水下散体颗粒滑坡产生海啸波的实验研究

海底滑坡海啸作为仅次于地震海啸的重要海啸形态,常常发生于靠近海岸带的陆架和陆坡等区域,且由于其近岸灾害影响显著、物理机制复杂、难以监测和预警等特点,给靠近海岸带的居民造成了巨大的生命财产损失．关于水上滑坡海啸的实验研究相对比较充分,而对水下滑坡海啸和部分淹没滑坡海啸的研究则相对较少．本研究在大型波浪水槽中进行了斜坡上散体水下滑坡激发海啸的机理实验,研究了滑坡体的滑移距离、海啸波的形成过程以及海啸波的幅值、波速、非线性等特征,系统地认识了滑坡体质量、水深以及滑坡角度对滑坡海啸波高的影响规律,并提出了改进的水下滑坡海啸特征参数经验公式．     

海沟内海底地震激发的表面波动

通过底面运动学边界条件引入底面运动影响,采用高阶Boussinesq方程计算了光滑海底变形引起的表面波动形态.对于线性问题,与线性势流波浪理论进行了比较,二者结果符合良好.运用高阶Boussinesq波浪模型,针对冲绳海沟的实际地形,模拟海沟内不同震级的海底地震激发的海啸,分析了不同强度地震引起的表面波扰动形态及其非线性和色散效应.     

General solution for interaction of solitary waves including head-on collisions

A corrected version of the Boussinesq equation for long water waves is derived and its general solution for interaction of any number of solitary waves, including head-on collisions, is given. For two solitary waves in head-on collision (which includes the case of normal reflection) the results agree with the experiments known.     

Finite difference representations of non-linear waves

The work concerns cnoidal and solitary wave solutions of the Boussinesq equations in the context of finite difference methods. The existence of permanent wave-forms is discussed and approximate solutions are found for one particular discrete formulation by perturbation techniques. These techniques can be applied to most difference and regular element discretizations of equations describing weakly non-linear and dispersive waves. No proof of convergence of the perturbation expansions is established, but the appropriateness of the solutions is confirmed through comparison with the results of computer simulations. From the perturbation series it is found that the phase speed of solitons is useless for the evaluation of numerical methods and that asymmetries in the discrete equations may ruin the soliton solution. The availability of a discrete closed-form solution is especially important for discussions concerning the existence and accuracy of permanent wave-forms with oblique orientations relative to the grid.     

Integration of the boussinesq equations for steady channel and jet flows

The equations of long nonlinear waves in round jets and channels of arbitrary cross section are considered with account for the transverse acceleration of the fluid particles (Boussinesq approximation). In the general case of steady flows, the equations in the form of shallow water equations with the pressure expressed in terms of the variational derivative of the kinetic energy of a thin transverse fluid layer, have three first integrals with three arbitrary constants. Examples of solutions of the equations for solitary capillary-gravitation waves in rectangular and triangular channels are presented and compared with the higher approximations. The shape of the free boundary of the round jet is determined. In the case of outflow from a conical nozzle an analytical dependence of the jet contraction ratio on the conicity angle is obtained. The dependence is in agreement with the experimental data for angles of less than 45°.     

BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS IN VARIANT BOUSSINESQ EQUATIONS

The bifurcations of solitary waves and kink waves for variant Boussinesq equations are studied by using the bifurcation theory of planar dynamical systems. The bifurcation sets and the numbers of solitary waves and kink waves for the variant Boussinesq equations are presented. Several types explicit formulas of solitary waves solutions and kink waves solutions are obtained. In the end, several formulas of periodic wave solutions are presented.     

海底火山喷发大气冲击波激发的轴对称海啸波数值模型

海底火山喷发引发海啸具有多源激发机制, 包括水下爆炸、边坡失稳、火山口坍塌、碎屑流、地震以及大气扰动. 为了深入认识轴对称移动气压扰动激发海啸的机理, 探究气压扰动参数对水波形态的影响规律, 本文在柱面孤立波Boussinesq模型的基础上, 考虑水面移动气压扰动作用, 建立了由火山喷发激发的轴对称移动气压场所驱动的海啸波数值模型. 利用不同地形上柱面波的传播算例验证了本模型的精确性与稳定性. 数值模拟了2022年汤加火山喷发大气扰动激发海啸事件, 并与太平洋DART浮标实测数据比较, 较好地复演了大气扰动驱动海啸波的远场传播过程, 并讨论了波动在深水区的色散行为. 研究了轴对称气压扰动的径向移速、强度及尺度对波动演化特征的影响, 结果显示: 气压移速与浅水波速的相对大小显著影响波形, 当二者接近时将激发Proudman共振. 在共振条件下, 波幅与径向传播距离呈近似线性增长关系, 波幅放大因子随气压尺度增大而减小. 在远离共振条件时, 气压强度和尺度对波幅放大因子的影响相对较小, 受波能流守恒约束柱面自由波幅则沿程衰减, 受迫波幅值近似按气压衰减规律变化.     

论一类四阶Boussinesq方程的变浅性能

Boussinesq 类水波模型在港口、海岸以及海洋工程领域应用广泛,但以前对这类模型的变浅性能的研究不够充分. 针对Madsen 和Schäffer 提出的一组四阶Boussinesq 方程,从理论和数值两个方面对这一问题进行了探讨. 理论分析了其变浅性能,指出该文献中参数α₂ 和β₂ 的取值是不合理的,并重新确定其取值. 在交错网格下建立了基于混合4 阶Adams-Bashforth-Moulton 格式的预报-校正数值模型. 数值模拟了两个典型算例： 一是缓变平坡地形上波浪的传播变形,二是波浪在淹没梯形潜堤上的波浪演化过程. 计算结果分别与解析结果、物理模型实验结果进行了比较,发现变浅系数的取值对数值结果影响很大,新参数比原文参数模拟结果的吻合程度更高,这佐证了理论分析.     

Impulsive Tension of Ethanol under Shock Loading

This paper reports results from experimental studies of the strength of ethanol under impulsive tension due to interaction of a triangular compression pulse with the free surface. The experiments were performed in the range of strain rates 4 ⋅ 10⁴-4 ⋅ 10⁵ sec⁻¹. It is established that the failure of ethanol is a two-stage process. In the first stage at a negative pressure of about 14 MPa, pore formation begins, which proceeds at a rather low rate and is manifested as an inflection on the free-surface velocity profile. In the second stage, the porosity growth rate increases, resulting in formation of a spalling pulse. The possibility of using the model of homogeneous nucleation to interpret experimental data is discussed.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 29–38, July–August, 2005.     

ON BREAKING WAVES AND WAVE-CURRENT INTERACTION IN SHALLOW WATER: A 2DH FINITE ELEMENT MODEL

A two-dimensional (horizontal plane) coastal and estuarine region model, capable of predicting the combined effects of gravity surface shallow- water waves (shoaling, refraction, diffraction, reflection and breaking), and steady currents, is described and numerical results are compared with those obtained experimentally. Two series of observations within a wave flume and a combined wave-current facility were developed. In the first case, the wave was generated via a hinged paddle located within a deepened section at one end of the channel, as, in the second case, the wave propagating with or against the current was generated by a plunger-type wavemaker; the re-circulating current was introduced via one passing tank connected to a centrifugal pump. Several comparisons for a number of 1D situations and one 2D horizontal plane case are presented.     

基于流变理论的滑坡海啸数值模拟研究

基于Herschel-Bulkley流变理论建立表征粘塑性泥石流滑坡过程的数学模型,利用有限体积法求解非剪切层与剪切层的质量和动量平衡过程,计算滑体失稳与滑动过程中不同时刻滑坡体厚度的变化特性．在传统的非线性浅水波方程中计及底面运动边界条件,发展可用于模拟海底滑坡激发海啸的生成、传播和爬高淹没过程的数值模型．复演了1998年巴布亚新几内亚滑坡海啸,结合实测数据验证该模型的可靠性．针对我国南海的白云滑坡和文莱滑坡可能存在的大规模滑坡,分别模拟计算了白云滑坡体积为50 km3和100 km3、文莱滑坡体积为1200 km3的滑坡演化过程,及其引起的滑坡海啸．根据计算得到的南海滑坡海啸的最大波幅分布和近岸的波面时间序列,分析了南海潜在的滑坡海啸传播演化规律和对我国近岸的灾害性影响特征．