Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
33
1
2006
PREFACE
1-1
Victor T.
Grinchenko
Institute of Hydromechanics, National Academy of Science of Ukraine, Kyiv, Ukraine
Rama Subba Reddy
Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA
Simulation of Surface Waves Induced by Landslides
2-14
Z. I.
Fedotova
Institute of Computational Technologies, Siberian Branch of Russsian Academy of Sciences, Academician M. A. Lavrentjev Ave., 6, 630090, Novosibirsk, Russia
L. B.
Chubarov
Institute of Computational Technologies, Siberian Branch of Russsian Academy of Sciences, Academician M. A. Lavrentjev Ave., 6, 630090, Novosibirsk, Russia
Yu. I.
Shokin
Institute of Computational Technologies, Siberian Branch of Russsian Academy of Sciences, Academician M. A. Lavrentjev Ave., 6, 630090, Novosibirsk, Russia
The paper addresses the problems of construction of numerical models for generation and transformation of long surface waves induced by landslides. The authors specify the basic mathematical models, expound the principles, on which the computational algorithms are constructed, and discuss the computational result.
Propagation of the Dec. 26, 2004, Indian Ocean Tsunami: Effects of Dispersion and Source Characteristics
15-43
Sylfest
Glimsdal
Simula Research Laboratory P.O. Box 134, N-1325 Lysaker; Department of Informatics, University of Oslo; International Center for Geohazards (ICG), Oslo, Norway
G. K.
Pedersen
Department of Mathematics, Mechanics Division, University of Oslo, P.O. Box 1053, N-0316 Oslo; International Center for Geohazards (ICG), Oslo, Norway
K.
Atakan
Department of Earth Science, University of Bergen, Norway
C. B.
Harbitz
Norwegian Geotechnical Institute (NGI); International Center for Geohazards (ICG), Oslo, Norway
H. P.
Langtangen
Simula Research Laboratory P.O. Box 134, N-1325 Lysaker, Department of Informatics, University of Oslo, Norway
F.
Lovholt
Norwegian Geotechnical Institute (NGI), Oslo; International Center for Geohazards (ICG), Oslo, Norway
This work presents numerical simulations of the tsunami generated by the Dec. 26, 2004, Sumatra-Andaman earthquake. The numerical models employed include the linear shallow water equations, a weakly nonlinear and dispersive model (Boussinesq equations), and ray theory for linear hydrostatic waves. Four different tsunami sources, constructed from inversion models based on seismo-logical recordings, are studied. We have investigated the sensitivity to the choice of mathematical model, grid resolution, source parameters, and delay of tsunami generation at the northern part of the source area. The results are compared to surface elevation recordings. Numerical simulations show that the effect of dispersion may modify the waves (slightly) during long propagation times only, and dispersion is not observed in the tsunami generation phase. In some shallow regions, on the other hand, nonlinear steepening of the wave front may enhance dispersion, and undular bores may be produced, which cannot be modeled by the standard shallow water equations commonly used for tsunami simulation. The sensitivity analysis results provide important insights to the source complexity of the Dec. 26, 2004, earthquake.
Modeling of Tsunami Wave Generation and Propagation
44-54
Igor T.
Selezov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Zhelyabov St., 8/4, Kyiv, 03680, MSP, Ukraine
The paper deals with the problem of tsunami wave generation and propagation. Two problems are considered. One problem is the tsunami wave generation by disturbed floor. The corresponding initial boundary value problems are considered to analyze the influence of the sharpness of axisymmetric bottom vertical displacement and the sharpness of time excitation on tsunami wave generation. Another problem considers nonlinear water wave propagation and evolution over the disturbed and elastically compliant floor. Some features and indeterminacy is setting the initial boundary value problems for tsunami origination and generation are discussed.
Impulsive Free-Surface Flow Due to Rapid Deflection of an Initially Horizontal Bottom. Part I. Formulation and Temporal Expansion
55-75
K. B.
Haugen
Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P. O. Box 5003, 1432 As, Norway
P. A.
Tyvand
Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P. O. Box 5003, 1432 As, Norway
An analytical third-order small-time expansion is developed for the inviscid, incompressible free-surface flow generated by impulsive deflection of an initially horizontal bottom. The deflection starts with nonzero velocity. The deflection is rapid, which means that its duration is smaller than the gravitational time. The deflection function obeys the constraint of being separable in space and time, but is otherwise arbitrary. Nonlinear effects are taken into account at the bottom as well as at the free surface. Temporal functions are determined to third order. Three special cases are demonstrated.
Impulsive Free-Surface Flow Due to Rapid Deflection of an Initially Horizontal Bottom. Part II. Spatial Dependency
76-105
K. B.
Haugen
Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P. O. Box 5003, 1432 As, Norway
P. A.
Tyvand
Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P. O. Box 5003, 1432 As, Norway
An analytical third-order small-time expansion is developed for inviscid, incompressible free-surface flow generated by impulsive deflection of an initially horizontal bottom. The deflection is rapid, and the deflection function is assumed separable in space and time. Nonlinear effects are taken into account at the bottom as well as at the free surface. The theory is formulated in both two and three dimensions. The spatial solutions to each order are given in terms of Fourier integrals. These solutions are evaluated numerically for rising rectangular and cylindrical blocks.
Tsunami Wave Runup on Coasts of Narrow Bays
106-118
E. N.
Pelinovsky
Departement de Physique, Universite des Antilles et de la Guyane, UFR Sciences, Campus de Fouillole, 97159 Pointe a Pitre Cedex, Guadeloupe, France; Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia
N.
Zahibo
Departement de Physique, Universite des Antilles et de la Guyane, UFR Sciences, Campus de Fouillole, 97159 Pointe a Pitre Cedex, Guadeloupe, France
V.
Golinko
Department of Applied Mathematics, Nizhny Novgorod Technical University, 24 Minin Str., Nizhny Novgorod, 603950, Russia
N.
Osipenko
Department of Applied Mathematics, Nizhny Novgorod Technical University, 24 Minin Str., Nizhny Novgorod, 603950, Russia
The runup of tsunami waves on the coasts of the narrow bays, channels and straits is studied in the framework of the nonlinear shallow water theory. Using the narrowness of the water channel, the one-dimensional equations are applied; they include the variable cross-section of the channel. It is shown that the analytical solutions can be obtained with the use of the hodograph (Legendre) transformation similar to the wave runup on the plane beach. As a result, the linear wave equation is derived and all physical variables (water displacement, fluid velocity, coordinate and time) can be determined. The dynamics of the moving shoreline (boundary of the flooding zone) is investigated in details. It is shown that all analytical formulas for the moving shoreline can be obtained explicitly. Two examples of the incident wave shapes are analyzed: sine wave and parabolic pulse. The last example demonstrates that even for approaching of the crest only, the flooding can appear very quickly; then water will recede relatively slowly, and then again quickly return to the initial state.