Second-mode nonlinear internal waves over a sloping bottom

The characteristic features of second-mode internal wave propagation over a sloping bottom are investigated by numerical simulation based on the Korteweg-de Vries equation. A comparison of the transformations that occur for first- and second-mode internal solitons in the course of their propagation over a sloping bottom under the hydrological conditions of the South China Sea is carried out. Convex and concave second-mode waves are considered, and the possibility of their transition from the first to the second state in the course of their propagation from the deep ocean to the shelf is demonstrated. This is an analog of the effect of a change in the internal wave polarity, which earlier was known to occur for only first-mode internal waves.     

Properties of straight and curved neutron guide tubes

The properties of straight and curved neutron guides for neutrons of the energy region 4·10^?7 eV≦E≦2·10^?6 eV (very cold neutrons) are investigated. Experimental data for the angular distribution of neutrons emerging from a straight neutron guide are presented and it is shown that they can be theoretically verified using Steyerl's approximation. In the second part we consider a strongly curved neutron guide. The effect of laminating such a guide is investigated experimentally and theoretically and the conditions for optimum transmission are discussed.     

Analysis and modeling of broadband airgun data influenced by nonlinear internal waves

To investigate acoustic effects of nonlinear internal waves, the two southwest tracks of the SWARM 95 experiment are considered. An airgun source produced broadband acoustic signals while a packet of large nonlinear internal waves passed between the source and two vertical linear arrays. The broadband data and its frequency range (10-180 Hz) distinguish this study from previous work. Models are developed for the internal wave environment, the geoacoustic parameters, and the airgun source signature. Parabolic equation simulations demonstrate that observed variations in intensity and wavelet time-frequency plots can be attributed to nonlinear internal waves. Empirical tests are provided of the internal wave-acoustic resonance condition that is the apparent theoretical mechanism responsible for the variations. Peaks of the effective internal wave spectrum are shown to coincide with differences in dominant acoustic wavenumbers comprising the airgun signal. The robustness of these relationships is investigated by simulations for a variety of geoacoustic and nonlinear internal wave model parameters.     

Horizontal refraction of sound rays due to short-period internal waves in the ocean

The effect of a short-period internal wave measured in field conditions on the horizontal (side) refraction of sound rays is estimated. The angle of horizontal refraction, i.e., the angle between the direction of the signal arrival in the horizontal plane and the true direction to the sound source, is determined. The influence of various factors, such as the position of the receiving system in depth with respect to the layer of high sound velocity gradients, the rotation of the transmitter-receiver track with respect to the internal wave front, etc., on the horizontal refraction is estimated. Numerical calculations are carried out. Conclusions about the possible errors that arise in determining the azimuth direction to the sound source because of the effect of short-period internal waves are derived.     

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.     

On the localization of 2D nonlinear internal waves in a two-layer fluid

A 2D generalized Gardner equation is used to describe 2D nonlinear internal waves in a two-layer fluid. Unlike the previous model based on the Kadomtsev-Petviashvili equation, the model considered here allows for the instability of a plane internal solitary wave. Such a possibility causes the wave to be localized in any direction. Relationships between the thicknesses and densities of the layers under the instability conditions are obtained.     

Acoustic multipath arrivals in the horizontal plane due to approaching nonlinear internal waves

Simultaneous measurements of acoustic wave transmissions and a nonlinear internal wave packet approaching an along-shelf acoustic path during the Shallow Water 2006 experiment are reported. The incoming internal wave packet acts as a moving frontal layer reflecting (or refracting) sound in the horizontal plane. Received acoustic signals are filtered into acoustic normal mode arrivals. It is shown that a horizontal multipath interference is produced. This has previously been called a horizontal Lloyd's mirror. The interference between the direct path and the refracted path depends on the mode number and frequency of the acoustic signal. A mechanism for the multipath interference is shown. Preliminary modeling results of this dynamic interaction using vertical modes and horizontal parabolic equation models are in good agreement with the observed data.     

Characteristics of vertical bent coupling between straight and curved rectangular optical waveguides

In terms of the coupled mode theory (CMT) and the transfer matrix method, we present a technique and relative formulas including the bent coupling coefficient, amplitude coupling ratio, amplitude transmission ratio and propagation power for analyzing the vertical bent coupling between a curved rectangular waveguide and a straight one. Investigations show that the bent coupling appears in an effective coupling region by both sides of the central coupling point. Beyond this effective coupling region, however, the bent coupling is very weak, and the propagation power in the waveguide is closer to a constant. As the bent radius increases, or the thickness of the coupling layer between these two waveguides decreases, this effective coupling region becomes wider, in which the coupling behavior becomes stronger.     

An iterative method to solve a regularized model for strongly nonlinear long internal waves

We present a simple iterative scheme to solve numerically a regularized internal wave model describing the large amplitude motion of the interface between two layers of different densities. Compared with the original strongly nonlinear internal wave model of Miyata [10] and Choi and Camassa [2], the regularized model adopted here suppresses shear instability associated with a velocity jump across the interface, but the coupling between the upper and lower layers is more complicated so that an additional system of coupled linear equations must be solved at every time step after a set of nonlinear evolution equations are integrated in time. Therefore, an efficient numerical scheme is desirable. In our iterative scheme, the linear system is decoupled and simple linear operators with constant coefficients are required to be inverted. Through linear analysis, it is shown that the scheme converges fast with an optimum choice of iteration parameters. After demonstrating its effectiveness for a model problem, the iterative scheme is applied to solve the regularized internal wave model using a pseudo-spectral method for the propagation of a single internal solitary wave and the head-on collision between two solitary waves of different wave amplitudes.     

Localization of nonlinear excitations in curved waveguides and chains of nonlinear oscillators

It is shown that the interplay of curvature and nonlinearity in systems with finite curvature: bent waveguides, curved chains of nonlinear oscillators, etc can lead to the qualitative effects, such as symmetry breaking of the nonlinear excitations and their trapping by the bending. The finite curvature of the waveguide with infinite hard walls (Dirichlet boundary conditions) provides a stabilizing effect on otherwise unstable localized states of repelling nonlinear Schr?dinger excitations. The number of quanta which the curved waveguide can bind monotonically increases when the radius of curvature decreases. In the waveguides with Neumann boundary conditions at the confining walls the curved region might manifest itself as a two-hump potential barrier with interbarrier space acting as a potential valley. A threshold character of the scattering process, i.e. transmission, trapping, or reflection of the moving nonlinear excitation passing through the bending, is demonstrated.     

Scattering of electromagnetic waves from nonlinear thin dielectric coatings

In this paper the reflection and diffraction properties of nonlinear thin dielectric coatings are investigated. A quite simple geometry consisting of two semi-infinite homogenous linear spaces separated by a non-linear coating is considered. An incident plane wave propagating along the z direction towards the nonlinear thin coating is taken. The nonlinear thin coating is divided into elementary sectors, within each one of which one propagating and one reflected wave exists. The boundary conditions are then applied in order to develop an efficient numerical alogirthm to study the properties of the nonlinear thin coating.     

Scattering of waves from nonlinear media with rough surfaces

Abstract

Reflection and scattering of waves from plane and statistically rough interfaces between nonlinear media are studied theoretically. New hysteresis-type dependences of the reflection and transmission coefficients on the amplitude of the incident wave and on the angle of incidence are predicted. Scattering diagrams for diffusely reflected and transmitted fields are calculated. It is found that when the dielectric constant is a steep function of the incident amplitude, nonlinearity suppresses the Bragg resonant scattering mechanism. Smooth roughness of the boundary is shown to enhance the penetration of evanescent waves into nonlinear media.     

Interaction dynamics of elastic waves with a complex nonlinear scatterer through the use of a time reversal mirror

This Letter reports on work performed to locate and interrogate a nonlinear scatterer in a linearly elastic medium through the use of a time reversal mirror in combination with nonlinear dynamics. Time reversal provides the means to spatially and temporally localize elastic energy on a scattering feature while the nonlinear dynamics spectrum allows one to determine whether the scatterer is nonlinear (e.g., mechanical damage). Here elastic waves are measured in a solid and processed to extract the nonlinear elastic response. The processed elastic signals are then time reversed, rebroadcast, and found to focus on the nonlinear scatterer, thus defining a time-reversed nonlinear elastic wave spectroscopy process. Additionally, the focusing process illuminates the complexity of the nonlinear scatterer in both space and time, providing a means to image and investigate the origins and physical mechanisms of the nonlinear elastic response.     

Nonlinear internal resonance interaction between surface waves and internal waves in an inhomogeneous laminated liquid

Eight nonlinear resonances may arise in a two-layer liquid with a free surface, as follows from asymptotic calculations of the second order of smallness. Two of them involve waves generated by either surface, and six mixed resonances involve waves generated by different surfaces. Of these six resonances, two are degenerate and the remaining four are secondary combination resonances. However, not all of them are observed in practice. In the mixed combination resonances, interaction arises only between surface waves provided that the internal wave (which does not change its parameters but is necessary for the resonance to occur) has a catalytic influence.     

Resonance scattering of electromagnetic waves from a rectangular groove on a metallic mirror

Scattering diagrams, calculated from a rigorous theory, are presented for wavelengths comparable to the magnitude of the groove shape parameters.