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1.
The role of bottom friction in the runup of nonbreaking long waves on the shore is analyzed. The case of the normal incidence of monochromatic waves is considered. The relief of the model region consists of an even horizontal bottom area conjugated with a flat slope. The energy dissipation is estimated as the work of bottom friction forces over the wave field obtained using the known analytical solution based on the Carrier-Greenspan transforms. Estimates of energy losses for waves whose periods are typical for tsunami waves have been obtained. The energy dissipation is shown to be not concentrated in the shore line area as a rule. The question about the practicability of using partially reflecting boundary conditions on the coast to take into account the bottom friction in large-scale models of tsunami propagation is considered. 相似文献
2.
M. A. Nosov G. N. Nurislamova A. V. Moshenceva S. V. Kolesov 《Izvestiya Atmospheric and Oceanic Physics》2014,50(5):520-531
The linear theory of long waves was applied to study horizontal motions of the water layer in a rotating ocean which appear after tsunami generation by an earthquake. The structures of residual potential and eddy fields are analyzed on the basis of the analytical solution of a model axisymmetric problem for an ocean of constant depth. The estimates of the horizontal displacements of water particles, velocity of the eddy current, and energy of the geostrophic eddy are calculated for typical conditions of the tsunami source. Particular features of the residual fields related to the existence of stable stratification are considered. Static and dynamic numerical models are described that allow us to calculate the residual potential field and its evolution related to the realistic events. The field of residual horizontal displacements of water particles for the catastrophic earthquake near the coasts of Japan on March 11, 2011, is calculated and analyzed. 相似文献
3.
A. Hayir B. Seseogullari İ. Kilinc A. Erturk H.K. Cigizoglu M.S. Kabdasli O. Yagci K. Day 《Coastal Engineering》2008
In this paper the tsunamis resulting from a submarine mass failure such as slides and slumps triggered by earthquakes or other environmental effects, which is settled at the bottom of the north eastern Sea of Marmara are examined in one sample region. As the solution method, one hybrid method is developed. The main objective of this method is to combine an analytical solution presenting near-field tsunami amplitudes above the submarine mass failure with a numerical solution indicating the tsunami amplitudes in the coastal regions. For this purpose, one common linear boundary between analytical and numerical solution domains is defined. Movements of Submarine Mass Failures (SMF) are modeled using one simple kinematics source model and the amplitudes of the tsunamis at the region that are closer to the landslide are computed by using the analytical method. SMF is modeled approximately from the bottom geometry, and an average depth is used. Scenarios of SMF are established depending on the velocities and thicknesses of the failure, and near-field tsunami amplitudes are obtained in the open sea during the source time. After the source times, the solutions are found in the numerical region using TELEMAC-2D software system with the mentioned boundary above. In this boundary, the output of the analytical solutions is taken as the boundary conditions or the disturbances for the numerical method. With these disturbances, the numerical method is performed and the amplitudes are calculated in the coastal area. The generation, propagation and coastal amplifications of the tsunamis are illustrated at some certain points and regions both in the open sea and near the coast line. The results have been visualized and discussed. 相似文献
4.
Abstract In this article three main stages of tsunami wave evolution are investigated. At first, the development of disturbances from a given patched elevation of the bottom surface in an incompressible nonviscous fluid of the uniform depth is considered. Then, a tsunami wave diffraction by underwater bottom elevation or cavity is investigated. In this case the shallow water equations are already used, and it is supposed that a cylindrical wave is spread from patched water elevation over the epicentrum. Last, the tsunami propagation and transformation in a shallow water region and its run‐up on a beach are investigated on the basis of the improved shallow water theory, taking into consideration the nonlinear and dispersive terms of higher order. The proposed theory is tested in a problem of collisions of two solutions. Solutions of the first and the second problems are obtained by the method of integral Laplace's transformation with following numerical inversion of transformations. A finite difference method for a solution of the last problem is used. 相似文献
5.
Using a linear statement, the paper studies surface waves occurring due to minor shifts of the bottom sections. A plane case
is considered. An analytical solution to the problem has been derived using Fourier transforms. Asymptotic laws for the degeneration
of waves propagating over finite bottom deformations have been defined. Numerical analysis of the integrals is applied to
study the effect of the horizontal extent of a wave generation area and bottom irregularities on the shape of waves and their
amplitudinal and energetic parameters. Attention is focused on the manifestation of frequency dispersion at the stage of wave
generation as a developed wave process.
Translated by Vladimir A. Puchkin. 相似文献
6.
An analytical solution to shallow-water nonlinear equations determining the height of tsunami waves leaving the source is obtained. The initial water-level displacement in the source and the distribution of particle velocities are set. The numerical solution showed that analytical estimates fit well with source characteristics varying in a broad range, even if the waves produced by the source collapse. 相似文献
7.
In this paper the aim is to investigate whether there are differences between the dispersion and non-dispersion solutions on tsunami propagation. For this purpose, two numerical models of tsunami propagation are compared. One of these numerical models is a nondispersive model that uses Saint Venant equations and the other is a dispersive model that uses Boussinesq equations. The tsunamis resulting from a submarine mass failure (SMF) which is settled at the bottom of the north eastern Sea of Marmara are examined. An analytical solution considering wave dispersion is developed for obtaining near-field tsunami amplitudes above the submarine mass failure. Numerical modeling is used at the sea surface from the common boundary called as liquid boundary with incident waves up to the coastal regions to get the tsunami amplitudes. The output of the analytical model is taken as the disturbances for the numerical method. In the numerical solutions TELEMAC-2D software system is used for both dispersive and nondispersive modeling. The results of the dispersive and nondispersive models are compared to each other. Both temporal and spatial differences in the amplitudes and wave shapes are examined. The obtained results demonstrate that there are no noticeable differences between the dispersion and non-dispersion solutions except some special cases and some special landslide velocities. 相似文献
8.
The aim of this paper is to present an analytical expression for the vertical distribution of the correlation between the horizontal (
) and vertical (
) wave velocity components. This quantity,
, which appears explicitly in the time-averaged momentum balance equations, has been shown to play an important role in the vertical distribution of wave-induced currents.The proposed formulation for
is based on an identity that relates the effective (wave) shear stress
to the effective (wave) normal stresses (
2 and
2) and to the vorticity of the oscillatory flow
gw. This general expression has been applied to simplified situations and has been shown to degenerate into other existing formulations with comparable simplifying assumptions, viz. irrotational waves in shallow water over an arbitrary bottom topography and breaking waves over a horizontal bottom.The model has also been applied to the case of waves interacting with a depth-varying current over a horizontal bottom, in which preliminary results have been obtained for a simplified situation invoking linear (small-amplitude) wave theory. 相似文献
9.
10.
N. P. Kurian K. Rajith B. T. Murali Krishnan N. Nirupama T. S. Murty 《Marine Geodesy》2006,29(4):277-281
During the Indian Ocean tsunami of December 26, 2004, specific observations were made by our survey team about the arrival times of several tsunami waves, their amplitudes, maximum extent of horizontal inundation on land and initial withdrawal of the ocean. Here the observations on the horizontal inundation and initial withdrawal are presented and briefly discussed. 相似文献
11.
The Okinawa Trench in the East China Sea and the Manila Trench in the South China Sea are considered to be the regions with high risk of potential tsunamis induced by submarine earthquakes. Tsunami waves will impact the southeast coast of China if tsunamis occur in these areas. In this paper, the horizontal two-dimensional Boussinesq model is used to simulate tsunami generation, propagation, and runnp in a domain with complex geometrical boundaries. The temporary varying bottom boundary condition is adopted to describe the initial tsunami waves motivated by the submarine faults. The Indian Ocean tsunami is simulated by the numerical model as a validation case. The time series of water elevation and runup on the beach are compared with the measured data from field survey. The agreements indicate that the Boussinesq model can be used to simulate tsunamis and predict the waveform and runup. Then, the hypothetical tsunamis in the Okinawa Trench and the Manila Trench are simulated by the numerical model. The arrival time and maximum wave height near coastal cities are predicted by the model. It turns out that the leading depression N-wave occurs when the tsunami propagates in the continental shelf from the Okinawa Trench. The scenarios of the tsunami in the Manila Trench demonstrate significant effects on the coastal area around the South China Sea. 相似文献
12.
This paper presents a local tsunami simulation, including the initial displacement field model of tsunami source and tsunami wave propagation model. We deduced the tsunami wave equation; applied the ma... 相似文献
13.
A. B. Rabinovich 《Izvestiya Atmospheric and Oceanic Physics》2014,50(5):445-458
Deep-sea tsunami measurements play a major role in understanding the physics of tsunami wave generation and propagation, and in the creation of an effective tsunami warning system. The paper provides an overview of the history of tsunami recording in the open ocean from the beginning (about 50 years ago) to the present day. It describes modern tsunami monitoring systems, including the Deep-ocean Assessment and Reporting of Tsunamis (DART), innovative Japanese bottom cable projects, and the NEPTUNE-Canada geophysical bottom observatory. The specific peculiarities of seafloor longwave observations in the deep ocean are discussed and compared with those recorded in coastal regions. Tsunami detection in bottom presure observations is exemplified based on analysis of distant (22000 km) records of the 2004 Sumatra tsunami in the northeastern Pacific. 相似文献
14.
N. P. Kurian K. Rajith B. T. Murali Krishnan N. Nirupama T. S. Murty 《Marine Geodesy》2013,36(4):277-281
During the Indian Ocean tsunami of December 26, 2004, specific observations were made by our survey team about the arrival times of several tsunami waves, their amplitudes, maximum extent of horizontal inundation on land and initial withdrawal of the ocean. Here the observations on the horizontal inundation and initial withdrawal are presented and briefly discussed. 相似文献
15.
S. N. Bulgakov 《Physical Oceanography》1991,2(3):171-178
A three-dimensional linear model of the stationary water circulation in the Bosphorus due to the river's outflow, density differences at the ends of the straits, and win is considered allowing for the earth's rotation and the bottom topography. The channel approximation and the method of the separation of variables are used to obtain the analytical solution of the problem. The solution obtained describes the main circulation elements which are know from observations. The influence of different parameters on the formation of vertical and horizontal structures of the velocity field is analysed.Blocking conditions for the Bosphorus undercurrent are estimated. Possible variations in the structure of flows in the straits related to the regulated outflow of the rivers of the Black Sea basin are discussed.Translated by Mikhail M. Trufanov. 相似文献
16.
海啸波传播的线性和非线性特征及近海陆架效应影响的数值研究 总被引：3，自引：2，他引：1
浅水方程被广泛应用于海啸预警报业务及研究,而针对线性浅水方程与非线性浅水方程在不同海区水深地形条件下的适用范围、计算效率问题是海啸研究人员急需了解的。本文应用基于浅水方程的海啸数值预报模型就海啸波在南海、东海传播的线性、非线性特征以及陆架对其传播之影响进行了数值分析研究。海啸波在深水的传播表征为强线性特征,此时线性系统对海啸波幅的模拟计算具有较高的精度和效率,而弱的非线性特征及弱的色散特征对海啸波幅的预报影响甚微,可以忽略不计。海啸波传播至浅水大陆架后受海底坡度变化、海底粗糙度等因素影响,波动的非线性效应迅速传播、积累,与线性浅水方程计算的海啸波相比表现出较大差异,主要表现为:在南海区,水深小于100m时,海啸波首波以后的系列波动非线性特征比较明显,两者波幅差别较大,但首波波幅的区别不大,因此对于该区域在不考虑海啸爬高的情况下,应用线性系统计算得到的海啸波幅也可满足海啸预警报的要求;在东海区由于陆架影响,海啸波非线性特征明显增强,水深小于100m区域,首波及其后系列波波幅均差异较大,故在该区域必须考虑海啸波非线性作用。本文就底摩擦项对海啸波首波波幅的影响进行了数值对比分析,结果表明:底摩擦作用对海啸波首波波幅影响仅作用于小于100m水深。最后,该文通过敏感性试验,初步分析了陆架宽度及陆架边缘深度对海啸波波幅的影响,得出海啸波经陆架传播共振、变形后,海啸波幅的放大或减小与陆架的宽度及陆架边缘水深有关。 相似文献
17.
Through a simple analytical model, we examine the shear dispersion associated with oscillatory winds in an unstratified coastal ocean. As noted previously in the tidal regime, the vertical-integrated (total) horizontal diffusivity has a maximum where the water depth equals the diffusive depth – defined as the reach of the vertical diffusion during one forcing cycle. Due principally to the long synoptic timescale that characterizes the wind forcing, this depth lies over the outer shelf. When combined with effective mixing of the slope water by meso-scale eddies, the total diffusivity exhibits a minimum around the shelf break, thus facilitating frontogenesis. Due again to the long forcing period, the bottom Ekman flow is well developed at the diffusive depth, which would accentuate the gradient enhancement of the front over the inshore water, which however is bounded above by doubling.Calculations from a primitive-equation numerical model are carried out for both unstratified and stratified oceans. From an initially uniform property gradient, a front is seen to emerge around the shelf break after an oscillating wind is switched on, in a visual demonstration of the proposed frontogenesis. The unstratified solution closely agrees with the analytical solution, and although the front is not particularly sharp, it is comparable to that observed. The stratified solution renders a more realistic simulation of the observed front, but it retains the basic features, suggesting the dominance of the proposed mechanism even in the presence of the cross-frontal circulation. 相似文献
18.
Riley J.M. Glegg S.A.L. LaVigne A.E. Coulson R.K. 《Oceanic Engineering, IEEE Journal of》1997,22(2):211-218
Experimental measurements have been carried out to identify the effects of a realistic bottom bathymetry on detecting a source with a horizontal line array. The measurements have been conducted over a 1:10000 scale model of the Santa Lucia Escarpment. The experiments measured the bearing error obtained in locating a CW source with a horizontal line array using plane-wave beamforming. The error in the detected bearing is caused by the bending of sound rays in the horizontal plane, commonly referred to as horizontal or bathymetric refraction. The results of the experiment demonstrate large bearing errors which vary rapidly and do not increase monotonically with range. The rapid variation of the bearing errors was unexpected and was a result which has not been previously identified. The magnitude of the errors was also a function of the across slope look direction and frequency, with bearing errors as large as 26° for low frequencies. At higher frequencies, the bearing error is reduced. An analytical solution for the acoustic field over a shear supporting sloping bottom has been used to approximate the results of the experiment. The simulation confirmed the trends in the experimental results by showing bearing errors of the same order of magnitude with the same dependence on across slope direction and frequency. Most importantly, the theoretical results also showed a rapidly varying bearing error as a function of across slope range 相似文献
19.
While the destruction caused by a tsunami can vary significantly owing to near- and onshore controls, we have only a limited quantitative understanding of how different local parameters influence the onshore response of tsunamis. Here, a numerical model based on the non-linear shallow water equations is first shown to agree well with analytical expressions developed for periodic long waves inundating over planar slopes. More than 13,000 simulations are then conducted to examine the effects variations in the wave characteristics, bed slopes, and bottom roughness have on maximum tsunami run-up and water velocity at the still water shoreline. While deviations from periodic waves and planar slopes affect the onshore dynamics, the details of these effects depend on a combination of factors. In general, the effects differ for breaking and non-breaking waves, and are related to the relative shift of the waves along the breaking–non-breaking wave continuum. Variations that shift waves toward increased breaking, such as steeper wave fronts, tend to increase the onshore impact of non-breaking waves, but decrease the impact of already breaking waves. The onshore impact of a tsunami composed of multiple waves can be different from that of a single wave tsunami, with the largest difference occurring on long, shallow onshore topographies. These results demonstrate that the onshore response of a tsunami is complex, and that using analytical expressions derived from simplified conditions may not always be appropriate. 相似文献
20.
The process of tsunami generation by the moving horizontal bottom displacement is studied numerically. The influence produced by the displacement rate and the range of the run on the parameters of the wave generated is studied. A comparison with the results derived using the linear theory of long waves is made.Translated by Mikhail M. Trufanov. 相似文献