The transformation of a solitary wave on an underwater step is studied analytically and numerical... more The transformation of a solitary wave on an underwater step is studied analytically and numerically. The theoretical model includes the linear potential description of the wave transformation on a step and the weakly nonlinear theory of long waves based on the Korteweg-de Vries equation for reflected and transmitted waves far from a step. Numerical simulation of solitary wave transformation on an underwater step is performed in the framework of an extended 1D Boussinesq-like system and fully nonlinear fully dispersive 2D Navier-Stokes equations. The results of numerical simulations for the incident solitary wave of weak amplitude are in agreement with the theoretical predictions for the wave shapes of the secondary solitons, but not with the predictions for travel times. It is in press: E. Pelinovsky et al., Solitary wave transformation on the underwater step: Asymptotic theory and numerical experiments, Appled Mathematics Computation (2010), doi:10.1016/j.amc.2009.10.029
... Acknowledgments Belinda Barnes has made valuable contributions to this work. ... J. Phys. Oce... more ... Acknowledgments Belinda Barnes has made valuable contributions to this work. ... J. Phys. Oceanogr., 8, 1016 - 1024. Fennel, W., Seifert, T. and Kayser, B. (1991). Rossbi radii and phase speeds in the Baltic Sea, Cont. Shelf Res., 11, 23-36. Gan, J., and RC Ingran. (1992). ...
Various models are used to describe the avalanche and landslide motion: solid block model, shallo... more Various models are used to describe the avalanche and landslide motion: solid block model, shallow-water friction model, nonlinear-dispersive Boussinesq system, Reynolds-averaged Navier-Stokes equations. The solid block approximation allows to obtain the analytical solutions and easily realized numerically (Harbitz, 1993; Pelinovsky & Poplavsly, 1997; Watts, 2000). The shallow-water approximation is actively used to model the avalanche, volcanic flow, aerial and submarine landslides. Analytical solutions in the framework of simplified version of the shallow-water model are obtained by Mangeney et al (2000) and Rudenko et al (2007). Given paper extends this analysis and presents new solutions for the 2D landslide motion on the inclined plate.
Data of freak waves recorded by buoys (sensor: gyrometer, sampling rate: 2Hz, measurement duratio... more Data of freak waves recorded by buoys (sensor: gyrometer, sampling rate: 2Hz, measurement duration: 10min) in Taiwanese shallow waters are presented. Four events are discussed: 1) January 20, 2010, Abnormality index Ai = 2.56, Hualien buoy, depth 30 m, distance to the shore 1 km; 2) November 11, 2010, Abnormality index 2.53, Eluanbi Buoy, depth 40 m, distance to the shore 3 km; 3) August 9, 2009, Abnormality index 2.23, Hsinchu Buoy, depth 26 m, distance to the shore 2.5 km; and 4) May 4, 2009, Abnormality index 2.26, Longdong Buoy, depth 30 m, distance to the shore 1 km. All freak waves have sign-variable shape. The modeling of the freak waves is performed in the framework of the variable-coefficient Korteweg - de Vries equation taken into account the variability of the water depth in both, onshore and offshore directions. Results of numerical simulations are used to estimate the life-time of freak waves.
The transformation of a solitary wave on an underwater step is studied analytically and numerical... more The transformation of a solitary wave on an underwater step is studied analytically and numerically. The theoretical model includes the linear potential description of the wave transformation on a step and the weakly nonlinear theory of long waves based on the Korteweg-de Vries equation for reflected and transmitted waves far from a step. Numerical simulation of solitary wave transformation on an underwater step is performed in the framework of an extended 1D Boussinesq-like system and fully nonlinear fully dispersive 2D Navier-Stokes equations. The results of numerical simulations for the incident solitary wave of weak amplitude are in agreement with the theoretical predictions for the wave shapes of the secondary solitons, but not with the predictions for travel times. It is in press: E. Pelinovsky et al., Solitary wave transformation on the underwater step: Asymptotic theory and numerical experiments, Appled Mathematics Computation (2010), doi:10.1016/j.amc.2009.10.029
... Acknowledgments Belinda Barnes has made valuable contributions to this work. ... J. Phys. Oce... more ... Acknowledgments Belinda Barnes has made valuable contributions to this work. ... J. Phys. Oceanogr., 8, 1016 - 1024. Fennel, W., Seifert, T. and Kayser, B. (1991). Rossbi radii and phase speeds in the Baltic Sea, Cont. Shelf Res., 11, 23-36. Gan, J., and RC Ingran. (1992). ...
Various models are used to describe the avalanche and landslide motion: solid block model, shallo... more Various models are used to describe the avalanche and landslide motion: solid block model, shallow-water friction model, nonlinear-dispersive Boussinesq system, Reynolds-averaged Navier-Stokes equations. The solid block approximation allows to obtain the analytical solutions and easily realized numerically (Harbitz, 1993; Pelinovsky & Poplavsly, 1997; Watts, 2000). The shallow-water approximation is actively used to model the avalanche, volcanic flow, aerial and submarine landslides. Analytical solutions in the framework of simplified version of the shallow-water model are obtained by Mangeney et al (2000) and Rudenko et al (2007). Given paper extends this analysis and presents new solutions for the 2D landslide motion on the inclined plate.
Data of freak waves recorded by buoys (sensor: gyrometer, sampling rate: 2Hz, measurement duratio... more Data of freak waves recorded by buoys (sensor: gyrometer, sampling rate: 2Hz, measurement duration: 10min) in Taiwanese shallow waters are presented. Four events are discussed: 1) January 20, 2010, Abnormality index Ai = 2.56, Hualien buoy, depth 30 m, distance to the shore 1 km; 2) November 11, 2010, Abnormality index 2.53, Eluanbi Buoy, depth 40 m, distance to the shore 3 km; 3) August 9, 2009, Abnormality index 2.23, Hsinchu Buoy, depth 26 m, distance to the shore 2.5 km; and 4) May 4, 2009, Abnormality index 2.26, Longdong Buoy, depth 30 m, distance to the shore 1 km. All freak waves have sign-variable shape. The modeling of the freak waves is performed in the framework of the variable-coefficient Korteweg - de Vries equation taken into account the variability of the water depth in both, onshore and offshore directions. Results of numerical simulations are used to estimate the life-time of freak waves.
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