Symmetric waves are traveling waves for a shallow water equation modeling surface waves of moderate amplitude

Following a general principle introduced by Ehrnström, Holden and Raynaud in 2009, we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.     

Rogue waves in shallow water

Most of the processes resulting in the formation of unexpectedly high surface waves in deep water (such as dispersive and geometrical focusing, interactions with currents and internal waves, reflection from caustic areas, etc.) are active also in shallow areas. Only the mechanism of modulational instability is not active in finite depth conditions. Instead, wave amplification along certain coastal profiles and the drastic dependence of the run-up height on the incident wave shape may substantially contribute to the formation of rogue waves in the nearshore. A unique source of long-living rogue waves (that has no analogues in the deep ocean) is the nonlinear interaction of obliquely propagating solitary shallow-water waves and an equivalent mechanism of Mach reflection of waves from the coast. The characteristic features of these processes are (i) extreme amplification of the steepness of the wave fronts, (ii) change in the orientation of the largest wave crests compared with that of the counterparts and (iii) rapid displacement of the location of the extreme wave humps along the crests of the interacting waves. The presence of coasts raises a number of related questions such as the possibility of conversion of rogue waves into sneaker waves with extremely high run-up. Also, the reaction of bottom sediments and the entire coastal zone to the rogue waves may be drastic.     

Noncontact transportation in water using ultrasonic traveling waves

A noncontact transport experiment in water using ultrasonic traveling waves was investigated. Acrylic, aluminum, and brass discs were used as test objects. Traveling waves were generated using two ultrasonic transducers attached at the ends of a vibrating plate. One side was used as the wave-source side and the other side was used as the wave-receiving side. Acrylic plates cemented to the sides of the vibrating plate formed a tank to hold water. Object transportation was accomplished by adding a small amount of water to the vibrating structure. The transport velocity of floating objects in water is faster than for floating transport in air because of buoyancy. The transport velocity of an object depends on water height. The minimum value of the velocity occurs when the disc thickness is equal to the water height. The transport velocity increases as the height of water increases. For very shallow depths, the largest velocity is obtained when cavitation-induced streaming occurs.     

On infrasound radiation of shallow water waves

Sound waves generated by low-frequency gravity modes have been studied. It has been shown that the response function is inversely proportional to the fourth power of the wave number.     

Properties of underwater acoustic communication channels in shallow water

Underwater acoustic channels are band-limited and reverberant, posing many obstacles to reliable, phase-coherent acoustic communications. While many high frequency communication experiments have been conducted in shallow water, few have carried out systematic studies on the channel properties at a time scale relevant for communications. To aid communication system design, this paper analyzes at-sea data collected in shallow water under various conditions to illustrate how the ocean environments (sea surface waves and random ocean medium) can affect the signal properties. Channel properties studied include amplitude and phase variations, and temporal coherence of individual paths as well as the temporal and spatial coherence of multipaths at different time scales. Reasons for the coherence loss are hypothesized.     

大尺度浅水波方程中相互调制的非线性波

基于一般的浅水波方程, 根据大尺度正压大气的特点, 得到无量纲的控制大尺度大气的动力学非线性方程组. 利用多尺度法, 由无量纲的动力学方程组导出了扰动位势的非线性控制方程. 采用椭圆方程构造该扰动位势控制方程的解, 获得了扰动位势和速度的多周期波与冲击波(爆炸波) 并存的解析解. 扰动位势的解表明经向和纬向具有不同周期和波长的周期波, 且都受纬向孤波的调制; 速度的解表明大尺度大气流动存在气旋和反气旋周期性分布的现象. 关键词： 浅水波方程 大尺度正压大气 解析解 非线性波     

Topological soliton solutions for three shallow water waves models

In this article, we investigate three distinct physical structures for shallow water waves models by the improved ansatz method. The method was improved and can be used to obtain more generalized form topological soliton solutions than the original method. As a result, some new exact solutions of the shallow water equations are successfully established and the obtained results are exhibited graphically. The results showed that the improved ansatz method can be applied to solve other nonlinear differential equations arising from mathematical physics.     

Oscillatory traveling waves in excitable media

A new type of waves in an excitable medium, characterized by oscillatory profile, is described. The excitable medium is modeled by a two-component activator-inhibitor system. Reaction-diffusion systems with diagonal and cross diffusion are examined. As an example, a front (kink) represented by a heteroclinic orbit in the phase space is considered. The wave shape and velocity are analyzed with the use of exact analytical solutions for wave profiles.     

Geometric scaling as traveling waves

We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale.     

Coherence of acoustic modes propagating through shallow water internal waves

The 1995 Shallow Water Acoustics in a Random Medium (SWARM) experiment [Apel et al., IEEE J. Ocean. Eng. 22, 445-464 (1997)] was conducted off the New Jersey coast. The experiment featured two well-populated vertical receiving arrays, which permitted the measured acoustic field to be decomposed into its normal modes. The decomposition was repeated for successive transmissions allowing the amplitude of each mode to be tracked. The modal amplitudes were observed to decorrelate with time scales on the order of 100 s [Headrick et al., J. Acoust. Soc. Am. 107(1), 201-220 (2000)]. In the present work, a theoretical model is proposed to explain the observed decorrelation. Packets of intense internal waves are modeled as coherent structures moving along the acoustic propagation path without changing shape. The packets cause mode coupling and their motion results in a changing acoustic interference pattern. The model is consistent with the rapid decorrelation observed in SWARM. The model also predicts the observed partial recorrelation of the field at longer time scales. The model is first tested in simple continuous-wave simulations using canonical representations for the internal waves. More detailed time-domain simulations are presented mimicking the situation in SWARM. Modeling results are compared to experimental data.     

负跃层浅海声传播的一个新现象——远程传播中的海底散射波

本文分析了负跃层浅海中的一次声传播实验。爆炸声源位于跃层之下,两个接收水听器分别位于跃层上、下。在远距离处跃层上水听器接受到的信号由两部分组成:从声源直接传播到接收点的多途信号(穿透波)和一个随后到达的强度比前者大得多的信号(散射波)。通过理论计算和数值拟合,我们认为后者是跃层下传播的声波激发的海底散射信号,这部分信号不但可应用于远距离传输,而且还可能用来反演三维海底散射的有关参数。     

Effect of shallow water internal waves on ocean acoustic striation patterns

Contour plots of underwater acoustic intensity, mapped in range and frequency, often exhibit striations. It has been claimed that a scalar parameter 'beta', defined in terms of the slope of the striations, is invariant to the details of the acoustic waveguide. In shallow water, the canonical value is β=1. In the present paper, the waveguide invariant is modelled as a distribution rather than a scalar. The effects of shallow water internal waves on the distribution are studied by numerical simulation. Realizations of time-evolving shallow water internal wave fields are synthesized and acoustic propagation simulated using the parabolic equation method. The waveguide invariant distribution is tracked as the internal wave field evolves in time. Both random background internal waves and more event-like solitary internal waves are considered.     

Effect of shallow water internal waves on ocean acoustic striation patterns

Abstract

Contour plots of underwater acoustic intensity, mapped in range and frequency, often exhibit striations. It has been claimed that a scalar parameter ‘beta’, defined in terms of the slope of the striations, is invariant to the details of the acoustic waveguide. In shallow water, the canonical value is β=1. In the present paper, the waveguide invariant is modelled as a distribution rather than a scalar. The effects of shallow water internal waves on the distribution are studied by numerical simulation. Realizations of time-evolving shallow water internal wave fields are synthesized and acoustic propagation simulated using the parabolic equation method. The waveguide invariant distribution is tracked as the internal wave field evolves in time. Both random background internal waves and more event-like solitary internal waves are considered.     

Frequency dependence and intensity fluctuations due to shallow water internal waves

A theory and experimental results for sound propagation through an anisotropic shallow water environment are presented to examine the frequency dependence of the scintillation index in the presence of internal waves. The theory of horizontal rays and vertical modes is used to establish the azimutal and frequency behavior of the sound intensity fluctuations, specifically for shallow water broadband acoustic signals propagating through internal waves. This theory is then used to examine the frequency dependent, anisotropic acoustic field measured during the SWARM'95 experiment. The frequency dependent modal scintillation index is described for the frequency range of 30-200 Hz on the New Jersey continental shelf.