scholarly journals RUN-UP OF TSUNAMIS BY LINEAR AND NONLINEAR THEORIES

1980 ◽  
Vol 1 (17) ◽  
pp. 42 ◽  
Author(s):  
Chiaki Goto ◽  
Nobuo Shuto
Keyword(s):  
Numerical Results ◽  
Long Waves ◽  
Lagrangian Description ◽  
Practical Application ◽  
Linear And Nonlinear ◽  
Run Up

Linear and nonlinear sets of equations of long waves in the Lagrangian description are solved numerically to obtain run-up heights. Numerical results are compared -with theoretical ones in case of simple topographies and the agreement is quite satisfactory. As a practical application, the computation is carried out for the Okkirai Bay in Japan. The computed run-up neighs agree fairly well with the recorded ones.

scholarly journals Reduction of maximum tsunami run-up due to the interaction with beachfront development – application of single sinusoidal waves

2013 ◽  
Vol 13 (11) ◽  
pp. 2991-3010 ◽  
Author(s):  
N. Goseberg
Keyword(s):  
Long Waves ◽  
Practical Application ◽  
Similarity Parameter ◽  
Wave Flume ◽  
Concrete Blocks ◽  
Run Up ◽  
Tsunami Run Up ◽  
The Waves ◽  
Development Application ◽  
Horizontal Bottom

Abstract. Experiments are presented that focus on the interaction of single sinusoidal long waves with beachfront development on the shore. A pump-driven methodology is applied to generate the tested waves in the wave flume. The approaching waves firstly propagate over a horizontal bottom, then climbing up a 1 in 40 beach slope. The experiments reported here are confined to the surf similarity parameter of the waves ranging from ξ =7.69–10.49. The maximum run-up of the tested waves under undisturbed conditions agrees well with analytical results of of Madsen and Schäffer (2010). Beachfront development is modelled with cubic concrete blocks (macro-roughness (MR) elements). The obstruction ratio, the number of element rows parallel to the shoreline as well as the way of arranging the MR elements influences the overall reduction of maximum run-up compared to the undisturbed run-up conditions. Staggered and aligned as well as rotated and non-rotated arrangements are tested. As a result, nomograms are finally compiled to depict the maximum run-up reduction over the surf similarity parameter. In addition, some guidance on practical application of the results to an example location is given.

scholarly journals Focusing of long waves with finite crest over constant depth

2013 ◽  
Vol 469 (2153) ◽  
pp. 20130015 ◽  
Author(s):  
Utku Kânoğlu ◽  
Vasily V. Titov ◽  
Baran Aydın ◽  
Christopher Moore ◽  
Themistoklis S. Stefanakis ◽  
...  
Keyword(s):  
Source Region ◽  
Wave Theory ◽  
Long Waves ◽  
Constant Depth ◽  
Large Wave ◽  
Weakly Nonlinear ◽  
Scaling Relationships ◽  
2011 Japan Tsunami ◽  
Wave Heights ◽  
Run Up

Tsunamis are long waves that evolve substantially, through spatial and temporal spreading from their source region. Here, we introduce a new analytical solution to study the propagation of a finite strip source over constant depth using linear shallow-water wave theory. This solution is not only exact, but also general and allows the use of realistic initial waveforms such as N -waves. We show the existence of focusing points for N -wave-type initial displacements, i.e. points where unexpectedly large wave heights may be observed. We explain the effect of focusing from a strip source analytically, and explore it numerically. We observe focusing points using linear non-dispersive and linear dispersive theories, analytically; and nonlinear non-dispersive and weakly nonlinear weakly dispersive theories, numerically. We discuss geophysical implications of our solutions using the 17 July 1998 Papua New Guinea and the 17 July 2006 Java tsunamis as examples. Our results may also help to explain high run-up values observed during the 11 March 2011 Japan tsunami, which are otherwise not consistent with existing scaling relationships. We conclude that N -waves generated by tectonic displacements feature focusing points, which may significantly amplify run-up beyond what is often assumed from widely used scaling relationships.

A Coupled-Mode Technique for the Run-Up of Non-Breaking Dispersive Waves on Plane Beaches

2006 ◽  
Author(s):  
K. A. Belibassakis ◽  
G. A. Athanassoulis
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Wave Equations ◽  
Neumann Boundary ◽  
Breaking Waves ◽  
Numerical Results ◽  
Coupled Mode Theory ◽  
Mode Theory ◽  
Coupled Mode ◽  
Run Up

A coupled-mode model is developed and applied to the transformation and run-up of dispersive water waves on plane beaches. The present work is based on the consistent coupled-mode theory for the propagation of water waves in variable bathymetry regions, developed by Athanassoulis & Belibassakis (1999) and extended to 3D by Belibassakis et al (2001), which is suitably modified to apply to a uniform plane beach. The key feature of the coupled-mode theory is a complete modal-type expansion of the wave potential, containing both propagating and evanescent modes, being able to consistently satisfy the Neumann boundary condition on the sloping bottom. Thus, the present approach extends previous works based on the modified mild-slope equation in conjunction with analytical solution of the linearised shallow water equations, see, e.g., Massel & Pelinovsky (2001). Numerical results concerning non-breaking waves on plane beaches are presented and compared with exact analytical solutions; see, e.g., Wehausen & Laitone (1960, Sec. 18). Also, numerical results are presented concerning the run-up of non-breaking solitary waves on plane beaches and compared with the ones obtained by the solution of the shallow-water wave equations, Synolakis (1987), Li & Raichlen (2002), and experimental data, Synolakis (1987).

scholarly journals RUN-UP OF PERIODIC WAVES ON BEACHES OF NON-UNIFORM SLOPE

1984 ◽  
Vol 1 (19) ◽  
pp. 23 ◽  
Author(s):  
Yoshinobu Ogawa ◽  
Nobuo Shuto
Keyword(s):  
Experimental Data ◽  
Wave Theory ◽  
Breaking Waves ◽  
Lagrangian Description ◽  
Periodic Waves ◽  
Swash Zone ◽  
Slope Method ◽  
Long Wave ◽  
Run Up ◽  
Better Than

Run-up of periodic waves on gentle or non-uniform slopes is discussed. Breaking condition and run-up height of non-breaking waves are derived "by the use of the linear long wave theory in the Lagrangian description. As to the breaking waves, the width of swash zone and the run-up height are-obtained for relatively gentle slopes (less than 1/30), on dividing the transformation of waves into dissipation and swash processes. The formula obtained here agrees with experimental data better than Hunt's formula does. The same procedure is applied to non-uniform slopes and is found to give better results than Saville's composite slope method.

Run-Up of Long Waves on a Sloping Beach

1967 ◽  
Vol 10 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Nobuo Shuto
Keyword(s):  
Long Waves ◽  
Run Up ◽  
Sloping Beach

scholarly journals Run-up of long waves generated by bottom-tilting wave maker

2019 ◽  
Vol 58 (1) ◽  
pp. 47-59 ◽  
Author(s):  
Heng Lu ◽  
Yong Sung Park ◽  
Yong-Sik Cho
Keyword(s):  
Long Waves ◽  
Wave Maker ◽  
Run Up

scholarly journals A High Accurate and Stable Legendre Transform Based on Block Partitioning and Butterfly Algorithm for NWP

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 966
Author(s):  
Fukang Yin ◽  
Jianping Wu ◽  
Junqiang Song ◽  
Jinhui Yang
Keyword(s):  
Computational Complexity ◽  
Error Analysis ◽  
Numerical Stability ◽  
High Order ◽  
Numerical Results ◽  
Computational Time ◽  
Legendre Transform ◽  
Practical Application ◽  
Block Partitioning ◽  
Very High

In this paper, we proposed a high accurate and stable Legendre transform algorithm, which can reduce the potential instability for a very high order at a very small increase in the computational time. The error analysis of interpolative decomposition for Legendre transform is presented. By employing block partitioning of the Legendre-Vandermonde matrix and butterfly algorithm, a new Legendre transform algorithm with computational complexity O(Nlog2N /loglogN) in theory and O(Nlog3N) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm.

A Discriminant Parameter Determining Technique in Variational Multiscale Method for Stokes Equations

2016 ◽  
Vol 14 (05) ◽  
pp. 1750048
Author(s):  
Lin-Feng Chen ◽  
Xu-Qu Hu
Keyword(s):  
Constrained Optimization ◽  
Stokes Equations ◽  
Nonlinear Models ◽  
Multiscale Method ◽  
Numerical Results ◽  
Variational Multiscale Method ◽  
Scale Invariant ◽  
Variational Multiscale ◽  
Linear And Nonlinear

A Goal-Oriented and Model-Constrained Optimization (GOMCO) approach was proposed as a discriminant technique for the Variational Geomano Method (VGM) in the coefficient determinations of variational multiscale Unresolved-Scale (URS) model in steady Stokes equations. Numerical implementations using both linear and nonlinear models were performed with both the GOMCO and VGM. Numerical results show that the coefficients determined by the GOMCO are scale-invariant, while they are scale-variant by the VGM. The GOMCO technique is found to be more appropriate for coefficient determinations in steady Stokes equations, as the VGM is sensitive to the computing procedures. Moreover, the GOMCO could provide reliable coefficients for the URS model.

Blade Life: A Comparison by Cumulative Damage Theories

1999 ◽  
Vol 123 (4) ◽  
pp. 886-892 ◽  
Author(s):  
J. S. Rao ◽  
A. Pathak ◽  
A. Chawla
Keyword(s):  
Modal Analysis ◽  
Turbine Blade ◽  
Flow Path ◽  
Cumulative Damage ◽  
Practical Application ◽  
Dynamic Stresses ◽  
Linear And Nonlinear ◽  
Comparison Of The Results

A turbine blade is modeled as a rotating pretwisted beam and subjected to aerodynamic excitation from the flow path interference. The resonant stresses are determined using a modal analysis. With the help of steady steam bending and centrifugal stresses and the dynamic stresses, life estimates are made using the linear and nonlinear cumulative damage theories and a comparison of the results is presented. Based on these results, recommendations are made on the usefulness of different theories for practical application.

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