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Symmetry and Symmetry-Breaking in Fluid Dynamics

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A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 17637

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Special Issue Editors

Prof. Andrzej Herczyński

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Guest Editor

Department of Physics, Boston College, Chestnut Hill, MA 02467, USA
Interests: fluid dynamics; physics of art

Prof. Roberto Zenit

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Co-Guest Editor

Zenit Research Lab, School of Engineering Brown, University Providence, Great Falls, RI 02912, USA
Interests: fluid mechanics

Special Issue Information

Dear Colleagues,

Symmetry underlies many fluid phenomena and often provides a key to a better understanding as well as simpler analytical or numerical solutions for a variety of flows. This special issue of Symmetry aims to stimulate new insights and perspectives into the role of symmetry in a wide range of fluid flows, symmetry-breaking phenomena, and flows, which are symmetric partially, locally, or intermittently – in space or time.

Symmetric cases in two dimensions include flows along flat surfaces, liquid sheets, draining flows from plates, and radially spreading drops. Three-dimensional flows offer even greater variety of geometric symmetries, axial, translational, mirror, spiral, helical, etc. Conversely, flows of high degree of regularity may suffer symmetry breaking through instabilities or other mechanisms. In fact, the origin of many well-studied hydrodynamic instabilities is directly related to the emergence of symmetry breaking.

For example, while liquids impinging on surfaces and scraping flows reduce symmetry because of the imposed boundary conditions, fragmenting streams or coiling jets break symmetry spontaneously.

All contributions are welcome, including research articles, review papers, educational assessments, and methods tutorials. The flows considered may be of any scale or complexity, from microfluidic to galactic, from single-component to multi-phase, from inactive to driven by living organisms.

Topics may include but are not limited to:

Rotational and axisymmetric fluid or granular flows
Exact solutions of the Navier-Stokes Equations and their symmetries
Bubbles, drops, and foams exhibiting or reducing symmetry
Symmetry breaking instabilities in viscous liquids
Smoke, flames, and combustive flows
Non-Newtonian effects breaking or establishing symmetry
Multicomponent and/or multiphase flows
Thermally induced convection in various geometries
Flows in gravity-free environments, stratified flows
Active flows and flows induced by micro-swimmers
Self-similar, fractal, and turbulent flows
Time-symmetries, periodic and quasi-periodic flows

Prof. Andrzej Herczyński
Prof. Roberto Zenit
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Symmetric flows
symmetry-breaking flows
circular, axisymmetric
cylindrical
spherical
periodic
rotation
spiral
helical
convection, instabilities
self-similarity
fractal
active flows
bio-fluid dynamics
hydrodynamic instabilities

Published Papers (11 papers)

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Research

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28 pages, 3356 KiB

Open AccessArticle

Anchored and Lifted Diffusion Flames Supported by Symmetric and Asymmetric Edge Flames

by Zhanbin Lu and Moshe Matalon

Symmetry 2023, 15(8), 1547; https://doi.org/10.3390/sym15081547 - 06 Aug 2023

Viewed by 1051

Abstract

Numerous combustion applications are concerned with the stabilization of diffusion flames formed by injecting gaseous fuels into a co-flowing stream containing an oxidizer. The smooth operation of these devices depends on the attachment and lift-off characteristics of the edge flame at the base of the diffusion flame. In this paper, we address fundamental issues pertinent to the structure and dynamics of edge flames, which have attributes of both premixed and diffusion flames. The adopted configuration is the mixing layer established in the wake of a splitter plate where two streams, one containing fuel and the other oxidizer, merge. The analysis employs a diffusive-thermal model which, although it excludes effects of gas expansion, systematically includes the influences of the overall flow rate, unequal strain rates in the incoming streams, stoichiometry, differential and preferential diffusion, heat loss and gas–solid thermal interaction, and their effect on the edge structure, speed, and temperature. Conditions when the edge flame is anchored to the plate, lifted-off and stabilized in the flow, or blown-off, are identified. Two stable modes of stabilization are observed for lifted flames; the edge flame either remains stationary at a specified location or undergoes spontaneous oscillations along a direction that coincides with the trailing diffusion flame. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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9 pages, 274 KiB

Open AccessArticle

Spreading or Contraction of an Axisymmetric Viscous Drop between Two Plates in a Rapidly Rotating Frame

by M. G. E. Roach and Herbert E. Huppert

Symmetry 2022, 14(12), 2488; https://doi.org/10.3390/sym14122488 - 24 Nov 2022

Viewed by 888

Abstract

We analyse the motions of a axisymmetric drop expanding between two rotating discs. We restrict to the case of a highly viscous fluid and a rapid rate of rotation. Therefore, we make modelling assumptions following from both a low Reynolds number and a low Rossby number. We investigate both the squeezing problem, where the top disc is pushed down on the drop; and the contraction problem, where the top plate is pulled away from the drop. Both problems have similar solutions to the non-rotating case but we find that the rotation term in the contraction problem allows a critical rotation rate that prevents the plates from moving apart. This exists because pressure in the fluid layer is lowered by the rotation and thus there is a suction effect between the two plates which promotes adhesion. We also complete the linear instability analysis of the squeezing problem and determine the critical values where the system shifts from symmetrical to asymmetrical. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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10 pages, 8110 KiB

Open AccessArticle

Viscous Thread Falling on a Spinning Surface

by Maciej Lisicki, Łukasz Adamowicz, Andrzej Herczyński and Henry Keith Moffatt

Symmetry 2022, 14(8), 1550; https://doi.org/10.3390/sym14081550 - 28 Jul 2022

Cited by 1 | Viewed by 1325

Abstract

A rotational version of the fluid-mechanical sewing machine (FMSM) is investigated experimentally. A thin thread of silicon oil was dispensed at a constant flow rate Q from a height H and fell on a table rotating at an angular speed

ω

, at [...] Read more.

ω

, at a distance R from the axis. In all experimental runs, the values of Q and H were kept constant while the radius R was changed manually after each full rotation. Preliminary results show that the usual stitching patterns ensue as the local linear speed

V = ω R

approaches the critical transition speeds seen in the FMSM scenario but with subtle asymmetries introduced by rotational (centrifugal) effects. In some instances, arcs and loops of the traces were noticeably more pronounced when directed outward compared to those pointing toward the axis of rotation. Moreover, we observed stitching patterns not reported before. Overall, the symmetry-breaking features, while clearly visible, were rather subtle. Their morphological characteristics, such as differences in local curvature of traces relative to those in FMSM, are estimated to be below 10% in most cases. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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19 pages, 1268 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

The Stability of a Hydrodynamic Bravais Lattice

by Miles M. P. Couchman, Davis J. Evans and John W. M. Bush

Symmetry 2022, 14(8), 1524; https://doi.org/10.3390/sym14081524 - 26 Jul 2022

Cited by 2 | Viewed by 1920

Abstract

We present the results of a theoretical investigation of the stability and collective vibrations of a two-dimensional hydrodynamic lattice comprised of millimetric droplets bouncing on the surface of a vibrating liquid bath. We derive the linearized equations of motion describing the dynamics of a generic Bravais lattice, as encompasses all possible tilings of parallelograms in an infinite plane-filling array. Focusing on square and triangular lattice geometries, we demonstrate that for relatively low driving accelerations of the bath, only a subset of inter-drop spacings exist for which stable lattices may be achieved. The range of stable spacings is prescribed by the structure of the underlying wavefield. As the driving acceleration is increased progressively, the initially stationary lattices destabilize into coherent oscillatory motion. Our analysis yields both the instability threshold and the wavevector and polarization of the most unstable vibrational mode. The non-Markovian nature of the droplet dynamics renders the stability analysis of the hydrodynamic lattice more rich and subtle than that of its solid state counterpart. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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17 pages, 13358 KiB

Open AccessFeature PaperArticle

Symmetry and Asymmetry in the Fluid Mechanical Sewing Machine

by Neil M. Ribe, Pierre-Thomas Brun and Basile Audoly

Symmetry 2022, 14(4), 772; https://doi.org/10.3390/sym14040772 - 08 Apr 2022

Cited by 3 | Viewed by 1933

Abstract

The ‘fluid mechanical sewing machine’ is a device in which a thin thread of viscous fluid falls onto a horizontal belt moving in its own plane, creating a rich variety of ‘stitch’ patterns depending on the fall height and the belt speed. This review article surveys the complex phenomenology of the patterns, their symmetries, and the mathematical models that have been used to understand them. The various patterns obey different symmetries that include (slightly imperfect) fore–aft symmetry relative to the direction of belt motion and invariance under reflection across a vertical plane containing the velocity vector of the belt, followed by a shift of one-half the wavelength. As the belt speed decreases, the first (Hopf) bifurcation is to a ‘meandering’ state whose frequency is equal to the frequency

Ω_{c}

of steady coiling on a motionless surface. More complex patterns can be studied using direct numerical simulation via a novel ‘discrete viscous threads’ algorithm that yields the Fourier spectra of the longitudinal and transverse components of the motion of the contact point of the thread with the belt. The most intriguing case is the ‘alternating loops’ pattern, the spectra of which are dominated by the first five multiples of

Ω_{c} / 3

. A reduced (three-degrees-of-freedom) model succeeds in predicting the sequence of patterns observed as the belt speed decreases for relatively low fall heights for which inertia in the thread is negligible. Patterns that appear at greater fall heights seem to owe their existence to weakly nonlinear interaction between different ‘distributed pendulum’ modes of the quasi-vertical ‘tail’ of the thread. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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8 pages, 361 KiB

Open AccessArticle

Moving Forward by Shaking Sideways

by Jean-Luc Thiffeault

Symmetry 2022, 14(3), 620; https://doi.org/10.3390/sym14030620 - 20 Mar 2022

Cited by 2 | Viewed by 1121

Abstract

We investigate a simple model for a self-propelled swimmer, which consists of a fluctuating force acting at a point on a rigid body. The rigid body is subject to Newton’s equations with linear friction, corresponding to drag in a viscous fluid. The force has zero time average, so net motion is challenging. We show that the swimmer can inch forward by shaking from side to side and exploiting friction coupled with nonlinearity. For large enough forcing amplitude it can reverse direction and swim backward. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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9 pages, 5197 KiB

Open AccessArticle

Buoyancy-Marangoni Fingering of a Miscible Spreading Drop

by Alireza Hooshanginejad and Sunghwan Jung

Symmetry 2022, 14(2), 425; https://doi.org/10.3390/sym14020425 - 21 Feb 2022

Cited by 2 | Viewed by 2489

Abstract

We experimentally investigate the interfacial instability that emerges when a water droplet is deposited on a bath of glycerol-water solution. Despite the absence of surface tension to stabilize short-wavelength undulations, we observe finite-size fingers that grow and pinch off from the drop. We show that the fingering patterns formed in the experiments resultes from a balance between the outward buoyancy effect and inward Marangoni flow. This induced Marangoni flow inhibits small perturbations and acts as an effective surface tension on the miscible interface of the spreading drop. To characterize the final size and shape of the drop, we perform systematic experiments by varying the drop volume and the glycerol-water volume fraction. In addition, we have developed scaling arguments for the drop’s final radius using key physical forces, and show that the final wavelength is inversely proportional to the Bond number. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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14 pages, 3252 KiB

Open AccessArticle

Numerical Investigation of the Automatic Air Intake Drag Reduction Strut Based on the Venturi Effect

by Hai An, Zhenyu Hu, Haozhe Pan and Po Yang

Symmetry 2022, 14(2), 367; https://doi.org/10.3390/sym14020367 - 12 Feb 2022

Cited by 1 | Viewed by 1194

Abstract

Drag reduction by injecting air is a promising engineering method for improving ship performance. A novel automatic air intake drag reduction strut structure based on the Venturi effect is proposed for the high-speed small water-plane area twin hull vessels in the present study. The drag reduction strut can achieve the function of automatic air intake when the vehicle is moving at high speed, and the air inhaled and the incoming flow form bubbly flows to cover the strut surface, effectively reducing the drag of the strut. Considering the longitudinal symmetry of the strut structure, a two-dimensional single-chip drag reduction strut structure is designed to facilitate analysis and a solution. The volume of fluid model is combined with the k-ω SST turbulence model, and a numerical simulation is carried out to investigate the variation of the air inflow, the air volume fraction in the bubbly flows of the strut and the drag reduction rate of the strut for different sailing speeds. The analysis result shows that when the proposed model reaches a certain speed, the external air is inhaled by the strut intake duct, and the bubbly flows are formed with the incoming flow covering the surface of the strut, thereby reducing the drag coefficient. Meanwhile, it is found that as the sailing speed increases, the drag reduction rate of the strut gradually rises and its maximum value reaches about 30%. For high sailing speeds, the drag reduction rate is affected by wave-making resistance so that it gradually declines. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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10 pages, 297 KiB

Open AccessArticle

Lack of Plasma-like Screening Mechanism in Sedimentation of a Non-Brownian Suspension

by Paweł Sznajder, Bogdan Cichocki and Maria Ekiel-Jeżewska

Symmetry 2022, 14(1), 63; https://doi.org/10.3390/sym14010063 - 03 Jan 2022

Viewed by 915

Abstract

We investigate qualitatively a uniform non-Brownian sedimenting suspension in a stationary state. As a base of our analysis we take the BBGKY hierarchy derived from the Liouville equation. We then show that assumption of the plasma-like screening relations can cancel some long-range terms in the hierarchy but it does not provide integrable solutions for correlation functions. This suggests breaking the translational symmetry of the system. Therefore a non-uniform structure can develop to suppress velocity fluctuations and make the range of correlations finite. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

20 pages, 454 KiB

Open AccessArticle

Possible Role of Non-Stationarity of Magnetohydrodynamic Turbulence in Understanding of Geomagnetic Excursions

by Krzysztof Andrzej Mizerski

Symmetry 2021, 13(10), 1881; https://doi.org/10.3390/sym13101881 - 05 Oct 2021

Cited by 2 | Viewed by 1470

Abstract

The natural simplifying assumptions often put forward in the theoretical investigations of the magnetohydrodynamic turbulence are that the turbulent flow is statistically isotropic, homogeneous and stationary. Of course, the natural turbulence in the planetary interiors, such as the liquid core of the Earth is neither, which has important consequences for the dynamics of the planetary magnetic fields generated via the hydromagnetic dynamo mechanism operating in the interiors of the planets. Here we concentrate on the relaxation of the assumption of statistical stationarity of the turbulent flow and study the effect of turbulent wave fields in the Earth’s core, which induces non-stationarity, on the turbulent resistivity in the non-reflectionally symmetric flow and the geodynamo effect. It is shown that the electromotive force, including the so-called

α

-effect and the turbulent magnetic diffusivity

\bar{η}

, induced by non-stationary turbulence, evolves slowly in time. However, the turbulent

\bar{α}

coefficient, responsible for the dynamo action and

\bar{η}

evolve differently in time, thus creating periods of enhanced and suppressed turbulent diffusion and dynamo action somewhat independently. In particular, periods of enhanced

\bar{α}

may coincide with periods of suppressed diffusion, leading to a stable and strong field period. On the other hand, it is shown that when enhanced diffusion occurs simultaneously with suppression of the

α

-effect, this leads to a sharp drop in the intensity of the large-scale field, corresponding to a geomagnetic excursion. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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Review

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24 pages, 10313 KiB

Open AccessReview

Discrete and Continuous Symmetries of Stratified Flows Past a Sphere

by Yuli D. Chashechkin

Symmetry 2022, 14(6), 1278; https://doi.org/10.3390/sym14061278 - 20 Jun 2022

Cited by 1 | Viewed by 1532

Abstract

This study presents the detailed experimental results of fine structures and dynamics in a stratified flow past a sphere, which is towed with constant velocity in a transparent basin. We developed experimental procedures based on the complete solutions of the truncated fundamental fluid equations. These complete solutions describe the waves and fine accompanying ligaments, as well as the vortices and other flow structures. To visualize the flow, a variety of classical schlieren and electrolytic precipitation procedures were used. Ligaments appear in the schlieren images of the flow as fine interfaces and fibers. They strengthen the influence of the relatively weak density gradient in a continuously stratified fluid (CSF). The symmetry in the wake is discrete at small Froude numbers with the domination of buoyancy effects. At increased velocity and high Froude numbers, when the inertial and non-linear effects turn out to be significant, an axial symmetry becomes continuous. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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