Experiments on generation of surface waves by an underwater moving bottom (original) (raw)
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Cornell University - arXiv, 2014
We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes a sudden upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are usually neglected in tsunami warning systems. Our results display good agreement with a prevailing linear theory without fitting parameter. Based on our experimental data, we provide a new theoretical approach for the rapid kinematics limit that is applicable even for non-flat bottoms: a key step since most approaches assume a uniform depth. This approach can be easily appended to tsunami simulations under arbitrary topography.
Water waves generated by a moving bottom
2006
Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results based on the analytical solutions are shown for the free-surface profiles, the horizontal and vertical velocities as well as the bottom pressure.
Transformation of Long Surface and Tsunami-Like Waves in the Ocean with a Variable Bathymetry
Pure and Applied Geophysics, 2019
We consider a transformation of long linear waves in an ocean with a variable depth.We calculate the transformation coefficients (the coefficients of transmission and reflection) as the functions of frequency and the total depth drop for three typical models of bottom profile variation: (i) piecewise-linear, (ii) piecewise-quadratic, and (iii) hyperbolic tangent profiles.For all these cases, exact solutions are obtained, analysed and graphically illustrated. This allows us to derive the transformation coefficients in the analytic form for the subsequent comparison with the results of approximate, numerical, or experimental study. We show that the results obtained are in agreement with both the energy flux conservation and Lamb's formulae in the limiting case of zero frequency. We also study wave transformation on the underwater barriers and trenches of different shapes and compare the results obtained.
Simulation of Tsunami Propagation with Space-varying Seafloor Topography
2010
Tsunami is generated by a sudden deformation of the seafloor, such as uplift and subsidence, caused by fault motion of an earthquake below the seafloor. Numerical simulation of tsunami propagation is frequently used to predict the arrival time and the order of magnitude of the inundation for disaster mitigation purposes. In the propagation process, reflected waves are generated by the change in water depths and influence the tsunami height estimation, in particular in the later phases. In this study, we try to simulate tsunami propagation to accommodate the 2-D varying seafloor topography. In our simulation code, we assume water as a non-viscous fluid. A finite difference method (FDM) is employed using three equations; the equations of continuity, motion, and barotropy. In this study, we simulate the tsunami generation by a sudden change in the water depth and the propagation, using the Pearson approximation to accommodate the spatially varying water depth. We impose the seafloor topography on the basis of the 500m-mesh bathymetry data that JODC (Japan Oceanographic Data Center) provides. We assume a domain included in the data region and simulate tsunami. By using this method, we are able to calculate not only the propagation velocity due to the change in the water depth, but also reflected waves at the same time.
Journal of Computational Physics, 2007
A fully nonlinear and fully dispersive method for the interaction between free surface waves and a variable bottom topography in space and time in three dimensions is derived. A Green function potential formulation expresses the normal velocity of the free surface in terms of the bathymetry and its motion. An explicit, fast version of the method is derived in Fourier space with evaluations using FFT. Practice shows that the explicit method captures the most essential parts of the wave field. This leads to a time-integration that is very accurate and orders of magnitude faster than existing full potential formulation methods. Fully resolved simulations of the nonlinear and dispersive wave fields are enabled from the generation to the shoaling of the waves, including the onshore flow which is handled by suitable numerical beaches.
Generation of two-dimensional water waves by moving bottom disturbances
2012
We investigate the potential and limitations of the wave generation by disturbances moving at the bottom. More precisely, we assume that the wavemaker is composed of an underwater object of a given shape which can be displaced according to a prescribed trajectory. We address the practical question of computing the wavemaker shape and trajectory generating a wave with prescribed characteristics. For the sake of simplicity we model the hydrodynamics by a generalized forced Benjamin-Bona-Mahony (BBM) equation. This practical problem is reformulated as a constrained nonlinear optimization problem. Additional constraints are imposed in order to fulfill various practical design requirements. Finally, we present some numerical results in order to demonstrate the feasibility and performance of the proposed methodology.
Journal of Marine Science and Engineering
According to recent investigations on bottom boundary layer development under tsunami, a wave boundary can be observed even at the water depth of 10 m, rather than a steady flow type boundary layer. Moreover, it has been surprisingly reported that the tsunami boundary layer remains laminar in the deep-sea area. For this reason, the bottom boundary layer under tsunami experiences two transitional processes during the wave shoaling: (1) flow regime transition in a wave-motion boundary layer from laminar to the turbulent regime, and (2) transition from non-depth-limited (wave boundary layer) to depth-limited boundary layer (steady flow boundary layer). In the present study, the influence of these two transition processes on tsunami wave height damping has been investigated using a wave energy flux model. Moreover, a difference of calculation results by using the conventional steady flow friction coefficient was clarified.
2006
The life of a tsunami is usually divided into three phases: the generation (tsunami source), the propagation and the inundation. Each phase is complex and often described separately. A brief description of each phase is given. Model problems are identified. Their formulation is given. While some of these problems can be solved analytically, most require numerical techniques. The inundation phase is less documented than the other phases. It is shown that methods based on Smoothed Particle Hydrodynamics (SPH) are particularly well-suited for the inundation phase. Directions for future research are outlined. 4 Energy of a tsunami 23 5 Tsunami run-up 23 6 Direction for future research 26
Geophysical Journal International, 2009
The present study investigates the tsunami generation process by using 3-D numerical simulations and the linear potential theory. First, we evaluate the relation between sea-bottom elevation and sea-surface elevation as function of source size L, sea depth H and source duration T, based on 3-D numerical simulations. The surface elevation decreases with increasing sea depth and source duration. The difference between the sea-bottom and the sea-surface elevation appears when the source size is smaller than approximately 10 times the sea depth for a short source duration. The linear potential theory can precisely predict the numerical simulation results. Based on the theory, we can consider the tsunami generation as two spatial lowpass filter processes, in which the cutoff wavenumbers are given by the sea depth and the source duration. The criteria for small source size and short source duration are given as L < 13H and T < L/(8c), respectively, where c is the phase velocity of the tsunami. We then simulate the tsunami generation of the 1896 Sanriku tsunami earthquake, Japan. The simulated sea-surface elevation is significantly different from the sea-bottom elevation, which suggests the need for correction of the sea depth and source duration for the precise evaluation of the initial water-height distribution. To include these effects in 2-D simulations, we can use the impulse response function and add the fractional sea-surface uplift within the time step to the sea surface, for each time step.