ISSN 1880-2818

数理解析研究所講究録2109

RIMS共同研究 (公開型)

Workshop on Nonlinear Water Waves

京都大学数理解析研究所
2019年4月

数理解析研究所講究録は，京都大学数理解析研究所の共同利用研究集会および共同
数理解析研究所講究録は,京都大学数理解析研究所の共同利用研究集会および 共同研究の記録として1964年に刊行が開始されました．当研究所が全国共同利用研究所研究の記録として1964年に刊行が開始されました。当研究所が全国共同利用研究所として発足した翌年のことでしたが，以来半世紀，毎年数十巻を刊行し，2016年にとして発足した翌年のことでしたが,以来半世紀, 毎年数十巻を刊行し,2016年には第2000巻が刊行されるに至りました．第1巻から第2000巻までに収録された論文は第2000巻が刊行されるに至りました.第1巻から第2000巻までに収録された論文数は29,265編，総頁数は342,960頁という膨大なものであり，最先端の数学・数理科数は29,265編,総頁数は342,960頁という膨大なものであり,最先端の数学·数理科学分野の研究状況を伝えるのみならず，我が国の数学・数理科学の発展の歴史を留学分野の研究状況を伝えるのみならず,我が国の数学,数理科学の発展の歴史を留める文献として，他に類例を見ない論文集となっています．
める文献として,他に類例を見ない論文集となっています。
講究録の内容は当研究所のウェブサイトおよび京都大学の学術情報リポジトリにお講究録の内容は当研究所のウェブサイトおよび京都大学の学術情報リポジトリにおいても公開され，年間の総アクセス数は1,380,032回（2017年度）を数えるなど，多いても公開され,年間の総アクセス数は1.380,032回(2017年度) を数えるなど、 多数の方にご利用いただいています．
数の方にご利用いただいています。

講究録の使用言語は論文著者の判断に任されていますが，結果的に日本語が多用さ講究録の使用言語は論文著者の判断に任されていますが,結果的に日本語が多用されていることが特徴の一つとなっています．その結果，講究録は，数学・数理科学れていることが特徴の一つとなっています。その結果,講究録は,数学·数理科学の広い領域における最先端の専門知識に母国語でアクセスできるものとして，近年近年の広い領域における最先端の専門知識に母国語でアクセスできるものとして,の英語化の流れの中で，重要な文献となりつつあります．の英語化の流れの中で,重要な文文献となりつつあります。
当研究所の共同利用事業に参加し講究録の論文を執筆していただいた多数の方々に当研究所の共同利用事業に参加し講究録の論文を執筆していただいた多数の方々に対し，講究録を大きく成長させていただいたことを深く感謝いたしますとともに，対し,講究録を大きく成長させていただいたことを深く感謝いたしますとともに,これからも, 当研究所の国際共同利用·共同研究拠点(*)としての活動にご参加いた
これからも，当研究所の国際共同利用・共同研究拠点(*)としての活動にご参加いただき，講究録の発展にご協力いただけますよう心よりお願い申し上げます．
だき,講究録の発展にご協力いただけますよう心よりお願い申し上げます。
*数理解析研究所は2018年11月13日，共同利用・共同研究拠点の認定が廃止され，*数理解析研究所は2018年11月13日, 共同利用·共同研究拠点の認定が廃止され,新しく国際共同利用・共同研究拠点に認定されました．
新しく国際共同利用·共同研究拠点に認定されました。

㻌

RIMS Kôkyûroku 2109

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WorkshopWorkshop on Nonlinear Water
Water Waves
Waves

㹼 25, 2018
May 2323~25,
editededited byby Sunao
Sunao Murashige
Murashige
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April, 2019April,2019Research Institute for Mathematical Sciences

Kyoto
JapanKyoto University,University, Kyoto,Kyoto, Japan

7KLVLVDUHSRUWRIUHVHDUFKGRQHDWWKH5HVHDUFK,QVWLWXWHIRU0DWKHPDWLFDOThis is a report of research done at the Research Institute for Mathematical 6FLHQFHVSciences,DQ,QWHUQDWLRQDO-RLQW8VDJH5HVHDUFK&HQWHUORFDWHGLQ.\RWR8QLYHUVLW\an International Joint Usage/Research Center located in Kyoto University.
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The papers contained herein are in final form and will not be submitted for publication elsewhere.

ㅮ✲㘓Kôkyûroku
RIMS Kôkyûroku was started in 1964 as the proceedings of symposia, colloquia and workshops
supported by RIMS, the Research Institute for Mathematical Sciences, Kyoto University. It was
the next year of the establishment of RIMS as one of the Nationwide Cooperative Research Centers.
For half a century since then, several dozen volumes have been issued each year, and the 2,000th
volume was issued in 2016. The volumes of Kôkyûroku from the 1st through the 2,000th,
containing enormous 29,265 articles and 342,960 pages, not only deliver the latest research
activities in mathematics and mathematical sciences but also constitute valuable andincomparable collections of articles that pass down history of progress of mathematics andmathematical science in Japan.
Articles in Kôkyûroku are available on the websites of RIMS and Kyoto University ResearchInformation Repository. They are very frequently accessed on the internet, with a total of as manyas 1,380,032 accesses in 2017.
The authors choose the languages to write articles, and many are written in Japanese, which isone of the characteristics of Kôkyûroku. As a result, Kôkyûroku is regarded as a significant andimportant literature which allows easy access to the latest specialized knowledge in the large fields
of mathematics and mathematical sciences written in native language for Japanese readers, whilemore and more research papers are being written in English in recent years.
We are deeply grateful to many of those who have participated in cooperative research activities
of RIMS and greatly developed Kôkyûroku. We heartily ask for your continuous participation inresearch activities at RIMS as an International Joint Usage/Research Center(*) and your warm
support and cooperation for the fruitful development of Kôkyûroku.
* RIMS was certified as an International Joint Usage/Research Center on Nov. 13, 2018.

PREFACE
COThis volume is a compilationof papers based on the talks given at the "Workshop on

Nonlinear Water Waves in honor of Professor Mitsuhiro Tanaka on the occasion of his retire-ment" held at the Research Institute for Mathematical Sciences, Kyoto University, Japan,May 23-25, 2018. Professor Tanaka has conducted pioneering studies in the field of fluid
mechanics, particularly nonlinear water waves, for many years and retired from Gifu University in March, 2019. For celebrating his outstanding achievements, many distinguishedscientists and engineers from the various countries participated in this workshop and enjoyed valuable and stimulating discussion. This special issue commemorates the wonderfulscientific interaction arranged on the occasion of honoring Professor Tanaka.

ACKNOWLEDGMENTS

This workshop was supported by the Research Institute for Mathematical Sciences, anInternational Joint Usage/Research Center located in Kyoto University and JSPS KAKENHIGrant No JP17H02856.

Finally, I would like to express my appreciation to all the participants in this workshop.

Iwould also like to thank Prof. Michio Yamada of Kyoto University and my co-organizersof this workshop for their continuous support.

Sunao Murashige
April 17, 2019

RIMS

Workshop on Nonlinear Water Waves
In honor of Professor Mitsuhiro Tanaka
onthe occasion of his retirement:May 23 (Wed) ~ 25 (Fri), 2018

DatePlace

http://murasige.sci.ibaraki.ac.jp/WS_Nonlinear_Water_Waves RIMS2018.html

URLOrganizers

Research Institute for Mathematical Sciences, Kyoto University
Room 111 of RIMS in North Campus::Takanori Hino (Yokohama National Univ.), Tatsuo Iguchi (Keio Univ.),
Taro Kakinuma (Kagoshima Univ.), Takeshi Kataoka (Kobe Univ.),
Ken-ichi Maruno (Waseda Univ.), Tetsu Mizumachi (Hiroshima Univ.),

Sunao Murashige (Ibaraki Univ.), Yasuhiro Ohta (Kobe Univ.)

Program
May 23 (Wed)13:00-13:10

13:10-13:40
13:40-14:10

Opening

Sunao Murashige (Ibaraki University)

Large-amplitude solitary waves on a linear shear current

Yoshihiro Niwa (University of Tokyo)
Estimation of baroclinic tide energy available for deep

ocean mixing based on three-dimensional global numerical simulations

Coffee break
14:30-15:20

Nail Akhmediev (Australian National University)
Classifying the rogue wave solutions of the nonlinear
Schrödinger equation

Coffee break
15:30-16:20

Wooyoung Choi (New Jersey Institute of Technology)
Onspectral formulation for nonlinear water waves andtheir applications

May 24 (Thu)
9:20-9:50

Taro Kakinuma (Kagoshima University)
Anumerical calculation for internal waves over a slope oramound

9:50-10:20

Takeshi Kataoka (Kobe University)

Transverse instability of surface solitary waves and break-ing

Coffee break
10:30-11:20

Triantaphyllos Akylas (Massachusetts Institute of Technology)
Parametric subharmonic instability of internal waves: locally confined beams versus monochromatic wavetrains

Coffee break
11:30-12:20

Roberto Camassa (University of North Carolina)
Hydrodynamic models and boundary confinement effects
Lunch

14:00-14:30

Takuji Waseda, Wataru Fujimoto and Yuki Kita (University ofTokyo)
Modulational instability in realistic directional seas

14:30-15:00

Naoto Yokoyama (Doshisha University / Kansai University) andMasanori Takaoka (Doshisha University)

Energy budget in stratified turbulence

Coffee break

15:10-16:00

Victor Shrira (Keele University)

Evolution of wind wave angular spectra: kinetic equations
vsdirect numerical simulations and observations

Coffee break
16:10-17:00

Mitsuhiro Tanaka (Gifu University)
Wave turbulence in a two-layer fluid system
Banquet (invitation only)May 25 (Fri)
9:20-9:50

Ken-ichi Maruno (Waseda University)
The interactions of dark line solitons in the DaveyStewartson II system

9:50-10:20

Yasuhiro Ohta (Kobe University)
Time-localized solutions for some soliton equations

Coffee break
10:30-11:20

Yuji Kodama (Ohio State University)
Mach Reflection of a Solitary Wave: RevisitedPart I: Theory

Coffee break

11:30-12:20 Harry Yeh (Oregon State University)

Mach Reflection of a Solitary Wave: RevisitedPart II: Experiments

Group PhotoLunch

14:30-15:20

David Lannes (The Université de Bordeaux)
The Boussinesq equations with a floating obstacle

Coffee break
15:30-16:00

Yoshimasa Matsuno (Yamaguchi University)
The N-soliton formulas for a multi-component modified
nonlinear Schrödinger system with nonzero boundary conditions

16:00-16:30

Tetsu Mizumachi (Hiroshima University)
Onthe phase shift of line solitary waves for the KP-IIequation

16:30-17:00

Tatsuo Iguchi (Keio University)
Kakinuma model for internal gravity waves in the rigid-lidcase

This workshop is supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (B)Grant Number JP17H02856.

科研費

KA KENHI

Workshop on Nonlinear Water Waves

RIMS 共同研究(公開型)報告集
2018年5月23日~ 5月25日

研究代表者 村重 淳(SunaoMurashige)
目次
1.

Wave turbulence in a two-layer fluid systemH#2.

岐阜大学(Gifu U.)%☆ (Mitsuhiro Tanaka)

Large-amplitude solitary waves on a linear shear current

Numerical simulations of baroclinic tide fields in the global ocean:
Estimation of baroclinic tide energy available for deep ocean mixing

丹羽
4.

Generalized integrable evolution equations with an infinite
Nail Akhmediev

33
Australian Nat. U.

Adrian Ankiewicz

Australian Nat. U.

Shalva Amiranashvili
Uwe Bandelow

WIAS

WIAS

Fifth-order nonlinear spectral model for surface gravity waves:
From pseudo-spectral to spectral formulations

Wooyoung Choi
6.

Anumerical calculation for internal waves over a slope or a mound8.

A (Takeshi Kataoka)

61

鹿児島大学(Kagoshima U.)

Transverse instability of surface solitary waves and breaking

HA47


New Jersey Inst. Tech.

柿沼 太郎(Taro Kakinuma)
7.

21


東京大学(U. Tokyo)

淑博(Yoshihiro Niwa)

number of free parameters

5.


9.

茨城大学(Ibaraki U.)

村重 淳(Sunao Murashige)
3.

1

70


神戸大学(Kobe U.)

Parametric subharmonic instability of internal waves:
Locally confined beams vs. monochromatic wavetrains

Triantaphyllos R. Akylas

MITi779.

Global gradient catastrophe and its unfolding in solutions of the Airy's79
model of shallow water waves

U.North Carolina

Roberto Camassa10.

Modulational instability in realistic directional seasRLO85


東京大学(U.Tokyo)

4 (Takuji Waseda)i (Wataru Fujimoto)

MS&AD インターリスク総研株式会社(MS&AD InterRisk Res. Consul. Inc.)

北 祐樹(Yuki Kita)
11.

東京大学(U.Tokyo)

横山 直人 (Naoto Yokoyama)
AM
12.

13.

E (Masanori Takaoka)

S.Y. Annenkov

Keele U.

Victor I. Shrira

Keele U.

The interactions of dark line solitons in the Davey-Stewartson II system- (Ken-ichi Maruno)

永原

早稲田大学(Waseda U.)

新(Arata Nagahara)

早稲田大学(Waseda U.)

Time-localized solutions for some soliton equations*#(Yasuhiro Ohta)

135


Oregon State U.

Several models for wave-structure interactions
David Lannes

128


Oregon State U.

Jeffrey Knowles
16.

115



神戸大学(Kobe U)

Mach reflection of a solitary wave: seeking the four-fold amplification

Harry Yeh

100


早稲田大学(Waseda U.)(DaichiSuyama)t

15.

F*E (Doshisha U.)/EX (Kansai U.)
同志社大学(Doshisha U.)

Modelling evolution of directional spectra of water waves

Ay

14.

97


Energy budget in stratified turbulence

U.Bordeauxii

14417.

The N-soliton formulas for a multi-component modified nonlinear

Schrödinger system with nonzero boundary conditions
松野18.

HAX☆ (Yamaguchi U.)

Onthe phase shift of line solitary waves for the KP-II equation
K#f

19.

好雅(Yoshimasa Matsuno)(Tetsu Mizumachi)

達雄(Tatsuo Iguchi)

171


広島大学(Hiroshima U.)

Kakinuma model for internal gravity waves in the rigid-lid case
井口156


慶應義塾大学(Keio U.)

ii177