〔Major achievements〕Two-dimensional stability analysis of finite-amplitude interfacial gravity waves in a two-layer fluid
Sunao Murashige and Wooyoung Choi, Lead
Journal of Fluid Mechanics, May 2022, [Reviewed]

Parasitic capillary waves on small-amplitude gravity waves with a linear shear current
Sunao Murashige and Wooyoung Choi, Lead
Journal of Marine Science and Engineering, Nov. 2021, [Reviewed]

〔Major achievements〕Linear stability of transversely modulated finite-amplitude capillary waves on deep water　　　　　　　　　　　　　　　
Sunao Murashige and Wooyoung Choi, Lead
Studies in Applied Mathematics, Feb. 2021, [Reviewed]

〔Major achievements〕Stability analysis of deep-water waves on a linear shear current using unsteady conformal mapping　　　　　　　　　　　　　　　
Lead
Journal of Fluid Mechanics, Feb. 2020, [Reviewed]

Long wave approximation using conformal mapping for large-amplitude internal waves in a two-fluid system
Sunao Murashige, This paper describes a new type of long wave model for periodic internal waves propagating in permanent form at the interface between two immiscible inviscid fluids. This model for irrotational plane motion of these waves is derived in the complex velocity potential planes where the flow domains are conformally mapped. Since no smallness assumption of wave amplitude is made and the wave elevation at the interface is represented by a single-valued function of the velocity potential, this model is applicable to large-amplitude motions of which wave profile may overhang. Numerical examples demonstrate that the proposed model can produce overhanging solutions, and variations of solutions with wavelength or wave amplitude are qualitatively similar to those of the full Euler system. It is also pointed out that the kinematic condition at the interface is exactly satisfied in the proposed model for all wave amplitudes, but not in an existing long wave model derived in the physical plane., Elsevier B.V.
Applied Numerical Mathematics, 2018, [Reviewed]

〔Major achievements〕A numerical study on parasitic capillary waves using unsteady conformal mapping
Sunao Murashige; Wooyoung Choi, This paper describes fully nonlinear computation of unsteady motion of parasitic capillary waves that appear on the front face of steep gravity waves progressing on water of infinite depth, within the framework of irrotational plane flow. As an alternative to the widely-used boundary integral method with mixed-Eulerian-Lagrangian (MEL) time updating, we focus on a numerical method based on unsteady conformal mapping, which will be hereafter referred to as the unsteady hodograph transformation (UHT) method. In this method, we solve the nonlinear evolution equations to find an unsteady conformal map in a complex plane with which the flow domain is mapped onto the unit disk while the free surface is fixed on the unit circle. The aim of this work is to compare the UHT method with the MEL method and find a more efficient method to compute parasitic capillary waves. From linear stability analysis, it is found that a critical difference between these two methods arises from the kernel of cotangent function in singular integrals, and the UHT method can avoid some numerical instability due to it. Numerical examples demonstrate that the UHT method is more suitable than the MEL method for not only parasitic capillary waves, but also capillary dominated waves. In particular, the UHT method requires no artificial techniques, such as filtering, to control numerical errors, in these examples. In addition, another major difference between the two methods is observed in terms of the clustering property of sample points on the free surface, depending on the restoring force of waves (gravity or surface tension). (C) 2016 Elsevier Inc. All rights reserved., ACADEMIC PRESS INC ELSEVIER SCIENCE
JOURNAL OF COMPUTATIONAL PHYSICS, Jan. 2017, [Reviewed]

A new method of convergence acceleration of series expansion for analytic functions in the complex domain
Sunao Murashige; Ken'ichiro Tanaka, This paper proposes a new method of convergence acceleration of series expansion of complex functions which are analytic on and inside the unit circle in the complex plane. This class of complex functions may have some singularities outside the unit circle, which dominate convergence of series expansion. In the proposed method, the singular points are moved away from the origin using conformal mapping, and the function is expanded using a sequence of polynomials orthogonalized on the boundary of the mapped complex domain. The decay rate of coefficients of the orthogonal polynomial expansion can be related to the convergence region in a similar form to the Cauchy-Hadamard formula for power series. Using this relation, we quantitatively evaluate and maximize the convergence rate of the improved series. Numerical examples demonstrate that the proposed method is effective for slowconvergent series, and may converge faster than Pade approximants., SPRINGER JAPAN KK
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, Mar. 2015, [Reviewed]

〔Major achievements〕HIGH-ORDER DAVIES' APPROXIMATION FOR A SOLITARY WAVE SOLUTION IN PACKHAM'S COMPLEX PLANE
Sunao Murashige; Wooyoung Choi, This paper considers a progressive solitary wave of permanent form in an ideal fluid of constant depth and explores Davies' approximation [Proc. R. Soc. Lond. A, 208 (1951), pp. 475486] with high-order corrections to Levi-Civita's surface condition for the logarithmic hodograph variable. Using a complex plane that was originally introduced by Packham [Proc. R. Soc. Lond. A, 213 (1952), pp. 234-249], it is shown that a singularity at infinity can be regularized. Therefore, the solutions in Packham's complex plane under high-order Davies' approximation maintain two critical properties of a solitary wave, the correct exponential decay in the outskirt of wave and the harmonic property of a solution, that are often violated in classical long wave approximations. After introducing an accurate numerical method to compute solitary wave solutions in Packham's complex plane, we compare high-order Davies' approximate solutions with fully nonlinear solutions as well as long wave approximate solutions. The results demonstrate that high-order Davies' approximation produces rapidly converging series solutions even for relatively large amplitude waves and that Davies' approximate solutions compare much better with the fully nonlinear solutions than the long wave approximate solutions., SIAM PUBLICATIONS
SIAM JOURNAL ON APPLIED MATHEMATICS, 2015, [Reviewed]

Davies' surface condition and singularities of deep water waves
Sunao Murashige, Davies' surface condition is an approximate free-surface condition on gravity waves progressing in permanent form on water of infinite depth. It is known that this condition preserves essential features of finite-amplitude waves including the highest one. This paper proposes a new surface condition that generalizes Davies' idea of approximation and covers a fully nonlinear condition. Analytic continuation of the proposed surface condition allows us to explore singularities of solutions that dominate the flow. The results of singularity analysis elucidate the connection between Davies' approximate solution and the fully nonlinear solution. In addition, it is shown that the nonmonotonic variation of wave speed with wave steepness can be predicted using a linear sum of a relatively small number of singularities. This suggests that a suitable choice of a parameter in the proposed surface condition can move singularities away from the flow field without changing their structure and may reduce numerical difficulties due to singularities for large-amplitude waves., SPRINGER
Journal of Engineering Mathematics, 2014, [Reviewed]

Convergence rates and explicit error bounds of Hill's method for spectra of self-Adjoint differential operators
Ken'ichiro Tanaka and Sunao Murashige, We present the convergence rates and the explicit error bounds of Hill's method, which is a numerical method for computing the spectra of ordinary differential operators with periodic coefficients. This method approximates the operator by a finite dimensional matrix. On the assumption that the operator is self-adjoint, it is shown that, under some conditions, we can obtain the convergence rates of eigenvalues with respect to the dimension and the explicit error bounds. Numerical examples demonstrate that we can verify these conditions using Gershgorin's theorem for some real problems. Main theorems are proved using the Dunford integrals which project an vector to a specific eigenspace., KINOKUNIYA CO LTD
Japan Journal of Industrial and Applied Mathematics, 2014, [Reviewed]

〔Major achievements〕Numerical use of exterior singularities for computation of gravity waves in shallow water
Sunao Murashige, This paper describes fully nonlinear, fully dispersive computation for two-dimensional motion of periodic gravity waves of permanent form in an ideal fluid of arbitrary uniform depth. The rate of convergence of a series solution of this motion becomes slow with decrease of the water depth-to-wavelength ratio, and a considerably large number of terms in series are required to obtain accurate numerical solutions for long waves in shallow water, even if the wave amplitude is small. Domb-Sykes plots for coefficients of the computed series solutions show that the slow rate of convergence is due to a singularity outside the flow domain in a conformally mapped complex plane. This exterior singularity can be theoretically estimated using analytic continuation of an ordinary differential equation given by the free surface condition. It is shown that a conformal mapping regularizes this singularity and enlarges the radius of convergence of a series solution. In addition, iterative use of this mapping for regularization further improves convergence. This work proposes a new method to compute long waves in shallow water using regularization of the exterior singularity. Numerical examples demonstrate that the proposed method can produce accurate enough solutions for a wide range of water depth-to-wavelength ratios. Validity of cnoidal wave solutions is also discussed using comparison with the computed results., SPRINGER
Journal of Engineering Mathematics, 2012, [Reviewed]

〔Major achievements〕On tsunami and the regularized solitary-wave theory
Theodore Y. Wu and Sunao Murashige, For ideal hydrodynamic modeling of earthquake-generated tsunamis, the principal features of tsunamis occuring in nature are abstracted to provide a fundamental case of a one-dimensional solitary wave of height a, propagating in a layer of water of uniform rest depth h for modeling the tsunami progressing in the open ocean over long range, with height down to a/h a parts per thousand integral 10(-4) as commonly known. The Euler model is adopted for evaluating the irrotational flow in an incompressible and inviscid fluid to attain exact solutions so that the effects of nonlinearity and wave dispersion can both be fully accounted for with maximum relative error of O(10(-6)) or less. Such high accuracy is needed to predict the wave-energy distribution as the wave magnifies to deliver any devastating attack on coastal destinations. The present UIFE method, successful in giving the maximum wave of height (a/h = 0.8331990) down to low ones (e.g. a/h = 0.01), becomes, however, impractical for similar evaluations of the dwarf waves (a/h < 0.01) due to the algebraic branch singularities rising too high to be accurately resolved. Here, these singularities are all removed by introducing regularized coordinates under conformal mapping to establish the regularized solitary-wave theory. This theory is ideal to differentiate between the nonlinear and dispersive effects in various premises for producing an optimal tsunami model, with new computations all regular uniformly down to such low tsunamis as that of height a/h = 10(-4)., SPRINGER
Journal of Engineering Mathematics, 2011, [Reviewed]

Dwarf solitary waves and low tsunamis
Sunao Murashige and Theodore Y. Wu, This work applies the regularized solitary wave theory to develop accurate computational method for evaluating the dwarf solitary waves, with amplitude-to-water depth ratio alpha <= 10(-2), as a useful model of one-dimensional tsunamis propagating in the open ocean. The algebraic branch singularities of these solitary waves magnifying with diminishing wave amplitude, making their computations insurmountable by existing methods, are removed by the regularized coordinates given by this new theory. Numerical examples show that this new method can produce accurate results even for alpha congruent to 10(-3) or less., CHINA OCEAN PRESS
Journal of Hydrodynamics, 2010, [Reviewed]

Computation of Floquet multipliers using an iterative method for variational equations
Yu Nureki and Sunao Murashige, This paper proposes a new method to numerically obtain Floquet multipliers which characterize stability of periodic orbits of ordinary differential equations. For sufficiently smooth periodic orbits, we can compute Floquet multipliers using some standard numerical methods with enough accuracy. However, it has been reported that these methods may produce incorrect results under some conditions. In this work, we propose a new iterative method to compute Floquet multipliers using eigenvectors of matrix solutions of the variational equations. Numerical examples show effectiveness of the proposed method., IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG
IEICE Transactions of Fundamentals of Electronics, Communications and Computer Sciences, 2009, [Reviewed]

Boundary conditions for numerical stability analysis of periodic solutions of ordinary differential equations
Sunao Murashige, This paper considers numerical methods for stability analyses of periodic solutions of ordinary differential equations. Stability of a periodic solution can be determined by the corresponding monodromy matrix and its eigenvalues. Some commonly used numerical methods can produce inaccurate results of them in some cases, for example, near bifurcation points or when one of the eigenvalues is very large or very small. This work proposes a numerical method using a periodic boundary condition for vector fields, which preserves a critical property of the monodromy matrix. Numerical examples demonstrate effectiveness and a drawback of this method., IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG
IEICE Transactions of Fundamentals of Electronics, Communications and Computer Sciences, 2008, [Reviewed]

再分割アルゴリズムを用いた力学系の定常分布の数値計算　　　　　　　　　　　　　　　
濡木 融; 村重 淳
電子情報通信学会論文誌, 2007, [Reviewed]

写像により変換された曲線の折り返し点を用いた位相的エントロピーの計算　　　　　　　　　　　　　　　
福島 真太朗; 村重 淳
電子情報通信学会論文誌, 2007, [Reviewed]

A practical method of numerical calculation of the mapping degree
Sunao Murashige, This paper proposes a simple and efficient method to numerically obtain the mapping degree deg(f, 0, B) of a C-1 map f : R-n --> R-n at a regular value 0 relative to a bounded open subset B c R'. For practical application, this method adopts Aberth's algorithm which does not require computation of derivatives and determinants, and reduces the computational cost with two additional procedures, namely preconditioning using the coordinate transformation and pruning using Krawczyk's method. Numerical examples show that the proposed method gives the mapping degree with 2n+1 operations using interval arithmetic., IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG
IEICE Transactions of Fundamentals of Electronics, Communications and Computer Sciences, 2006, [Reviewed]

自動微分とDE公式を用いた非整数階微分の数値計算
岡山 友昭; 村重 淳, This paper proposes a new method of numerical calculation for fractional derivatives. Conventional methods using difference approximation have some defects such as rounding errors and computation time. In this paper, fractional derivatives are expressed as the combination of ordinary derivatives and integrals which are calculated using automatic differentiation and double exponential formula, respectively. Numerical examples show that the proposed method gives high-precision results with practical computational cost., The Japan Society for Industrial and Applied Mathematics
日本応用数理学会論文誌, 2006, [Reviewed]

Numerical computation of the mapping degree using computational homology
Kansaku Nakakura; Sunao Murashige, This paper describes numerical computation of the mapping degree deg(f,Bd) for a continuous map f : Bd → ℝd on the d-dimensional ball Bd where d ∈ ℤ and ≥ 2. The mapping degree can be defined using a homomorphism which is induced on homology groups. We propose an efficient method to compute the homomorphism without direct calculation of homology groups, and obtain the mapping degree using computational homology.
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, SCAN 2006, Conference Post-Proceedings, 2006, [Reviewed]

〔Major achievements〕Numerical verification of solutions of Nekrasov's integral equation
Sunao Murashige and Shin'ichi Oishi, This paper describes numerical verification of solutions of Nekrasov's integral equation which is a mathematical model of two-dimensional water waves. This nonlinear and periodic integral equation includes a logarithmic singular kernel which is typically found in some two-dimensional potential problems. We propose the verification method using some properties of the singular integral for trigonometric polynomials and Schauder's fixed point theorem in the periodic Sobolev space. A numerical example shows effectiveness of the present method., SPRINGER WIEN
Computing, 2005, [Reviewed]

Analysis of flagellar bending in hamster spermatozoa: characterization of an effective stroke
Kinukawa; M.; Ohmuro; J.; Baba; S.A.; Murashige; S.; Okuno; M.; Nagata; M.; and Aoki; F., The mechanism by which flagella generate the propulsive force for movement of hamster spermatozoa was analyzed quantitatively. Tracing points positioned 30, 60, 90, and 120 mu m from the head-midpiece junction on the flagellum revealed that they all had zigzag trajectories. These points departed from and returned to the line that crossed the direction of progression. They moved along the concave side (but not the convex side) of the flagellar envelope that was drawn by tracing the trajectory of the entire flagellum. To clarify this asymmetry, the bending rate was analyzed by measuring the curvatures of points 30, 60, 90, and 120 mu m from the head-midpiece junction. The bending rate was not constant through the cycle of flagellar bending. The rate was higher when bending was in the direction described by the curve of the hook-shaped head (defined as a principal bend [P-bend]) to the opposite side (R-bend). We measured a lower bending rate in the principal direction (R-bend to P-bend). To identify the point at which the propulsive force is generated efficiently within the cycle of flagellar bending, we calculated the propulsive force generated at each point on the flagellum. The value of the propulsive force was positive whenever the flagellum bent from an R-bend to a P-bend (when the bending rate was lowest). By contrast, the propulsive force value was zero or negative when the flagellum bent in the other direction (when the bending rate was higher). These results indicate that flagellar bending in hamster spermatozoa produces alternate effective and ineffective strokes during propulsion., SOC STUDY REPRODUCTION
Biology of Reproduction, 2005, [Reviewed]

〔Major achievements〕On necessary and sufficient conditions for numerical verification of double turning points
Ken'ichiro Tanaka; Sunao Murashige and Shin'ichi Oishi, This paper describes numerical verification of a double turning point of a nonlinear system using an extended system. To verify the existence of a double turning point, we need to prove that one of the solutions of the extended system corresponds to the double turning point. For that, we propose an extended system with an additional condition. As an example, for a finite dimensional problem, we verify the existence and local uniqueness of a double turning point numerically using the extended system and a verification method based on the Banach fixed point theorem., SPRINGER HEIDELBERG
Numerische Mathematik, 2004, [Reviewed]

Numerical verification of solutions of periodic integral equations with a singular kernel
Murashige; S. and Oishi; S., This paper proposes the method of numerical verification of solutions of a periodic integral equation with a logarithmic singular kernel, which is typically found in some two-dimensional potential problems. The verification method utilizes a property of the singular integral for trigonometric polynomials, the periodic Sobolev space and Schauder's fixed point theorem., KLUWER ACADEMIC PUBL
Numerical Algorithms, 2004, [Reviewed]

Bifurcation structures of period-adding phenomena in an ocean internal wave model
Tanaka; G.; Murashige; S.; and Aihara; K., In this paper, we study bifurcation structures of period-adding phenomena in an internal wave model that is a mathematical model for ocean internal waves. It has been suggested that chaotic solutions observed in the internal wave model may be related to the universal property of the energy spectra of ocean internal waves. In numerical bifurcation analyses of the internal wave model, we illustrate bifurcation routes to chaos and parameter regions where chaotic behavior is observed. Furthermore, it is found that the chaotic solutions are related to the period-adding sequence, that is, successive generations of periodic solutions with longer periods as a control parameter is changed. Considering the period-adding sequence as successive local bifurcations, we discuss a mechanism of the phenomena from the viewpoint of bifurcation analysis. We also consider similarity between period-adding phenomena in the internal wave model and ones in the Lorenz model., WORLD SCIENTIFIC PUBL CO PTE LTD
International J. of Bifurcation and Chaos, 2003, [Reviewed]

Boundary element simulation of large amplitude standing waves in vessels
Hamano; K.; Murashige; S.; and Hayami; K., In this paper, a fluid in a vessel is considered and large amplitude standing waves (LASW) of the fluid are simulated directly using the boundary element method (BEM).
In the simulation, two problems come out. The first problem is that the energy of the LASW increases gradually when using double nodes at corners in the BEM. The second problem is that projection-like profiles appear near the point where the free surface meets the vessel wall when regridding is not used at each time step. These projection-like profiles are not physical and indicate numerical error, and cause the simulation to break down.
We found that the use of discontinuous elements solves the first problem, and the use of the 'half shift technique' solves the second problem.
In addition, a method called RIG for highly accurate simulation using regridding is proposed and verified. (C) 2003 Elsevier Science Ltd. All rights reserved., ELSEVIER SCI LTD
Engineering Analysis with Boundary Elements, 2003, [Reviewed]

〔Major achievements〕Nonlinear analyses of roll motion of a flooded ship in waves
Sunao Murashige; Taiji Yamada and Kazuyuki Aihara, This paper investigates nonlinear responses of a flooded ship in regular waves. In previous experimental work, we found that the roll motion of a flooded ship can exhibit complicated irregular behaviour even in waves of a moderate height. First, we analyse the fractal dimension and the Lyapunov exponents of the experimental data and Show that they have chaotic characteristics. We also show that a radial basis function network obtained directly from the data can reproduce a geometrical structure of the reconstructed attractor and provide good short-term prediction on the dynamical motion. Next, in order to understand this nonlinear phenomenon, we derive a simple mathematical model for the nonlinearly coupled motion of roll and hooded water in regular waves. This model has a form of coupled Duffing's equations with a bistable restoring term and a nonlinear inertial coefficient matrix. We obtain bifurcation diagrams of periodic solutions of this model and examine the intricate structure of this nonlinear system. Chaotic responses are found in wide regions of the parameter space, even if the wave-exciting moment is not large. Furthermore, the attractor structure of the chaotic solution is similar to that of the measured chaotic motion in the experiments. The results suggest that bifurcation analyses in this work help us understand the complex dynamics of nonlinear motion of a flooded ship in waves., ROYAL SOC LONDON
Phil. Trans. R. Soc. Lond. A, 2000, [Reviewed]

2次元しきい値分布を利用した流行現象の数理モデルとその解析　　　　　　　　　　　　　　　
河根 拓文; 村重 淳; 合原 一幸
電子情報通信学会論文誌 A, 2000, [Reviewed]

Bifurcation and resonance of a mathematical model for non-linear motion of a flooded ship in waves
Sunao Murashige; Kazuyuki Aihara and Motomasa Komuro, A flooded ship can exhibit undesirable non-linear roll motion even in waves of moderate amplitude. In order to understand the mechanism of this non-linear phenomenon, the nan-linearly coupled dynamics of a ship and flood water are considered using a mathematical model for the simplified motion of a flooded ship in regular beam waves. This paper describes bifurcation and resonance of this coupled system. A bifurcation diagram shows that large-amplitude subharmonic motion exists in a wide range of parameters, and that the Hopf bifurcation is observed due to the dynamic effects of flood water. Resonance frequencies can be determined by linearization of this model. Comparison between the resonance points and the bifurcation curves suggests that non-linear resonances of this model can bring about large-amplitude subharmonic motion, even if it is in the non-resonant state of the linearized system. (C) 1999 Academic Press., ACADEMIC PRESS LTD
J. of Sound and Vibration, 1999, [Reviewed]

〔Major achievements〕Experimental study on chaotic motion of a flooded ship in waves
Sunao Murashige and Kazuyuki Aihara, This paper investigates the nonlinear roll motion of a flooded ship in waves by using model experiments. It is found that roll response of a flooded ship can exhibit irregular and complicated behaviour, even in regular beam waves with moderate amplitude. Nonlinear analyses indicate that they can be chaotic. Nonlinearity in the restoring moment and dynamic effects of flooded water cause this complicated motion., ROYAL SOC
Proc. R. Soc. Lond. A, 1998, [Reviewed]

Coexistence of periodic roll motion and chaotic one in a forced flooded ship
Murashige; S. and Aihara; K., This letter describes the coexistence of periodic and chaotic roll motion of a flooded ship in waves. We found experimentally, both with a flooded ferry model and with a simplified box-shaped model, that the two types of roll motion can coexist under the same wave condition. A trajectory reconstructed in a delay-coordinate state space from the time series data of the measured roll angle looks like a low-dimensional strange attractor. Moreover, a mathematical model for the simplified box-shaped ship shows the coexistence of a periodic solution and a chaotic one with a positive maximum Liapunov exponent., WORLD SCIENTIFIC PUBL CO PTE LTD
International Journal of Bifurcation and Chaos, 1998, [Reviewed]

損傷した RO-RO 客船の横波中転覆に関する模型実験
原口 富博; 石田 茂資; 村重 淳, 公益社団法人日本船舶海洋工学会
日本造船学会論文集, 1998, [Reviewed]

Nonlinear Roll Motion of a Ship with Water-on-Deck in Regular Waves(Summaries of Papers Published by Staff of Ship Research Institute at Outside Organizations)
村重 淳; 合原 一幸; 山田 泰司, National Maritime Research Institute
Report of Ship Research Institute, 12 Mar. 1997

Nonlinear roll motion of a flooded ship in regular waves, J. Society of Naval Architects of Japan
Murashige; S. and Aihara; K., This paper describes dynamic effects of flooded water on nonlinear roll motion of a ship in regular beam waves. Experiments using a ferry model demonstrate nonlinear roll response of a flooded ship in waves. It is found that two kinds of roll motion with different amplitudes and periods coexist and that one of them is particularly irregular and complicated even in regular waves of relatively moderate amplitude. The reconstructed attractor of the roll motion in a delay-coordinate state space shows that it is not simple harmonic motion. In order to further study this complicated roll motion, we derived model equations which include both the nonlinear effects of the restoring moment and the coupling effects of roll and flooded water. The dynamic motion of flooded water produces the coupling effects which have been neglected in most previous works. Numerical solutions of the model equations show that this coupled system yields nonlinear phenomena similar to the experimental results. In addition, we also experimentally studied motion of a box-shaped model with flooded water in regular waves. The experimental results show that the roll response varies with changing the wave height in a complicated manner which also depends on the amount of flooded water, and that some of complicated roll motion have typical properties of low-dimensional deterministic chaos. These results suggest that the nonlinearly coupled dynamics of a ship and flooded water is a key to solve this problem., The Japan Society of Naval Architects and Ocean Engineers
J. Society of Naval Architects of Japan, 1997, [Reviewed]

波浪中における RO-RO 客船の甲板上浸水と損傷時復原性に関する研究
石田 茂資; 村重 淳; 渡辺 巌; 小川 剛孝; 藤原 敏文, 公益社団法人 日本船舶海洋工学会
日本造船学会論文集, 1996

〔Major achievements〕An ideal ocean wave focusing lens and its shape
Sunao Murashige and Takeshi Kinoshita, A hydrodynamic singularity distribution for an ideal wave focusing lens is derived on the assumption of its slenderness and high frequency of incident waves. The result indicates that its sectional shape should satisfy necessary conditions which are equivalent to geometrical optics. Some experiments and computations show that an array of submerged circular cylinders almost satisfy the above necessary conditions for a wide band of wave frequencies. Furthermore, using the slender ship theory, it is shown that a convex circular cylinder type gives better wave focusing performance than a flat plate type, which has been used in previous work, particularly in irregular waves., ELSEVIER SCI LTD
Applied Ocean Research, 1992, [Reviewed]

Ocean wave focusing : experiments and nonlinear computations　　　　　　　　　　　　　　　
Murashige; S.; Kinoshita; T. and Suzuki; T.
International Journal of Offshore and Polar Engineering, 1992, [Reviewed]

海洋波集波レンズの基礎的研究（第二報）－水槽実験－
村重 淳; 木下 健, 日本造船学会
日本造船学会論文集, 1991, [Reviewed]

Are incident waves split into symmetrical and anti-symmetrical scattering wave systems with equal energy by two dimensional obstacles?
Sunao Murashige and Takeshi Kinoshita, Kato et al. reported that a wave height of a symmetrical component and an antisymmetrical component of scattered waves is exactly one half of that of incident waves, that is, "equally energy splitting law", and that in two dimensional diffraction problems this law does not require symmetry of a body geometry. It gives us valuable information as an invariant property. In the present note, however, we show that it is invalid in the case of an asymmetrical body, although it is reviewed as valid by Kan., The Japan Society of Naval Architects and Ocean Engineers
J. Kansai Soc. N.A., Japan, 1991, [Reviewed]

海洋波集波レンズの基礎的研究
村重 淳; 木下 健, Wave focusing has been attracting ocean engineers as one of the most promising techniques to control ocean waves. It creates a calm sea area and helps efficient utilization of wave energy. In the present work, a hydrodynamic singularity distribution which expresses a wave focusing lens is derived by the method of matched asymptotic expansion, assuming slenderness of the lens and high frequency of incident waves. The singularity distribution gives the following necessary conditions for scattered waves in each section of the lens : there is no reflection from the lens and the transmitted waves suffer a phase shift in passing the lens. The phase shift is given by the wavenumber and the distance between the section and the focus. From these conditions, we examine a sectional shape of the lens and determine the whole geometry. It is shown by experiments and numerical computations using the two dimensional doublet distribution method that a submerged chevron shape plate, which is suitably folded, scatters a wave system which satisfies the above conditions at a certain wave frequency, but not in wide band of wave frequencies because of dispersion of water waves. Then it is shown by experiments that a certain number of submerged circular cylinders,which are horizontally arranged at intervals just like a raft, transmits waves which have enough phase shift to focus waves but reflects almost no waves in wide band of wave frequencies. Finally, we examine performances of three types of lens, namely, submerged fiat plate, submerged chevron shape plate, and submerged circular cylinders, in both regular and irregular waves. It is shown by numerical computations that the wave focusing efficiency of the lens consisting of circular cylinders is about twice that of the fiat plate type lens and that the drift force acting on the former is less than half of that on the latter in irregular waves., The Japan Society of Naval Architects and Ocean Engineers
日本造船学会論文集, 1990, [Reviewed]

Singularity distribution for ocean wave focusing　　　　　　　　　　　　　　　
Sunao Murashige and Takeshi Kinoshita
Proc. Japan Assoc. Coastal Zone Studies, 1990, [Reviewed]

〔Major achievements〕Internal fronts and gravity currents　　　　　　　　　　　　　　　
Recent Advances in Nonlinear Water Waves, 28 Mar. 2023

2層流体の界面で発生する内部ボアの定常進行波解　　　　　　　　　　　　　　　
日本流体力学会 年会2022, 27 Sep. 2022

線形シアー流上で発生する parasitic capillary waves の数値的研究　　　　　　　　　　　　　　　
日本流体力学会年会2021, 23 Sep. 2021

Effects of a linear shear current on surface waves in deep wate　　　　　　　　　　　　　　　
Sunao Murashige
Online seminar on nonlinear water waves and related topics, 16 Jul. 2021

有限振幅表面張力波の3次元的線形安定性解析　　　　　　　　　　　　　　　
村重 淳
日本流体力学会 年会2020, 20 Sep. 2020

等角写像を用いた表面張力波の線形安定性解析　　　　　　　　　　　　　　　
村重 淳
RIMS 研究集会 「非線形波動現象の数理とその応用」, 17 Oct. 2019

等角写像を用いた大振幅・定常進行水面波の線形安定性解析　　　　　　　　　　　　　　　
村重 淳
日本流体力学会 年会2019, 14 Sep. 2019

〔Major achievements〕Stability of deep-water waves with constant vorticity　　　　　　　　　　　　　　　
Sunao Murashige
Nonlinear waves, Theory, Computations and Real-World Applications, Jan. 2019, [Invited]

線形シアー流上を進行する周期的深水波の2次元的定常運動　　　　　　　　　　　　　　　
村重 淳
RIMS 研究集会 「非線形波動現象の数理とその応用」, 18 Oct. 2018

水波問題と複素解析　　　　　　　　　　　　　　　
村重 淳
AIMap異分野ワークショプ「海岸・海洋における非線形問題に対する数学的手法の展開 ーモデリング，解析，数値計算ー」, 06 Oct. 2018, [Invited]

線形シアー流上を進行する水波の2次元的定常運動　　　　　　　　　　　　　　　
村重 淳
日本流体力学会 年会2018, 06 Sep. 2018

〔Major achievements〕Two-dimensional stability of solitary waves on a linear shear current　　　　　　　　　　　　　　　
Sunao Murashige
SIAM Conference on Nonlinear Waves and Coherent Structures, 11 Jun. 2018

〔Major achievements〕Large-amplitude solitary waves on a linear shear current　　　　　　　　　　　　　　　
Sunao Murashige
Workshop on Nonlinear Water Waves -- In honor of Professor Mitsuhiro Tanaka on the occasion of his retirement --, 23 May 2018

〔Major achievements〕Large amplitude motion of periodic internal waves in a two fluid system of finite depth　　　　　　　　　　　　　　　
Sunao Murashige
Workshop on nonlinear water waves and related phenomena, 19 Feb. 2018, [Invited]

線形シアー流上を進行する定常水波に対する長波モデル　　　　　　　　　　　　　　　
村重 淳
RIMS 研究集会 「非線形波動現象の数理とその応用」, 11 Oct. 2017

〔Major achievements〕Numerical and theoretical studies of nonlinear water waves using the hodograph transformation　　　　　　　　　　　　　　　
Sunao Murashige
Dispersive hydrodynamics and oceanography: from experiments to theory, Aug. 2017, [Invited]

〔Major achievements〕Long wave approximation with hodograph transformation for periodic internal waves in a two-fluid system　　　　　　　　　　　　　　　
Sunao Murashige
The Tenth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, 30 Mar. 2017

海洋における非線形波動の数理　　　　　　　　　　　　　　　
村重 淳
第12回数理工学セミナー, Dec. 2016, 田中 健一郎（武蔵野大学）, [Invited]

非定常ホドグラフ変換を用いた水波の非線形運動の数値計算　　　　　　　　　　　　　　　
村重 淳
RIMS 研究集会 「非線形波動現象の数理とその応用」, Oct. 2016, 村重 淳

波長の長い重力水波に対する級数展開の収束性　　　　　　　　　　　　　　　
村重 淳
日本流体力学会 年会2016, Sep. 2016

〔Major achievements〕Generalization of Stokes' decay rate formula for solitary waves　　　　　　　　　　　　　　　
Murashige; S.
Mini-Workshop on Nonlinear Waves in Fluids -- In honor of Professor Funakoshi on the occasion of his retirement --, May 2016, 村重 淳

非定常等角写像を用いた重力・表面張力水波の強非線形計算　　　　　　　　　　　　　　　
村重 淳
日本流体力学会 年会2015, Sep. 2015

〔Major achievements〕Fully nonlinear computation of unsteady water waves using a non-stationary conformal mapping　　　　　　　　　　　　　　　
Murashige; S.
Workshop on Nonlinear Waves and Fluid Mechanics, Aug. 2015, Wooyoung Choi (New Jersey Institute of Technology), [Invited]

Improvement of convergence of series expansion for water wave solutions　　　　　　　　　　　　　　　
Murashige; S.
Mini-Workshop on Nonlinear Water Waves, Dec. 2014, 村重 淳

水面波に対する Davies 近似とその改良　　　　　　　　　　　　　　　
村重 淳
RIMS 研究集会 「非線形波動現象のメカニズムと数理」, Oct. 2014, 田中 光宏（岐阜大学）

孤立波に対する高次 Davies 近似について　　　　　　　　　　　　　　　
村重 淳
日本流体力学会 年会2014, Sep. 2014

〔Major achievements〕Davies approximation of Levi-Civita's surface condition for water waves in the complex domain　　　　　　　　　　　　　　　
Murashige; S.
SIAM Conference on Nonlinear Waves and Coherent Structures, Aug. 2014