NONLINEAR WAVE PACKET EVOLUTION IN SHALLOW WATER

Efim Pelinovsky,타타냐타리포바,Eliezer Kit,Ori Eitan 한국해안해양공학회 1999 학술강연회 발표논문초록집 Vol.2 No.1

Wave group evolution in shallow water of constant depth is simulated numerically applying the Korteweg-de Vries equation. Decomposition into harmonics is performed and the results are presented separately for the carrier wave frequency, the 2^(nd) and the low harmonics. Experiments are performed for three values of the forcing amplitude at the wavemaker. The effect of the nonlinearity parameter and its ratio to the dispersion parameter on the evolution of the wave group along the tank is studied. Advantage is taken of the relatively simple theoretical model employed in order to analyse the relative importance of various terms in the governing equation. Good agreement between the available experimental and the numerical results is obtained.

A Mathematical Model for Nonlinear Waves due to Moving Disturbances in a Basin of Variable Depth

Efim N. Pelinovsky(에핌 페리높스키),Hang Soon Choi(최항순) 한국해안해양공학회 1993 한국해안해양공학회 논문집 Vol.5 No.3

Redistribution of Passive Impurity by Long Waves in Coastal Zone

Pelinovsky, Efim,Talipova, Tatjana 한국해안해양공학회 1993 한국해안해양공학회 논문집 Vol.5 No.3

연안역에서의 파동이 오염원의 확산에 미치는 영향에 관한 연구를 수행하였다. 천해근사를 사용하여 기존의 확산방정식을 수심에 관하여 적분함으로써, 임의의 진폭을 갖는 장파조건 및 임의의 흐름조건에 대하여 적용가능한 방정식을 유도하였다. 수립된 방정식을 사용하여 장파가 오염원의 농도에 영향을 미치는 여러 경우에 대하여 고찰하였다. In this paper the effect of wave motion acting on the natural folds of dispersed material in the coastal zone is studied. After integrating the usual diffusion equation with respect to the depth using shallow-water approximation simpler equation for integrated concentration was obtained. which holds for long waves of arbitrary amplitude and far any arbitrary barotropic flows. Different situations of long wave action on impurity concentration in the frame of this equation are considered.

Nonlinear Dispersion Model of Sea Waves in the Coastal Zone

Pelinovsky, Efim N.,Stepanyants, Yu.,Talipova, Tatiana 한국해안해양공학회 1993 한국해안해양공학회 논문집 Vol.5 No.4

파랑의 비선형성 및 분산을 고려한, 연안역에서의 파랑변형에 관한 연구를 수행하였다. 규칙파의 변형에 관한 수학적 모형은 비선형 ray모델에 기초하였으며, ray 및 파동장에 관한 방정식들을 수립하였다. 비선형 파동장은 수정 Korteweg-de Vries 식으로서 나타내었으며, 이에 대한 몇몇 해석 해들을 구하였다. 또한 Caustic 변형 및 감쇄효과를 수학적 모형에 포함하였다. Korteweg-de Vries 방정식에 대한 수치계산 알고리즘과 안정조건을 기술하였으며, 연안역에서의 비선헝 파랑변형 계산 결과를 제시하였다. The problem of sea wave transformation in the coastal zone taking into account effects of nonlinearity and disperison has been studied. Mathematical model for description of regular wave transformation is based on the method of nonlinear ray theory. The equations for rays and wave field have been produced. Nonlinear wave field is described by the modified Korteweg-de Vries equation. Some analytical solutions of this equation are obtained. Caustic transformation and dissipation effects are included in the mathematical model. Numerical algorithm of solution of the Korteweg-de Vries equation and its stability criterion are described. Results of nonlinear transformation of sea waves in the coastal zone are demonstrated.

Nonlinear Models of Tsunami Wave Propagation

에핌페리높스키 한국해안해양공학회 1992 학술강연회 발표논문초록집 Vol.1 No.1

The paper is devoted to one of the branches tsunami wave hydrodynamics. The theory of propagation, transformation and runup of tsunami waves taking into account the nonlinearity and the dispersion is exposed. The available data on real tsunamis are reviewed. The results of laboratory and numerical experiments are reported which point to the necessity of taking into account simultaneously the tsunami wave nonlinearity and dispersion. The theory of nonlinear and dispersion tsunami waves is developed taking into account the wave refraction. The nonlinear ray method is proposed. The part played by the nonlinearity and dispersion in the propagation of tsunami wave transformation near the shoreline and wave runup on a beach is proposed. The theory is used for estimating the tsunami risk and the maximum wave runup in the Pacific coast of Russia, The conclusions of the theory are compared with the available data on real tsunami and the results of laboratory and numerical experiments. Some of results of nonlinear theory of tsunami propagation and corresponding numerical algorithms were published in books: 1. Pelinovsky E. N. Nonlinear Dynamics of Tsunami Waves. - Gorky: Applied Physics Institute Press, 1982, 226 p. 2. Pelinovsky E. N. (ed) The Climbing of Tsunami Waves on the Beach. - Gorky : Applied Physics Institute Press. 1985. 215 p. 3. Engelbrecht Ju. K., Fridman V. E., Pelinovsky E. N. Nonlinear Evolution Equations (Pitman Research Notes in Mathematics Series, N. 180). London : Longman Science & Technical Groups. 1988. 122 p. 4. Voltsinger N. E., Klevanny K. A., Pelinovsky E. N. Long - Wave Dynamics of the Coastal Zone. - Leningrad : Gidrometeoizdat. 1989. 271 p. 5. Nekrasov A. V., Pelinovsky E. N. (eds). Practical Book on Dynamics of the Ocean. - St. Petersburg : Gidrometeoizdat. 1982. 318 p.

Criteria of Sea Wave Breaking in Basins of Complex Topography

Pelinovsky, Efim N. 한국해안해양공학회 1992 한국해안해양공학회 논문집 Vol.4 No.2

경사가 일정한 해안에서 단조파의 쇄파조건을 다룬 Carrier-Greenspan 이논을 일반화시켜 복잡한 실제 지형에까지 적용시킬 수 있게 하였으며 따라서 종래 주로 경험에만 의존하던 쇄파대내의 파낭변형에 이논적 배경을 제공하였다. 포물선형태의 지형을 대상으로 계산하였으며 이들 결과로부터 비선형성이 강한 쳐오름(run-up) 문제를 선형화시킴으로 나타나는 영향에 대하여도 검토하였다. Empirical criteria for wave breaking on the coastal slope are substantiated theoretically for complex-shape basins. The theory developed here is a generalization of Carrier-Greenspan theory for a plane beach. The place and role of the linear theory for the description of run-up problem is discussed. The height of run-up on the beach of the basins with a “parabolic” profile is calculated for originally monochromatic wave.

Nonlinear Transformation of Long Waves at a Bottom Step

Mrichina, Nina R.,Pelinovsky, Efim N. 한국해안해양공학회 1992 한국해안해양공학회 논문집 Vol.4 No.3

서로 다른 유한수심을 갖는 두 영역을 연결하는 해저단위로 전파하는 비분산 유한진폭장파를 고려한다. 2차원 운동을 가정하고, 파봉선이 단과 평행하며, 비점성류체에서의 비회전운동으로 본다. 유한진폭파의 변형을 기술하기 위하여 유한진폭 천해정식과, 단위의 연결부에서 Riemann 변수로 나타낸 질양보존 및 압력연속조건들을 사용한다. 식들에 의하면 Riemann 불변양이 일정한 네 조의 특성유선과 입사, 반사 및 전달파의 진폭을 관련지어 주는 2개의 비선형방정식이 정의된다. 얻어진 방정식계는 통상의 형태로는 해석하기가 어려워 지진 해일파에 실용적으로 사용할 수 있는 특수한 경우만 고려한다. 얻어진 결과들을 장파이론과 비교하였고 아주 작은 진폭의 파인 경우에도 뚜렷한 비선형 효과가 제시되었다. We consider the preparation of long finite amplitude nondispersive waves over a step bottom between two regions of finite different depths. Two dimensional motion is assumed. with the wave crests parallel to the step, and irrotational flow in the inviscid fluid is considered. To describe the transformation of finite amplitude waves we use the finite-amplitude shallow-water equations, the conditions of mass flow conservation and pressure continuity at the cut above the step in Riemann's variables. The equations define four families of curves-characteristics on which the values of the Riemann's invariants remain constant and a system of two nonlinear equations that relates the amplitudes of incident reflected and transmitted waves. The system obtained is difficult to analyze in common form. Thus we consider some special cases having practical usage for tsunami waves. The results obtained are compared with the long wave theory and significant nonlinear effects are found even for quite small amplitude waves.

비선형 천해파의 스펙트라

Narcisse Zahibo,Ira Didenkulova,Efim Pelinovsky 한국해안,해양공학회 2007 한국해안해양공학회 논문집 Vol.19 No.4

The process of the nonlinear shallow water wave transformation in a basin of a constant depth is studied. Characteristics of the first breaking of the wave are analyzed in details. The Fourier spectrum and steepness of the nonlinear wave are calculated. It is shown that the spectral amplitudes can be expressed using the wave front steepness, which allows the practical estimations. 본 논문에서는 수심이 일정한 수조에서의 비선형 천해파의 변형 과정에 대한 연구를 수행하였다. 파랑의 최초 쇄파에 대한 특성을 자세히 분석하고, 비선형파의 경사 및 퓨리에 스펙트럼을 산정하였다. 분석결과 스펙트럼의 진폭은 실용적으로 추산이 가능한 파랑 경사를 이용하여 표현할 수 있다.

Transoceanic Propagation of 2011 East Japan Earthquake Tsunami

최병호,김경옥,민병일,Efim Pelinovsky 한국해양과학기술원 2014 Ocean and Polar Research Vol.36 No.3

The 2011 Tohoku earthquake triggered extremely destructive tsunami waves which propagated over the Pacific Ocean, Atlantic Ocean through Drake Passage and Indian Ocean respectively. A total of 10 tide-gauge records collected from the UNESCO/IOC site were analyzed through a band-pass digital filtering device to examine the observed tsunami characteristics. The ray tracing method and finite-difference model with GEBCO 30 arc second bathymetry were also applied to compare the travel times of the Tohoku-originated tsunami, particularly at Rodrigues in the Indian Ocean and King Edward Point in the Atlantic Ocean with observation-based estimates. At both locations the finite-difference model produced the shortest arrival times, while the ray method produced the longest arrival times. Values of the travel time difference however appear to be within tolerable ranges, considering the propagation distance of the tsunami waves. The observed tsunami at Rodrigues, Mauritius in the west of the Madagascar was found to take a clockwise travel path around Australia and New Zealand, while the observed tsunami at King Edward Point in the southern Atlantic Ocean was found to traverse the Pacific Ocean and then passed into the Atlantic Ocean through the Drake Strait. The formation of icebergs captured by satellite images in Sulzberger in the Antarctica also supports the long-range propagation of the Tohoku-originated tsunami.

Nonlinear Focusing Wave Group on Current

Touboul, Julien(쥬리언 투보),Pelinovsky, Efim(에핌 페리높스키),Kharif, Christian(크리스티안 카리프) 한국해안해양공학회 2007 한국해안해양공학회 논문집 Vol.19 No.3

심해에서 생성된 최극해파가 파랑과 상호작용하는 현상에 대한 연구를 수행하였다. 이러한 파랑은 분산집중을 이용하여 산정하였다. 이러한 과정은 선형 및 비선형 방정식의 해를 구하여 얻을 수 있다. 상호작용에서 비선형성의 역할을 강조하였다. Formation of freak waves is studied in deep water from transient wave packets propagating on current. Those waves are obtained by means of dispersive focusing. This process is investigated by solving both linear and nonlinear equations. The role of nonlinearity is emphasized in this interaction.