メールマガジン No.44（2019 年 7 月）

APCOM2019 のご案内
岡田
The Asian Pacific Congress on Computational Mechanics
2019 (APCOM2019)が2019年12月18日（水）～21日（土）にTaipei International Convention Center, Taipei, Taiwanで開催されます．
会議の詳細はWEBページ：

裕JACM 会長（東京理科大学）

http://www.apcom2019.orgに掲載されております．
JACM会員の皆様におかれてはAPCOM2019に奮ってご参加の程お願いいたします．

JACM 総会のご案内
岡田裕

JACM 会長（東京理科大学）

JACM 総 会 な ら び に 2019 JACM Awards 授 賞 式 を信によりお知らせします．

APCOM2019開催期間中に開催致します．開催日時と会場

JACM会 員の 皆 様に おか れて は APCOM2019な らびにの詳細については決まり次第，メールマガジンやメール配

JACM総会に奮ってご参加の程お願いいたします．

JACM 関連若手研究者の紹介（その 8）
JACM に関連する若手研究者の方々を順次紹介しています.
その第 8 回として，Tinh Quoc Bui 様（東京工業大学）と塚原 隆裕 様（東京理科大学）をご紹介いたします.

COMPUTATIONAL AND THEORETICAL
MODELING FOR FAILURE IN QUASIBRITTLE MATERIALS, COMPOSITES,
AND POROUS MEDIA
Tinh Quoc Bui（Tokyo Institute of Technology）
Thank you very much for being elected as The 2018 JACM
Award for Young Investigators in Computational Mechanics.
It was a great honor for me to be the recipient of this award.
Thank you to those who nominated me and supported mynomination. A very special thanks to the JACM for giving me achance to introduce my study in the JACM Mail Magazine No.
44. This is my great pleasure to share all of you some of typicalresults that have been conducted over the past ten years.
Our research group on Computational Mechanics at the
Department of Civil and Environmental Engineering,
School of Environment and Society, Tokyo Tech is devoted
to the study of a wide range of physical and mechanicalphenomena and engineering problems in solids, multiphasecomposites, and porous media. Much of the research works
conducted within our group is based on theoretical modelingand advanced computational methods development,
computational mechanics, taking into account the behaviorof solids and advanced complex and multi-phase materials
under the actions of various types of loading. The problems
considered within the group are often, in whole or in part,interdisciplinary in nature, reflecting a combination of
methodologies, concepts and principles usually spanningseveral areas of civil and mechanical engineering, materialsciences, physics, mathematics, and computer science. We
are particularly interested in modeling softening behavior,discontinuities, topological and geometrical changes,
delamination, moving boundaries, localized failure andinstabilities in different materials such as solids, smart
functional materials, laminated composites, and porous
materials, by developing theoretical damage models andefficient and accurate numerical techniques.
I started pursuing pure mathematics with emphasis on partial
differential equations for my undergraduate at the National
Vietnam University-HCMC in 1996, two years later of theuniversity I changed my study subject to computational solidmechanics instead. Neither pure math nor computational
mechanics, which one is better than the other, it actually changed
my professional career. I finally completed my bachelor with aresearch topic on development of a symbolic computer codeusing MAPLE programming language for finite element
analysis of carbon-fiber laminated composite plates. I thenpursued my higher educations in civil and mechanicalengineering in different countries in Europe. I performed mymaster thesis at the University of Liège, Belgium under theguidance of Dr. Marc Duflot (he is now at MSC Software
Corporation) about development of particle meshfree methods
for error estimations and duality analysis. Soon after, I joined towork on an active research team led by Profs. H.J. Böhm andF.G. Rammerstorfer at the Institute for Lightweight Design and
Structural Biomechanics, Vienna University of Technology,
Austria, and conducted my doctoral research work focusing on
development of some non-traditional computational approaches
into modeling failure behavior of spot-welds, an importantjoining technique that is currently used in fabricating virtually
all car bodies. The studies are based on the capabilities of finite
element analysis and mesh-independent modeling offastener/connector in the explicit FE code ABAQUS/Explicit,
high-performing computing, stochastic analysis, and softcomputing methods (e.g., artificial neural networks, machinelearning, data mining, and genetic algorithm) [1].
At the Center of Structures and Material Sciences,
Department of Mechanics and Materials Processing, Ecole
Nationale Superieure des Mines de Saint-Etienne, France, where
I worked as a postdoctoral researcher for an industrially funded
project, I developed computer codes and subroutines integrated
into in-house Zebulon finite element solvers for delamination(bonding/debonding) in carbon-fiber laminated Z-pin joints
under pull-out, shear, and flexure dynamic loading conditions.
This Z-pin joining techniques play a crucial role in manyengineering applications including aerospace and automobile.
Fig. 1 shows two types of Z-pin failure by experimental testing.

unsaturated flow problems in porous media using isogeometricanalysis with non-uniform rational B-splines basis functions [7].
Fig. 2 depicts the water content for irrigation by furrows inwhich the contour lines represent the wetting front dependent on
the situation of moisture content. At low moisture level wherewater fronts beyond 30 cm in depth, the IGA offers smooth andless oscillation in comparison with the conventional approaches(not shown here) [7].

Fig. 2 Water content for irrigation by furrows
computed by the isogeometric analysis [7].

In 2016, I started establishing my research group at Tokyo
Institute of Technology concentrating on Computational
Mechanics and Fracture Modeling with several
undergraduate and graduate students. The group size is now
getting larger and larger. Generally, the ultimate goals or themain objectives of our research group devote to fourfold: (a)to discover new physical phenomena relevant to scientificengineering problems; (b) to improve and enhance
technological developments in terms of numericalsimulation using modern techniques; (c) to solve engineering
problems of a broad range of industries; and (d) to provide
effective tools of numerical solutions to explore phenomena
and predict behavior that may be used to advance concepts
and design in practical applications.
Quasi-brittle failure concerns a large number of geomaterials
such as rock, concrete, or limestone, which are of great
importance in many engineering applications especially ininfrastructure systems. We have proposed a novel smoothing
gradient-enhanced damage model with evolving anisotropic
nonlocal interactions, which goes beyond certain limitations ofconventional approaches, for localized failure in quasi-brittle
materials [8]. This new approach owns many desirable features
as it can eliminate non-physical spurious damage growth;
control softening behavior through fracture energy andcharacteristic length, and model well compressive shear-bandproblems. Fig. 3 shows mode-I failure simulation of three-point
bending limestone beams, in which three sizes of beams havebeen conducted and computed force-displacement responses arecompared with experimental data. The damage evolution grows
from the notch at the middle of the beams. This new gradientenhanced damage model has been now extended to solve somemore complicated problems, for instance, one is to take into
account the dynamic rate-dependent effect and another is toanalyze failure response of porous media in geomechanics
applications. For rate-dependent gradient damage model, adynamic damage model should be developed. For transport anddamage in porous media, a nonlocal damage-poroelastic model
should be introduced, and a monolithic algorithm in terms of

Fig. 1 Z-pin interface failure on the web (left) andcrack between the web and flange (right).

At the Department of Civil Engineering, University ofSiegen, Germany, where I subsequently worked as postdoctoral
fellowship and senior researcher, my main research goal there
was to modeling of dynamic fracture mechanics in multiphasesmart functional materials (e.g., functional piezoelectric andmagnetoelectroelastic) under thermal environment byenrichment techniques (e.g., extended finite elements andisogeometric analysis). Smart functional materials offer many
opportunities for engineers and designers to develop novel
devices and intelligent structures, for instance, transducers,
smart sensors, actuators, lasers, supersonics, and microwaves.
The key features lie in the surprising coupling effects among
mechanical, electrical, and magnetic fields. Due to the brittle innature, their imperfection or defects are unavoidable. I
successfully conducted 04 research projects funded by DFG and
DAAD, and achieved results have been published in a numberof scientific journals, e.g., [2, 3] .
In 2014, I honorably received a JSPS postdoctoral
fellowship (standard program), and two years later I was again
awarded another JSPS postdoctoral fellowship for seniorscientist (pathway program), both hosted by Prof. Sohichi
Hirose. During that time at Tokyo Tech, I conducted several
problems, for instance, cohesive crack growth in terms of
XFEM for quasi-brittle concrete [4], fatigue crack growth undervariable-amplitude cyclic loading, adaptive local-meshrefinement XFEM for 2D and 3D cracks in solids and functional
materials, transient crack analysis of generalized stress intensity
factors for multiphase smart composites by extended
isogeometric analysis [5], hybrid phase field model for dynamic
crack growth in functionally graded materials [6], or modeling- 2 -finite element method which must be developed to solve
coupled systems with a displacement-pressure-regularized
permeability element formulation. Both these works have been
under developments.

with the band width increasing to the maximum value and thendecreases to the constant band width as the initial state. The
crack here does not show to be branching since the energy
dissipated at crack-tip is not strong enough, see zone C. At zone
D, the crack reaches the saturated velocity without theoscillation in the crack band width.
In the past decades, the failure in layered heterogeneouscomposites and structures has been studied by many researchers
due to their critical role in mechanics and physics of solids. We
introduced a new methodology for better describing interface
cracks in 2D and 3D by a regularized interfacial transition zone
in the context of variational phase field model [10]. One of themain purpose of this new model is to circumvent drawbacks ofsharp-transition models as the jumps at mismatch material andgeometry discontinuity effects can be treated in astraightforward manner. Fig. 5 depicts the crack growth in 3D
layered heterogeneous beam and shows a comparison of crackmorphologies between the computed phase field model andexperiment for a multi-layered structure.

Fig. 3 Three-point bending limestone beams andnumerical results [8].

Fig. 5 Crack growth in 3D layered structure (top)and comparison of crack morphologies between phasefield model and experiment for a multi-layered
structures (bottom [10].

We have conducted 3D micromechanical modelling of
progressive failure in fiber-reinforced composites by using thephase field model. One of the advantages of the phase fieldmodel in modeling localized failure problems is its capability tomodel crack behaviors without requiring any additional ad-hoc
fracture criteria or crack tracking strategy. Conventional
numerical approaches such as discrete approaches for modelinga complete progressive failure of fiber-reinforced composite arestill challenging, and most of numerical methods are designed
for single failure mechanism. Generally, composite laminates
can be studied at three length scales (i.e., macro-, meso- andmicro-scales). This study is particularly devoted to micro-scale
failure modeling. Fig. 6 shows the interface phase field of the
30o/90o plies specimens and crack phase field at the end of theloading stage (top) and a comparison of crack patterns (i.e.,interface debonding and matrix cracking) between the phasefield model and experiment (bottom).

Fig. 4 Correlation between phase field
distribution and dissipated energy [9].

In line of the continuum damage model, we have studied
alternative emerged fracture mechanics method, the phase fieldmodel, which goes beyond certain limitations of LEFM theory
of Griffith. For instance, we developed a rate-dependent hybrid
phase field model for dynamic crack propagation in functional
composites, exploring the dissipated energy dependent crack
velocity, one of the important aspects of dynamic fracture [9].
Fig. 4 sketches the correlation between dissipated energy, which
is normalized by fracture energy, and the phase field distribution
for a polymethylmethacrylate (PMMA) rectangular plate.
Basically, the evolution of crack can be interpreted through therepresentation of the normalized dissipated energy. As indicatedin the figure, the zone A indicates the initial crack, when loaded,
the cracks starts propagating at which the energy dissipatedrapidly as shown in zone B. In this zone, the crack smeared out- 3 -years. We now have in hand many of the ingredients forpursuing the mentioned research area. The well support from the
Department of Civil and Environmental Engineering, the Schoolof Environmental and Society, and Tokyo Tech, has greatly
helped us in conducting the study as they have very strong
research capabilities in the areas of concrete structures, steel
structures, geomechanics, geotechnical engineering, and soforth. However, we have learnt that there are many other
unsolved problems that still remain and challenge us, and what
difficult tasks cannot be analyzed with commercial software, thegroup for sure will continue to develop new and effective
numerical approaches and more appropriate theoretical models
that allow us to solve the problems in better way.
In future, apart from other favorite research areas such as
fracture in solids and functional composites [12-13] andcontinuum damage model [8, 14], we are particularly more
focusing on theoretical and computational modeling approaches
for, for instance, multiscale fracture in porous media, dynamic
response, mass transport, and coupled systems, which are
currently a prominent research topic. This certainly is afascinating research area where several grand challenges ofcomputational mechanics come together, e.g., multi-physics
problem, multi-scale phenomena, or the interaction between
mechanical phenomena and one or more diffusion problems.
In recent years, collaborations with the field of computational
mechanics have been active, and in this way, we are conducting
research on numerical simulation deeply and on a wide range ofcomputational approaches. Please contact us if you areinterested in conducting research for the degrees of mater, anddoctoral, or postdoc programs.
Once again, I would like to thank the JACM for giving me achance to share some of my research interests. Many thanks to
all my former Advisors and Professors, my past and current
Colleagues, Collaborators, Students, and to those who have been
continuously supporting me.
“The experience of living in a different country and learning
different approaches to scientific problems broadens your mind
for research”, said by Nick Luscombe, a computational biologist
who found that moving from the UK to the USA for a postdoc
was “an eye-opener”. This interesting story from Science
Magazine has impressed me a lot as it would be true that theexperience living in different countries raised our own
confidence, but also reinforced our appreciation of time to think
through scientific problems.

Fig. 6 Interface phase field crack of a 30/90 plies
specimen (top) and comparison of crack patterns
between numerical approach and experiments.

We recently computed the phase field model to capture andinvestigate complex fracture behavior in cement-basedmaterials at early-age [11]. We developed a model that consistsof coupling the most important chemo-thermo-mechanicalprocesses to describe temperature evolution, variation of
hydration degree, and mechanical behavior. In fact, early-age
shrinkage and hydration heat induced defects in concrete havebeen a major research area in the past few decades. Since thechange of mechanical properties of early-age concrete isrelatively fast, and is largely dependent on physical andmechanical processes (i.e., hydration), modeling of suchcomplex fracture in cement-based materials at early-age stage
by means of conventional numerical approaches is not a trivial
task. Fig. 7 represents the computed results of crack growth,temperature, and hydration evolution for conducting crack in the
L-shaped structure.

References[1] Bui QT. Studies on Modeling the Failure Behavior of Spot
Welds. Vienna University of Technology, Austria, PhD
dissertation, 9/2009.
[2] Bui QT, Zhang Ch. Analysis of generalized dynamic
intensity factors of cracked mangeoelectroelastic solids by XFEM. Finite Elements in Analysis and Design 2013; 69:19-36.
[3] Liu P, Yu TT, Bui QT, Zhang Ch, Xu Y, Lim CW. Transient
thermal shock fracture analysis of functionally gradedpiezoelectric materials by the extended finite element method.
International Journal of Solids and Structures 2014; 51:21672182.
[4] Zhang XD, Bui QT. A fictitious crack XFEM with two new
solution algorithms for cohesive crack growth modeling in
concrete structures. Engineering Computations 2015; 32:473497.
[5] Bui QT. Extended isogeometric dynamic and static fracture
analysis for cracks in piezoelectric materials using NURBS.
Computer Methods in Applied Mechanics and Engineering
2015; 295:470-509.

Fig. 7 The evolution of phase field, temperature,and hydration of a L-shaped structure at a certain
time step.

I have presented in this note some major numerical results thathave been conducted either individually or collaboratively.
Computational and theoretical modeling works for failure
problems in composites, solids, or porous media are one of the
fields where computer-based simulations have been constantly
used. It is because that numerical simulations required for basic
design is roughly put to practical use. The team at Tokyo Tech
has a vast expertise in the area of computational mechanics as it
has been advancing computational fracture mechanics for many
- 4 -

[6] Doan HD, Bui QT, Nguyen DD, Fushinobu K. Hybrid phasefield simulation of dynamic crack propagation in functionally
graded glass-filled epoxy. Composites Part B: Engineering
2016; 99:266-276.
[7] Nguyen NM, Bui QT, Yu TT, Hirose S. Isogeometric analysis
for unsaturated flow problems. Computers and Geotechnics,
2014; 62:257-267.
[8] Nguyen HAT, Bui QT, Hirose S. Smoothing gradient damage
model with evolving anisotropic nonlocal interactions tailoredto low-order finite elements. Computer Methods in Applied
Mechanics and Engineering 2018; 328:498-541.
[9] Doan HD, Bui QT, Do VT, Nguyen DD. A rate-dependent
hybrid phase field model for dynamic crack propagation.
Journal of Applied Physics 2017; 122:115102.
[10] Nguyen TT, Waldmann D, Bui QT. Role of interfacialtransition zone in phase field modeling of fracture in layered
heterogeneous structures. Journal of Computational Physics

2019; 386:585-610.
[11] Nguyen TT, Waldmann D, Bui QT. Computational chemothermo-mechanical coupling phase-field model for complex
fracture induced by early-age shrinkage and hydration heat in
cement-based materials. Computer Methods in Applied
Mechanics and Engineering 2019; 348:1-28.
[12] Bui QT, Nguyen TN, Le VL, Nguyen NM, Truong TT.
Analysis of transient dynamic fracture parameters of cracked
functionally graded composites by improved meshfree methods.
Theoretical and Applied Fracture Mechabucs 2018; 96:642-657.
[13] Huynh DH, Nguyen NM, Cusatis G, Tanaka S, Bui QT. A
polygonal XFEM with new numerical integration for linear
elastic fracture mechanics. Engineering Fracture Mechanics
2019; 213:241-263.
[14] Bui QT. A local damage isogeometric model for localized
failure of concrete. Computers and Structures 2019; (Submitted).

壁乱流亜臨界遷移の DNS 基礎研究減が図られています．例えば，走行する車の丸ごと計算には，RANS や LES（large eddy simulation）またはそれらのハイブリッドで行われます．これの DNS は現存の最速大型計算機を用いても困難であり，平行平板間流れや平板境界層などのカノニカルな壁乱流に DNS の適用範囲は限られています．しかし，DNS で得られた知見とデータベ
ースは，乱流ダイナミクス解明と乱流モデル改善に役立てられ，大変に貴重なものとなります．閑話休題．大型ベクトル計算機を利用し，当時の世界最大級 DNS を実施した結果，私は院生時に平面クエット乱流の大規模構造や，亜臨界遷移の層流－乱流パターン形成を発見しました．
これは，新計算手法の開発によるわけでなく，大規模並列計算を実施した結果であり，単に幸運に恵まれたのかもしれません．しかし，発見自体に気付けたことや，少し異常なパラメータ設定と知りながら“遊んで”みることが新発見に繋がり，日々乱流計算と向き合って成し得たこと
とも思います．肝要なのは探求心と好奇心…当然のことですが多忙な業務に惑わされ初心を忘れてしまわないよう，自戒の念を込めてのお話です．本メルマガ読者の先輩方には退屈な話でございました．
現在も継続して取り組む研究テーマの一つが，上述の「亜臨界遷移の層流－乱流パターン形成」です．一般的に，レイノルズ数（流速または寸法の指標）が大きくなると流れは秩序立った層流状態から，大小様々な渦を伴い非定
常性・三次元性を有する乱流状態になります．流路形状が同じでも層流と乱流では，摩擦・伝熱・拡散性・混合性が顕著に異なるため，しばしば産業の場面で状態予測・制御の必要性に迫られます．その際，層流⇔乱流の切替わり，
いわゆる臨界レイノルズ数の知識が重要ですが，この値は経験的にしか特定できず，大規模な実験や DNS に頼らざるを得ないことが大半です．カノニカル壁乱流の一つ，
直円管内流れの臨界レイノルズ数は 2000～2300 程度と知られていますが，より厳密な特定（2040 ± 10）に至ったのは最近のことです[1]．これには，壁乱流の亜臨界遷移（線形安定性理論による臨界値よりも低いレイノルズ数で，有限撹乱に起因する乱流遷移）で層流と乱流が空間的に共存し，局在乱流が準秩序的で大規模なパターンを形成するという研究報告が背景にあります．この層流－乱流パターンの捕捉が，臨界レイノルズ数の決定に重要なのです．図 1 は，圧力勾配駆動の平行平板間チャネル乱流の亜臨界遷移過程で（小職の DNS により初めて）捉えた，

塚原 隆裕（東京理科大学）卒業研究で初めて計算力学と CFD（数値流体力学）の世界に触れ，即座にその可能性と奥深さに惚れ込んでから早 17 年，主に DNS（直接数値計算）による乱流研究に携わって参りました．学生時も“携わった”と言うには少々おこがましく，実際には只々無我夢中でした．最早，“若手”というには（JSPS 科学研究費補助金・若手研究の応募枠に依れば）ぎりぎりの年齢となった私が，2018 年
7 月に The JACM Young Investigator Award という栄誉ある賞を賜り，“大人の階段を登った”一人前の研究者として一層精進して参ろうと心新たに思う次第です．ご推薦ご選考を頂いた諸先生方には改めてお礼を申し上げます．
望外にも，
JACM メールマガジンにて小職の研究紹介の場を頂きましたこと，重ねて感謝申し上げます．
現在は，東京理科大学理工学部機械工学科に所属しておりますが，出身も同学科であり卒業研究から博士課程まで河村洋教授（現・東京理科大学名誉教授）のもとでDNS による壁乱流の研究に取り組んでおりました．卒研
配属当時，“乱流”が研究テーマになるほどの深みがあるとは全く知らず，単にランダムノイズとしか認識しておりませんでした．学生時代は講談社ブルーバックス等の自然科学啓蒙書が好きで，当時から“決定論的カオス”や“非平衡現象”，そして“パーコレーション”など自然の無秩序の中にある秩序に言い知れぬ魅力を感じておりました．この無知で好奇心しかなかった私に，河村先生からは壁乱流に潜むカオスを卒論テーマとするご提案を頂きました．一年間熱中して挑んだものの敵は手強く，結局，研究結果がカオスになったことは良い思い出です．院生
時代はターゲットを変えて，壁乱流に潜む大規模な準秩序構造を DNS により調査しました．ここで，DNS の簡単な紹介を致しますと，乱流モデルを一切用いずに流れの支配方程式（Navier-Stokes 方程式）を直接に計算する方法
であり，内在する乱流構造の全容を捉える“大きな計算領域”と最小渦（コルモゴロフスケール渦）も解像する“小さな要素（または格子幅）”を要するため計算負荷が膨大となります．一般的に産業界で使われる CFD ソフトウェ
アでは乱流モデルを用いた RANS 解析を行い，コスト軽- 5 -層流－乱流パターンの 3 次元可視化図です，この縞状の局在乱流を乱流縞と名付けました[2-3]．

学界・社会に寄与できるよう益々精進する所存です．

図２ ２次元スリット・オリフィスを過ぎるチャネル乱流のDNS．オリフィス直後の渦を可視化．（左）ニュートン流体，（右）同レイノルズ数の粘弾性流体では，渦が抑制される．

図１ チャネル乱流に現れる乱流縞．δはチャネル半幅．

流路形態に依存する層流―乱流パターン形成について，
統一的理解を目指した研究も進めてきました．環状ポア
ズイユ流の DNS により円管内流（のパフ）と平行平板間流（の乱流縞）の接続を試み[4-5]，環状クエット流の解析
では有向パーコレーションの特徴を持つ非定常で確率的な局在乱流現象を見出すことに成功しました[6]．乱流縞のロバスト性に関する解析も行い，粗面上では主流に垂直な乱流帯が形成されることを発見しました[7-8]．現在
は，乱流摩擦抵抗低減効果をもたらす粘弾性流体を対象に，乱流縞のロバスト性や特異な遷移過程（弾性乱流）に関心を持っており，その調査に向けて JSPS 特別研究員 PD
河田卓也博士と同 DC1 仁村友洋君に協力を得ながら DNS
基礎研究を進めております[9-10]．
上記テーマの他に，研究室では 4 つのメインテーマが走っています．1) 粘弾性流体乱流の DNS（図 2）と乱流モデル構築，2) 冠動脈ステントによる血流影響評価，3)
界面張力駆動の液滴・気泡操作の CFD，4) 乱流ビッグデータの機械学習，の 4 つでいずれも CFD シミュレーショ
ンが絡みます．将来，これらの成果も是非ご紹介したいものですが，再びこの度のような機会を頂くよう精一杯，研究に励んで参ります．変わらぬご指導ご鞭撻のほど，宜しくお願い申し上げます．

末筆ながら，河村洋先生の他，川口靖夫教授（東京理科大学），河原源太教授（大阪大学）をはじめ多くの先生方に乱流遷移研究の遂行において常に温かい励ましを頂きましたこと，深くお礼を申し上げます．環状流の DNS は
石田貴大博士（現・JAXA）が主体的に行い，その他の研究においても指導した卒研生・院生の貢献が無ければ実現しないものばかりでした．これからも乱流は勿論，計算
力学・CFD の魅力と技術を後世に伝えつつ，わずかでも参考文献[1] K. Avila, D. Moxey, A. de Lozar, M. Avila, D. Barkley, andB. Hof, “The onset of turbulence in pipe flow,” Science,
333 (6039), 192–196, 2011.
[2] T. Tsukahara, Y. Seki, H. Kawamura, and D. Tochio, “DNSof turbulent channel flow at very low Reynolds numbers.”
In: Proc. TSFP4, TSFP Digital Library Online, pp. 935–
940. 2005; arXiv preprint, arXiv:1406.0248.
[3] T. Tsukahara, Y. Kawaguchi, H. Kawamura, N. Tillmark,and P.H. Alfredsson, “Turbulence stripe in transitional
channel flow with/without system rotation,” In: Proc. 7th
IUTAM Symp. on Laminar-Turbulent Transition, IUTAM
Bookseries, 18, pp. 421–426, 2010.
[4] T. Ishida, Y. Duguet, and T. Tsukahara, “Transitional
structures in annular Poiseuille flow depending on radiusratio,” J. Fluid Mech., 794, R2, 2016.
[5] T. Ishida, Y. Duguet, and T. Tsukahara, “Turbulent
bifurcations in intermittent shear flows: from puffs to
oblique stripes,” Phys. Rev. Fluids, 2, 073902, 2017.
[6] K. Kunii, T. Ishida, Y. Duguet, and T. Tsukahara,“Laminar-turbulent coexistence in annular Couette flow,”
arXiv preprint, arXiv:1904.09160, 2019.
[7] T. Ishida, G. Brethouwer, Y. Duguet, and T. Tsukahara,“Laminar-turbulent patterns with rough walls,” Phy. Rev.
Fluids, 2, 073901, 2017.
[8] T. Tsukahara, T. Tomioka, T. Ishida, Y. Duguet, and G.
Brethouwer, “Transverse turbulent bands in rough plane
Couette flow,” J. Fluid Sci. & Tech., 13 (3), 0019, 2018.
[9] T. Nimura, T. Kawata, and T. Tsukahara, “Viscoelasticityinduced pulsatile motion of 2D roll cell in laminar wallbounded shear flow,” Int. J. Heat & Fluid Flow, 74, 65–75,
2018.
[10] T. Nimura, T. Kawata, and T. Tsukahara, “Viscoelastic
effect on steady wavy roll cells in wall-bounded shear flow,”
Fluid Dyn. Res., 50 (5), 051414, 2018.

編集責任者
萩原 世也（佐賀大学）