pp. 19-70 ◽

Cited By ~ 582

Author(s):

T. A. JOHNSON ◽

V. C. PATEL

Keyword(s):

Reynolds Number ◽

Symmetry Breaking ◽

Unsteady Flow ◽

Axisymmetric Flow ◽

Reynolds Numbers ◽

Numerical Results ◽

Near Wake ◽

Hairpin Vortices ◽

Breaking Mechanism ◽

Visualization Experiments

The flow of an incompressible viscous fluid past a sphere is investigated numerically and experimentally over flow regimes including steady and unsteady laminar flow at Reynolds numbers of up to 300. Flow-visualization experiments are used to validate the numerical results and to provide additional insight into the behaviour of the flow. Near-wake visualizations are presented for both steady and unsteady flows. Calculations for Reynolds numbers of up to 200 show steady axisymmetric flow and compare well with previous experimental and numerical observations. For Reynolds numbers of 210 to 270, a steady non-axisymmetric regime is found, also in agreement with previous work. To advance the basic understanding of this transition, a symmetry breaking mechanism is proposed based on a detailed analysis of the calculated flow field.Unsteady flow is calculated at Reynolds numbers greater than 270. The results at a Reynolds number of 300 show a highly organized periodic flow dominated by vortex shedding. An analysis of the calculated vortical structure of the wake reveals a sequence of shed hairpin vortices in combination with a sequence of previously unidentified induced hairpin vortices. The numerical results compare favourably with experimental flow visualizations which, interestingly, fail to reveal the induced vortices. Based on the deduced symmetry-breaking mechanism, an analysis of the unsteady kinematics, and the experimental results, a mechanism driving the transition to unsteady flow is proposed.

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Symmetry breaking in convergent-beam diffraction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100154378 ◽

1989 ◽

Vol 47 ◽

pp. 480-481

Author(s):

D.J. Eaglesham

Keyword(s):

Symmetry Breaking ◽

Point Group ◽

X Ray Diffraction ◽

Multiple Diffraction ◽

Space Groups ◽

Atomic Displacements ◽

Small Probe ◽

Phase Sensitive ◽

Convergent Beam

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs

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Centrosome Aurora A gradient ensures single polarity axis in C. elegans embryos

Biochemical Society Transactions ◽

10.1042/bst20200298 ◽

2020 ◽

Vol 48 (3) ◽

pp. 1243-1253 ◽

Cited By ~ 1

Author(s):

Sukriti Kapoor ◽

Sachin Kotak

Keyword(s):

Symmetry Breaking ◽

Cell Fate ◽

Cell Cortex ◽

Axis Formation ◽

Aurora A Kinase ◽

Aurora A ◽

C Elegans ◽

Cell Embryo ◽

Polarity Establishment

Cellular asymmetries are vital for generating cell fate diversity during development and in stem cells. In the newly fertilized Caenorhabditis elegans embryo, centrosomes are responsible for polarity establishment, i.e. anterior–posterior body axis formation. The signal for polarity originates from the centrosomes and is transmitted to the cell cortex, where it disassembles the actomyosin network. This event leads to symmetry breaking and the establishment of distinct domains of evolutionarily conserved PAR proteins. However, the identity of an essential component that localizes to the centrosomes and promotes symmetry breaking was unknown. Recent work has uncovered that the loss of Aurora A kinase (AIR-1 in C. elegans and hereafter referred to as Aurora A) in the one-cell embryo disrupts stereotypical actomyosin-based cortical flows that occur at the time of polarity establishment. This misregulation of actomyosin flow dynamics results in the occurrence of two polarity axes. Notably, the role of Aurora A in ensuring a single polarity axis is independent of its well-established function in centrosome maturation. The mechanism by which Aurora A directs symmetry breaking is likely through direct regulation of Rho-dependent contractility. In this mini-review, we will discuss the unconventional role of Aurora A kinase in polarity establishment in C. elegans embryos and propose a refined model of centrosome-dependent symmetry breaking.

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