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## General initial value problem for the nonlinear shallow water equations: runup of tsunamis on sloping beaches and bays

Physics Letters A. 2018. Vol. 382. No. 38. P. 2738-2743.

Pelinovsky E., Rybkin A., Nicolsky D., Raz A.

We formulate a new approach to solving the initial value problem of the shallow water-wave equations utilizing the famous Carrier–Greenspan transformation (Carrier and Greenspan (1957) [9]). We use a Taylor series approximation to deal with the difficulty associated with the initial conditions given on a curve in the transformed space. This extends earlier solutions to waves with near shore initial conditions, large initial velocities, and in more complex U-shaped bathymetries; and allows verification of tsunami wave inundation models in a more realistic 2-D setting

Pelinovsky E., Kurkin A. A., Костенко И. С. et al., Известия РАН. Физика атмосферы и океана 2016 Т. 52 № 1 С. 100-112

Проведено исследование особенностей распространения цунами 11 марта 2011 г. в северовосточ ной части Тихого океана для выявления степени влияния Курильских островов на проникновение цунами в Охотское море. Для этого проведена серия вычислительных экспериментов в рамках тео рии мелкой воды с использованием двух батиметрий: 1) с Курильскими островами; 2) без Куриль ских островов. Выполнен анализ рассчитанных ...

Added: October 29, 2016

Pelinovsky E., Choi B. H., Kim K. O. et al., Ocean and Polar Research 2015 Vol. 37 No. 1 P. 1-9

An approach based on the combined use of a 2D shallow water model and analytical 1D long
wave run-up theory is proposed which facilitates the forecasting of tsunami run-up heightsin a more rapid way, compared with the statistical or empirical run-up ratio method or resorting to complicated coastal inundation models. Its application is advantageous for long-term ...

Added: April 5, 2015

Pelinovsky E., Rybkin A., Nicolsky D. et al., Pure and Applied Geophysics 2015 Vol. 172 No. 3-4 P. 885-899

Abstract—Long nonlinear wave runup on the coasts of trapezoidal bays is studied analytically in the framework of one-dimensional (1-D) nonlinear shallow-water theory with crosssection averaging, and is also studied numerically within a twodimensional (2-D) nonlinear shallow water theory. In the 1-D theory, it is assumed that the trapezoidal cross-section channel is inclined linearly to the ...

Added: April 5, 2015

Pelinovsky E., Kurkin A. A., Костенко И. С. et al., Известия РАН. Физика атмосферы и океана 2016 Т. 52 № 2 С. 246-254

Произошедшее 24 мая 2013 г. в акватории Охотского моря землетрясение магнитудой 8.3 явилось наиболее сильным в этом регионе. Проведено моделирование возможного цунами от такого земле трясения. Расчеты подтвердили, что высоты волн достаточно малы, поскольку глубина гипоцентра землетрясения была 640 км. Дан анализ колебаний буев DART в окрестности очага землетрясения. Показано, что они не связаны с ...

Added: October 29, 2016

Зайцев А. И., Бабейко А. Ю., Kurkin A. A. et al., Известия РАН. Физика атмосферы и океана 2019 Т. 55 № 5 С. 462-469

Tsunami forecast possibilities for areas with a small base of historical tsunamis have been discussed
using the Probabilistic Tsunami Hazard Assessment (PTHA) method, which is based on a statistical analysis
of a sufficiently large number of real and predictive earthquakes with a subsequent calculation of possible tsunami
waves. This method has been used for a long-term tsunami hazard ...

Added: October 30, 2019

Pelinovsky E., Rybkin A., Nikolsky D. et al., JOURNAL OF GEOPHYSICAL RESEARCH-OCEANS 2018 Vol. 123 No. 3 P. 2066-2080

Modeling of tsunamis in glacial fjords prompts us to evaluate applicability of the crosssectionally
averaged nonlinear shallow water equations to model propagation and runup of long waves in
asymmetrical bays and also in fjords with two heads. We utilize the Tuck-Hwang transformation, initially
introduced for the plane beaches and currently generalized for bays with arbitrary cross section, to ...

Added: October 21, 2018

Zaytsev A. I., Kurkin A. A., Pelinovsky E. et al., Journal of Applied Mechanics and Technical Physics 2020 Vol. 61 No. 7 P. 1140-1152

Mathematical models that are applicable to the simulation of the generation and propagation
of tsunami waves from different sources, that is, underwater earthquakes, submarine landslides,
and meteotsunamis, are described. The models are based on the well-known nonlinear shallow-water
theory and its dispersion generalizations in two horizontal dimensions. Long wave dispersion related
to the finiteness of water depth increases the ...

Added: March 8, 2021

Oshmarina O. E., Averbukh E. L., Kurkin A. A., Труды НГТУ им. Р.Е. Алексеева 2010 № 2(81) С. 49-56

In the present work the results of different scenario of the cliff of Cape Canaille hypothetic collapse (South of France) are presented. Three scenarios were considered: falling of one block, falling of several blocks in one time and debris flow avalanche. The analysis of the entire scenario was done. ...

Added: November 5, 2012

Pelinovsky E., Didenkulova I., Pure and Applied Geophysics 2018 Vol. 175 No. 4 P. 1387-1391

We solve analytically a nonlinear problem of shallow water theory for the tsunami wave run-up on a vertical wall in
tidal environment. Shown that the tide can be considered static in the process of tsunami wave run-up. In this approximation, it is possible to obtain the exact solution for the run-up height as a function of the incident wave height. ...

Added: October 21, 2018

Pelinovsky E., Choi B. H., Kim K. O. et al., Natural Hazards and Earth System Sciences 2015 Vol. 15 No. 4 P. 747-755

The tsunami generated on 12 July 1993 by the Hokkaido–Nansei–Oki earthquake (Mw D7.8) brought about a maximum wave run-up of 31.7 m, the highest recorded in Japan during the 20th century, near the Monai Valley on the west coast of Okushiri Island (Hokkaido
Tsunami Survey Group, 1993). To reproduce the extreme run-up height, the three-dimensional non-hydrostatic ...

Added: August 4, 2015

Choi B. H., Min B. I., Pelinovsky E. et al., Natural Hazards and Earth System Sciences 2012 Vol. 12 P. 1463-1467

Data from a field survey of the 2011 Tohoku-oki tsunami in the Sanriku area of Japan is used to plot the distribution function of runup heights along the coast. It is shown that the distribution function can be approximated by a theoretical log-normal curve. The characteristics of the distribution functions of the 2011 event are ...

Added: May 17, 2012

Kurkin A., Belyakov V., Makarov V. et al., Science of Tsunami Hazards 2016 Vol. 35 No. 2 P. 68 -83

In our paper we describe some of the methods of the last 25 years which have been used extensively to examine and register tsunami traces - particularly by satellite imaging of coastal zones before and after a tsunami has struck, thus assessing quickly the extent of coastal inundation over large areas without the need of ...

Added: July 7, 2016

Pelinovsky E., Didenkulova I., Didenkulov O., J Ocean Engineering and Marine Energy, Springer 2015 Vol. 1 No. 2 P. 199-205

In practice, when tsunami approaches the coast and the time for decision making and issuing warning alert is limited, design formulas for fast estimation of tsunami runup characteristics are applied. Themost famous and themost used among them assume that incoming wave has a solitonic shape. However, the exact shape of the incoming wave is usually ...

Added: August 4, 2015

Родин А. А., Родина Н. А., Kurkin A. A. et al., Известия РАН. Физика атмосферы и океана 2019 Т. 55 № 4 С. 82-86

The influence of nonlinear interaction of oppositely directed nonlinear waves in a shallow basin is
studied theoretically and numerically within the nonlinear theory of shallow water. It is shown that this interaction
leads to a change in the phase of propagation of the main wave, which is forced to propagate along the
flow induced by the oncoming wave. ...

Added: October 30, 2019

Pelinovsky E., Choi B. H., Kim K. O. et al., Ocean and Polar Research 2015 Vol. 37 No. 2 P. 91-105

In this paper we investigated the phenomenon of extreme run-up at Babi Island in Indonesia
caused by the 1992 Flores earthquake (Mw = 7.8) using a series of three-dimensional numerical modeling experiments. Simulations were carried out to investigate how much the presence/absence of the coast of Flores affects the generation of the extreme inundation at Babi ...

Added: August 4, 2015

Rybkin A., Nikolsky D., Pelinovsky E. et al., Water Waves 2021 Vol. 3 No. 1 P. 267-296

We put forward a solution to the initial boundary value (IBV) problem for the nonlinear
shallow water system in inclined channels of arbitrary cross section by means of
the generalized Carrier–Greenspan hodograph transform (Rybkin et al. in J Fluid
Mech, 748:416–432, 2014). Since the Carrier–Greenspan transform, while linearizing
the shallow water system, seriously entangles the IBV in the hodograph ...

Added: April 21, 2021

Окубо Ю. undefined., Journal of Physics: Conference Series 2017 Vol. 804 No. 012036 P. 1-8

We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric functions. ...

Added: October 26, 2017

Andrew G. Semenov, Zaikin A., Physical Review B: Condensed Matter and Materials Physics 2013 Vol. 88 No. 5 P. 054505-1-054505-10

We investigate the effect of interacting quantum phase slips on persistent current and its fluctuations in ultrathin superconducting nanowires and nanorings pierced by the external magnetic flux. We derive the effective action for these systems and map the original problem onto an effective sine-Gordon theory on torus. We evaluate both the flux dependent persistent current ...

Added: February 9, 2015

Slunyaev A., Кокорина А. В., Water Waves, Springer 2019 P. 1-20

The issue of accounting of the wave breaking phenomenon in direct numerical simulations of oceanic waves is discussed. It is emphasized that this problem is crucial for the deterministic description of waves, and also for the dynamical calculation of extreme wave statistical characteristics, such as rogue wave height probability, asymmetry, etc. The conditions for accurate ...

Added: October 13, 2019

Marshakov A., Миронов А. Д., Морозов А. Ю., Journal of Geometry and Physics 2011 Vol. 61 P. 1203-1222

We present a summary of current knowledge about the AGT relations for conformal blocks with additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, when the conformal blocks satisfy hypergeometric-type differential equations in position of the degenerate operator. A special attention is devoted to representation of conformal block ...

Added: February 28, 2013

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Prazdnichnykh A., Glazov M., Ren L. et al., Physical Review B: Condensed Matter and Materials Physics 2021 Vol. 103 No. 8 P. 085302-1-085302-12

The exciton valley dynamics in van der Waals heterostructures with transition metal dichalcogenide monolayers is driven by the long-range exchange interaction between the electron and the hole in the exciton. It couples the states active in the opposite circular polarizations resulting in the longitudinal-transverse splitting of excitons propagating in the monolayer plane. Here we study ...

Added: March 5, 2021

Pelinovsky E., Didenkulova I., Rybkin A., Journal of Fluid Mechanics 2014 Vol. 748 P. 416-432

We present an exact analytical solution of the nonlinear shallow water theory for wave run-up in inclined channels of arbitrary cross-section, which generalizes previous studies on wave run-up for a plane beach and channels of parabolic cross-section. The solution is found using a hodograph-type transform, which extends the well-known Carrier–Greenspan transform for wave run-up on ...

Added: November 19, 2014

Pelinovsky E., Kurkin A. A., Kozelkov A. et al., European Journal of Mechanics - B/Fluids 2018 Vol. 72 P. 616-623

The paper presents results of numerical simulations of freely rising solid spheres in a viscous fluid. The
diameter of spheres was 5 mm, 7 mm, 10 mm, and 20 mm, and the corresponding Reynolds numbers
varies in the interval 1400 < Re < 10100. It has been found that the free rise path varies, as the
Galileo number ...

Added: October 21, 2018