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Mathematical models of fully nonlinear and unsteady phenomena of ocean waves and their verification

Research Project

Project/Area Number 23K22407
Project/Area Number (Other) 22H01136 (2022-2023)
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeMulti-year Fund (2024)
Single-year Grants (2022-2023)
Section一般
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionIbaraki University

Principal Investigator

村重 淳  茨城大学, 基礎自然科学野, 教授 (40302749)

Co-Investigator(Kenkyū-buntansha) 片岡 武  神戸大学, 工学研究科, 准教授 (20273758)
宝谷 英貴  東京大学, 大学院工学系研究科(工学部), 助教 (30636808)
柿沼 太郎  鹿児島大学, 理工学域工学系, 准教授 (70371755)
丸野 健一  早稲田大学, 理工学術院, 教授 (80380674)
Project Period (FY) 2022-04-01 – 2027-03-31
Project Status Granted (Fiscal Year 2024)
Budget Amount *help
¥14,300,000 (Direct Cost: ¥11,000,000、Indirect Cost: ¥3,300,000)
Fiscal Year 2026: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2025: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2024: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2023: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Keywords非線形波動 / 海洋波 / 数理モデル / 数値計算 / 流体力学 / 応用数学 / 数値解析
Outline of Research at the Start

実際の海洋で発生するローグ波(外洋で突発的に現れる巨大な波)や内部波(密度成層により海洋の内部で発生する波)は,大型船や海洋構造物を破壊するほど大きなエネルギーを持つことが知られている.このようなダイナミックな海洋波の運動は,波面が時間とともに大きく変化する強非線形・非定常現象であるため,未だ解析方法が確立されていない.本研究では,海洋波の運動の本質を捉えた数理モデルの導出と解析を行い,実際の海洋で観察される非線形現象のメカニズムの解明を目標とする.

Outline of Annual Research Achievements

本研究の目的は,振幅の大きいダイナミックな海洋波の非線形・非定常運動の解析に適した数理モデルの導出とその妥当性の検証である.令和5年度(2年目)は,以下の三つのテーマについて研究を実施した.研究成果は,発表論文8件(査読有6件,国際共著2件),学会発表25件(招待講演1件,国際講演14件)で公表されている.
1. 数理モデル:(1) 流体の密度差によって生じる重力流の数理モデルを導出した(村重).(2) 船舶の背後や地形を過ぎる流れにより励起される航跡波で観察される強い非線形現象を記述するための数学理論(指数漸近解析)を構築した(片岡).(3)解構造を保存する非線形波動方程式の離散化を提案した(丸野).
2. 数値計算:(1)重力流の複素解析に基づいた計算方法を提案した(村重).(2)航跡波の強い非線形現象を数値計算で示した(片岡).(3)波面のデータから内部流場を計算する方法を提案した(宝谷).(4)航空機が大型浮体空港上を移動する際に生成される浮体波を数値計算で調べた(柿沼).(5)弾性浮体と潜提を組み合わせた構造物の津波高さ低減効果について数値計算で調べた(柿沼).(6)多成分非線形波動方程式の自己適合移動格子スキームを提案した(丸野).
3. 実験:(1)航跡波の強い非線形現象を水槽実験で観察した(片岡).(2)水槽実験でステレオカメラにより波浪場を面的に計測する手法を開発した(宝谷).
また,国際研究集会 Workshop on Nonlinear Water Waves and Related Topics を令和5年11月6日から10日に湘南国際村センター(神奈川県葉山町)で開催した.26名(海外:16名)の非線形水波に関する専門家が参加し,最近の研究成果を発表した.発表の一部は,学術誌 Water Waves の特集号の論文として公表される予定である.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

令和5年度(2年目)は,実施計画にしたがい,以下のように研究を進めた.
1. 数理モデル:研究対象とする非線形性の強い海洋波(重力流(密度差により生じる波),航跡波(船の背後に形成される波),ローグ波,津波など)に対する数理モデルの導出と,それらに対する理論的考察を行った.
2. 数値計算:上記の問題に対する数値計算法を開発し,その有効性を数値実験で示した.
3. 実験:非線形性の強い水波の運動を水槽実験で精度よく計測する方法を開発した.
さらに,研究成果を公表して専門家と意見交換を行うために,秋(11月6日から10日)に湘南国際村センター(神奈川県葉山町)で国際研究集会を開催した.本研究集会では活発で有意義な議論が行われ,発表の一部は専門誌 Water Waves で公表される予定である.また,片岡氏の論文がトップジャーナル Physica D に掲載されたことは,特筆に値する.以上より,「おおむね順調に進展している」と判断した.

Strategy for Future Research Activity

本研究の最終的な目標は,振幅の大きいダイナミックな海洋波の非線形・非定常運動の解析に適した数理モデルの導出とその妥当性の理論・実験・数値計算による検証である.今後は,実施計画にしたがいさらに研究を進める.具体的な推進方法を,以下にまとめる.
1. 数理モデル:2年目(令和5年度)までの研究で導出した非線形性の強い海洋波(重力流(密度差により生じる波),航跡波(船の背後に形成される波),ローグ波,津波など)に対する数理モデルの妥当性の検証を,理論的・数値的・実験的に行う.
2. 数値計算:上記の数理モデルの検証のための数値計算を実行する.また,検証に必要となる計算結果の誤差評価法を開発する.
3. 実験:上記の数理モデルの計算結果と比較可能な実験データ,特に精度のよい定量的なデータを得る.
4. 実施計画では4年目(令和7年度)に開催が予定されている国際研究集会(7月 at 神戸を予定)の準備を行う.

Report

(2 results)
  • 2023 Annual Research Report
  • 2022 Annual Research Report
  • Research Products

    (60 results)

All 2024 2023 2022 Other

All Int'l Joint Research (3 results) Journal Article (12 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 11 results,  Open Access: 4 results) Presentation (40 results) (of which Int'l Joint Research: 21 results,  Invited: 4 results) Book (1 results) Remarks (2 results) Funded Workshop (2 results)

  • [Int'l Joint Research] Massachusetts Institute of Technology/New Jersey Institute of Technology/University of North Carolina(米国)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] Massachusetts Institute of Technology/New Jersey Institute of Technology/The University of North Carolina(米国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] Lishui University(中国)

    • Related Report
      2022 Annual Research Report
  • [Journal Article] Steady Radiating Gravity waves: An Exponential Asymptotics Approach2024

    • Author(s)
      Kataoka Takeshi、Akylas T. R.
    • Journal Title

      Water Waves

      Volume: 6 Issue: 1 Pages: 79-96

    • DOI

      10.1007/s42286-023-00081-z

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A delay analogue of the box and ball system arising from the ultra-discretization of the delay discrete Lotka?Volterra equation2024

    • Author(s)
      Nakata Kenta、Negishi Kanta、Matsuoka Hiroshi、Maruno Ken-ichi
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 57 Issue: 14 Pages: 145701-145701

    • DOI

      10.1088/1751-8121/ad3201

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonlinear Kelvin wakes and exponential asymptotics2023

    • Author(s)
      T. Kataoka, T. R. Akylas
    • Journal Title

      Physica D

      Volume: 454 Pages: 133848-133848

    • DOI

      10.1016/j.physd.2023.133848

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Combination of HOSM and FORM for extreme wave-induced response prediction of a ship in nonlinear waves2023

    • Author(s)
      Takami Tomoki、Fujimoto Wataru、Houtani Hidetaka、Matsui Sadaoki
    • Journal Title

      Ocean Engineering

      Volume: 286 Pages: 115643-115643

    • DOI

      10.1016/j.oceaneng.2023.115643

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stereo Reconstruction Method for 3D Surface Wave Fields around a Floating Body Using a Marker Net in a Wave Tank2023

    • Author(s)
      Higuchi Yuya、Houtani Hidetaka、Goncalves Rodolfo T.、Yoshimura Yasuo、Hirabayashi Shinichiro、Suzuki Hideyuki、Orihara Hideo
    • Journal Title

      Journal of Marine Science and Engineering

      Volume: 11 Issue: 9 Pages: 1683-1683

    • DOI

      10.3390/jmse11091683

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A Numerical Study on the Response of a Very Large Floating Airport to Airplane Movement2023

    • Author(s)
      Kakinuma Taro、Hisada Masaki
    • Journal Title

      Eng

      Volume: 4 Issue: 2 Pages: 1236-1264

    • DOI

      10.3390/eng4020073

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] 弾性浮体と潜堤を併用した津波高さの低減2023

    • Author(s)
      柿沼太郎
    • Journal Title

      津波工学研究報告

      Volume: 40 Pages: 153-158

    • Related Report
      2023 Annual Research Report
    • Open Access
  • [Journal Article] Integrable discretizations of the SIR model2023

    • Author(s)
      Y. Tanaka, K. Maruno
    • Journal Title

      RIMS Bessatsu

      Volume: 94 Pages: 85-115

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The coupled modified Yajima-Oikawa system: Model derivation and soliton solutions2023

    • Author(s)
      Chen Junchao、Feng Bao-Feng、Maruno Ken-ichi
    • Journal Title

      Physica D: Nonlinear Phenomena

      Volume: 448 Pages: 133695-133695

    • DOI

      10.1016/j.physd.2023.133695

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Nonlinear effects in steady radiating waves: An exponential asymptotics approach2022

    • Author(s)
      Kataoka Takeshi、Akylas T.R.
    • Journal Title

      Physica D: Nonlinear Phenomena

      Volume: 435 Pages: 133272-133272

    • DOI

      10.1016/j.physd.2022.133272

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Phase Convergence and Crest Enhancement of Modulated Wave Trains2022

    • Author(s)
      Houtani, H.; Sawada, H.; Waseda, T.
    • Journal Title

      Fluids

      Volume: 7(8) Issue: 8 Pages: 275-275

    • DOI

      10.3390/fluids7080275

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Soliton resonance and web structure in the Davey-Stewartson system2022

    • Author(s)
      Biondini Gino、Kireyev Dmitri、Maruno Ken-ichi
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 55 Issue: 30 Pages: 305701-305701

    • DOI

      10.1088/1751-8121/ac78db

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] 一定速度で動く物体により励起される水面波に関する室内実験2024

    • Author(s)
      磯﨑涼,中井正悟,筒井大生, 宮本健太郎, 片岡武
    • Organizer
      日本機械学会関西支部 第99期定時総会・講演会
    • Related Report
      2023 Annual Research Report
  • [Presentation] 2D Ship Waves and Exponential Asymptotics2023

    • Author(s)
      T.Kataoka, T.R.Akylas
    • Organizer
      OIST TSVP Symposium: Frontiers in Nonlinear Differential Equations and Stokes Phenomena Okinawa
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Ship waveの非線形解II(2次元モデル方程式を基とした理論)2023

    • Author(s)
      片岡武,T.R.Akylas
    • Organizer
      日本流体力学会年会2023
    • Related Report
      2023 Annual Research Report
  • [Presentation] 偏微分方程式に対する指数漸近解析2023

    • Author(s)
      片岡武,T.R.Akylas
    • Organizer
      京都大学数理解析研究所研究集会”非線形波動現象の数理とその応用”
    • Related Report
      2023 Annual Research Report
  • [Presentation] Exponential asymptotics and related wave phenomena2023

    • Author(s)
      T.Kataoka, T.R.Akylas
    • Organizer
      Workshop on Nonlinear Water Waves and Related Topics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 船波の数理モデルと指数漸近解析2023

    • Author(s)
      片岡武,T.R.Akylas
    • Organizer
      第37回数値流体力学シンポジウム
    • Related Report
      2023 Annual Research Report
  • [Presentation] Pressure field evaluation beneath nonlinear waves using the higher-order spectral method and its application to ship response simulations2023

    • Author(s)
      Houtani, H.
    • Organizer
      Workshop on Nonlinear Water Waves and Related Topics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical investigation of the statistics of vertical bending moments of ships in nonlinearly evolving irregular waves2023

    • Author(s)
      Houtani, H., Fujimoto, W. & Matsui, S.
    • Organizer
      In ASME 2023 42nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers Digital Collection, 2023.
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Extreme Wave and Vertical Bending Moment Predictions by Higher Order Spectrum Method and FORM2023

    • Author(s)
      Takami, T., Fujimoto, W., Houtani, H. & Matsui, S.
    • Organizer
      In ASME 2023 42nd International Conference on Ocean, Offshore and Arctic Engineering, American Society of Mechanical Engineers Digital Collection, 2023.
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] マーカーネットを用いた浮体周辺波浪場の面的計測2023

    • Author(s)
      樋口湧也,宝谷英貴,Rodolfo T Goncalves,芳村康男,平林紳一郎,鈴木英之,折原秀夫
    • Organizer
      日本船舶海洋工学会講演会
    • Related Report
      2023 Annual Research Report
  • [Presentation] Extreme Wave and Wave-induced Vertical Bending Moment Predictions in Higher Order Spectrum Waves using FORM2023

    • Author(s)
      Takami, T., Fujimoto, W., Houtani, H. Matsui, S.
    • Organizer
      日本船舶海洋工学会講演会
    • Related Report
      2023 Annual Research Report
  • [Presentation] 弾性浮体と潜堤を併用した津波高さの低減2023

    • Author(s)
      柿沼太郎
    • Organizer
      第13回巨大津波災害に関する合同研究集会
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Tsunamis generated and amplified by atmospheric pressure waves over seabed topography2023

    • Author(s)
      Kakinuma, T.
    • Organizer
      11th International Conference onAsian and Pacific Coasts (APAC 2023)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 航空機の離着陸によって大型浮体空港に生成される浮体波の数値解析2023

    • Author(s)
      柿沼太郎,久田方輝
    • Organizer
      第70回海岸工学講演会
    • Related Report
      2023 Annual Research Report
  • [Presentation] A numerical study on water waves generated and amplified by air pressure waves2023

    • Author(s)
      Kakinuma, T.
    • Organizer
      Workshop on Nonlinear Water Waves and Related Topics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 地形上で複数の気圧波によって生成される津波2023

    • Author(s)
      柿沼太郎
    • Organizer
      京都大学数理解析研究所 RIMS 共同研究(公開型)「非線形波動現象の数理とその応用」
    • Related Report
      2023 Annual Research Report
  • [Presentation] 気圧波によって生成される表面波及び内部波の数値解析2023

    • Author(s)
      柿沼太郎
    • Organizer
      土木学会第78回年次学術講演会
    • Related Report
      2023 Annual Research Report
  • [Presentation] 航空機の離着陸に対する大型浮体空港の応答の数値解析2023

    • Author(s)
      久田方輝, 柿沼太郎
    • Organizer
      土木学会第78回年次学術講演会
    • Related Report
      2023 Annual Research Report
  • [Presentation] Generation and amplification of tsunamis due to air pressure waves over topography2023

    • Author(s)
      Kakinuma, T.
    • Organizer
      4th Edition of World Congress on Geology and Earth Science
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Tsunami generation and amplification by multiple air pressure waves over seabed topography2023

    • Author(s)
      Kakinuma, T.
    • Organizer
      Global Scientific Congress on Geology and Earth Science
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Integrable fully discretizations of multi-component short pulse type equations2023

    • Author(s)
      Maruno, K.
    • Organizer
      ISLAND6: Dualities and Symmetries in Integrable Systems
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Soliton interactions of two-dimensional soliton equations2023

    • Author(s)
      Maruno, K.
    • Organizer
      Workshop “Extreme Waves”
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Self-adaptive moving mesh schemes for nonlinear waves and numerical computations2023

    • Author(s)
      Maruno, K.
    • Organizer
      Workshop on nonlinear water waves and related topics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 重力流と内部ボアの定常解2023

    • Author(s)
      村重淳
    • Organizer
      日本流体力学会年会2023
    • Related Report
      2023 Annual Research Report
  • [Presentation] A numerical study on energy-conserving gravity currents past an air cavity2023

    • Author(s)
      Murashige, S.
    • Organizer
      Workshop on Nonlinear Water Waves and Related Topics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Internal fronts and gravity currents2023

    • Author(s)
      村重 淳
    • Organizer
      Recent Advances in Nonlinear Water Waves
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 航跡波に表れる強い非線形性の実験的検証2023

    • Author(s)
      栗山 優真,由肥 辰之助,片岡 武
    • Organizer
      日本機械学会関西支部 第98期定時総会・講演
    • Related Report
      2022 Annual Research Report
  • [Presentation] Experimental verification of strong nonlinearity 1D ship wave2023

    • Author(s)
      片岡 武
    • Organizer
      Recent Advances in Nonlinear Water Waves
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Generation and amplification of tsunamis due to air pressure waves over topography2023

    • Author(s)
      柿沼 太郎
    • Organizer
      Recent Advances in Nonlinear Water Waves
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Nonlinear processes in crest enhancement of modulated wave trains2023

    • Author(s)
      宝谷 英貴
    • Organizer
      Recent Advances in Nonlinear Water Waves
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Exact solutions and soliton interactions of two-dimensional soliton equations2023

    • Author(s)
      丸野健一
    • Organizer
      Recent Advances in Nonlinear Water Waves
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 2層流体の界面で発生する内部ボアの定常進行波解2022

    • Author(s)
      村重 淳
    • Organizer
      日本流体力学会年会2022
    • Related Report
      2022 Annual Research Report
  • [Presentation] Ship waveの非線形解I(1次元モデル方程式を基とした理論)2022

    • Author(s)
      片岡 武,T.R.Akylas
    • Organizer
      日本流体力学会年会2022
    • Related Report
      2022 Annual Research Report
  • [Presentation] fKdV方程式におけるship waveの理論・数値解2022

    • Author(s)
      片岡 武,T.R.Akylas
    • Organizer
      第36回数値流体力学シンポジウム
    • Related Report
      2022 Annual Research Report
  • [Presentation] 河川津波の3次元数値解析2022

    • Author(s)
      柿沼太郎,楠原 嘉
    • Organizer
      第69回海岸工学講演会
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] 高次スペクトル法による波浪内部の圧力場の数値計算2022

    • Author(s)
      宝谷 英貴, 藤本 航, 松井 貞興
    • Organizer
      日本船舶海洋工学会 令和4年 秋季講演会
    • Related Report
      2022 Annual Research Report
  • [Presentation] On the crest height amplification of unstable Stokes wave trains in deep water2022

    • Author(s)
      宝谷 英貴
    • Organizer
      KOZWavinar
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 非線形時間発達を考慮した波浪場における船体縦曲げ応答の数値計算2022

    • Author(s)
      宝谷 英貴,松井 貞興,藤本 航
    • Organizer
      日本船舶海洋工学会 令和4年 春季講演会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Integrable discretizations of integrable nonlinear differential equations with hodograph transformations2022

    • Author(s)
      丸野 健一
    • Organizer
      Isaac Newton Institute for Mathematical Sciences (University of Cambridge) セミナー(オンライン)
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] ホドグラフ変換に関わる非線形微分方程式の解構造を保存する離散化 - 解構造を保存する適合格子細分化法 -2022

    • Author(s)
      丸野 健一
    • Organizer
      京都大学数理解析研究所研究集会「可積分系数理の発展とその応用」
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Book] Chapter 10, Application 1: Ship responses to freak waves”, in Science and Engineering of Freak Waves, eds. Mori, N., Waseda, T. and Chabchoub,A.2023

    • Author(s)
      Houtani, H.
    • Total Pages
      350
    • Publisher
      Elsevier
    • ISBN
      9780323917360
    • Related Report
      2023 Annual Research Report
  • [Remarks] 非線形水波に関する国際研究集会(湘南国際村センター)

    • URL

      http://murasige.sci.ibaraki.ac.jp/WS_Nonlinear_Water_Waves_Shonan_Village_Center_2023.html

    • Related Report
      2023 Annual Research Report
  • [Remarks] Recent Advances in Nonlinear Water Waves

    • URL

      http://murasige.sci.ibaraki.ac.jp/KAKEN_meeting_at_Tokyo_2023_SJIS.html

    • Related Report
      2022 Annual Research Report
  • [Funded Workshop] Workshop on Nonlinear Water Waves and Related Topics2023

    • Related Report
      2023 Annual Research Report
  • [Funded Workshop] Recent Advances in Nonlinear Water Waves2023

    • Related Report
      2022 Annual Research Report

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Published: 2022-04-19   Modified: 2024-12-25  

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