Gravity waves of the Stokes-type in a system of two horizontal layers of inviscid, stratified and miscible fluids are studied by applying a Lagrangian description of fluid motion. It is shown that for the total vertically-integrated Stokes drift (the Stokes flux) to become zero, the density must be continuous at the interface. This is not the case in a system of two immiscible homogeneous layers of

This manuscript describes the derivation of systems of equations for weakly nonlinear gravity waves in shallow water in the presence of constant vorticity. The derivation is based on a multi-layer generalization of the traditional columnar Ansatz. A perturbative development in a nonlinear parameter and a dispersive parameter allow us to obtain sets of equations, for the horizontal fluid velocity and

We propose a novel approach to design a tunable acoustic channel drop filter based on a fluid–fluid phononic crystal (PnC), using two ring resonators. A square lattice of infinitely long cylindrical water inclusions is embedded in the mercury matrix to characterize the PnC structure. We show that the output resonant frequency can be ultra-tuned by changing the location of each ring, and the quality

Particles or cells in suspension and exposed to ultrasonic waves experience an acoustic radiation force (FR) which, under certain conditions, drives them toward positions of acoustic equilibrium. In this paper, we present a three-dimensional model of the particle motions within the acoustic field generated by ultrasonic standing waves. This model allows a theoretical study of the three-dimensional

Propagation of acoustic waves is considered in a system consisting of two stiff quarter-spaces connected by a planar soft layer. The two quarter-spaces and the layer form a half-space with a planar surface. In a numerical study, surface waves have been found and analyzed in this system with displacements that are localized not only at the surface, but also in the soft layer. In addition to the semi-analytical

A generalized analytical approach for the propagation of Bleustein–Gulyaev wave in a piezoelectric material loaded on its surface with a viscoelastic fluid is established in this paper. The Bleustein–Gulyaev waveguide surface is subjected to various glycerol concentrations. The Maxwell and Kelvin–Voigt models are used to describe the viscoelasticity of this fluid. Exact dispersion equation is obtained

A ray dynamics describing wave transport on curved and smooth thin shells can be obtained from the underlying wave equations via the Eikonal approximation. We analyse mid-frequency effects near the ring frequency for curved plates consisting of a cylindrical region smoothly connected to two flat plates. Using classical shell theory, we treat a corresponding ray-tracing limit derived in the short wavelength

The propagation characteristics of feature guided waves (FGWs) in topographical waveguides, such as welded joints, have been widely investigated. However, most of these investigations analyzed linear acoustic characteristics. Considering the high sensitivity of nonlinear ultrasonic techniques in the nondestructive evaluation of microscopic defects in materials, such as identifying micro-defects at

The detection and evaluation of closed cracks are of prime interest in industry. Whereas conventional ultrasonic methods fail to detect these defects, nonlinear methods based on activation of the nonlinear behavior of closed cracks constitute an interesting alternative. The aim of this article is to give a better understanding of interactions between cracks and a longitudinal elastic wave for a quantitative

In this work, we examine generalized equal width (GEW) equation which is a highly nonlinear partial differential equation and describes plasma waves and shallow water waves. Nonlinearity of the equation is tackled by a linearization technique and finite difference approach is utilized for time derivatives. For spatial derivatives we first introduce delta-shaped basis functions which are relatively

We use the bilinear Kadomtsev–Petviashvili (KP) hierarchy reduction method for deriving new families of explicit lump–soliton solutions to the PT-symmetric nonlocal Fokas system. These lump–soliton solutions are semi-rational solitons that are classified into three different species under appropriate parametric restrictions: line solitons, rational lumps, and semi-rational lump–soliton solutions. There

In this work we study the effect caused by the so called Holian conjecture (HC) on the rarefied gases shock-wave structure under the continuum approach. This conjecture which was introduced to study hard spheres takes the longitudinal temperature to calculate the viscosity and thermal conductivity, a fact which makes the shock-wave structure be modified by the explicit lack of isotropy. We generalized

In this paper, propagation of Rayleigh surface wave in a compressible half-space solid with initial stress is discussed. The basic formulation of the problem includes the non linear theory of elasticity and theory of invariants. The equations governing infinitesimal motions superimposed on a finite deformation are used to study the combined effect of initial stress and finite deformation on wave speed

In this study, the propagation of surface water waves initially displaced by a tectonic seafloor deformation of arbitrary geometry was obtained considering the rupture kinematics. The developed solution was applied to a set of problems for wave generation by bottom motion with arbitrary spatiotemporal variations. First, a single bottom motion with different uplift speeds was considered; results showed

In this research, we applied a polynomial hybrid approach for modeling longitudinal guided waves propagating in anisotropic composites multi-layered pipes. Theoretically, dispersion characteristic equations in cylindrical coordinate system were derived by introducing the state vector form of displacement and stress components. In virtue of the orthogonality completeness and recursion properties of

A closely-spaced periodic array of identical thin rigid plates illuminated by incident waves is shown to exhibit properties of a negative refraction metamaterial under certain conditions. The close-spacing assumption is used as a basis for an approximation in which the region occupied by the plate array acts as an effective medium. Effective matching conditions on the plate array boundary are also

This paper investigates the wave propagation dispersion, spurious reflection and spurious bifurcation of flexural waves that occur in the numerical integration of the wave equation. To this end, the classic cubic beam finite elements of two nodes with a consistent mass matrix for integration in space and the Newmark average acceleration integration method of a single step for integration in time are

The multi-temperature model of binary mixture, developed within the framework of extended thermodynamics, is enhanced with viscous and thermal dissipation. The shock structure problem is analyzed for the influence of dissipation on the shock thickness, influence of Mach number on the thickness and temperature in viscous profiles, and influence of the mass ratio on the profiles of state variables. The

The role of various long-wave approximations in the description of the wave field and bottom pressure caused by surface waves, and their relation to evolution equations are being considered. In the framework of the linear theory, these approximations are being tested on the well-known exact solution for the wave spectral amplitudes and pressure variations. The famous Whitham, Korteweg–de Vries (KdV)

N-order solutions to the modified Korteweg–de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N, rational solutions as a quotient of polynomials in x and t depending on 2N real parameters. We construct explicit expressions of these rational solutions

Many of the widely used models for description of nonlinear surface gravity waves, in deep or shallow water, such as High Order Spectral Method (HOSM) and Boussinesq-type equations, rely on the elimination of the vertical coordinate from the basic three-dimensional Euler equations. From a numerical point of view such models are often computationally efficient, which is one of the main reasons that

Motivated by applications of recent interest related to propagation problems in the left-handed 2D inductor–capacitor metamaterial and standard 2D inductor–capacitor lattice with monochromatic inputs along the left and bottom boundary of a rectangular slab, we address the problem of wave diffraction on the 2D square lattice in a quadrant. The peculiar structure allows us to consider problems on half-plane

The resonance phenomena in parabolic and quartic lakes are investigated using a mathematical model. The model that we use here is formulated from Shallow Water Equations. We solve the model analytically so as to derive the fundamental natural wave period that can result in resonance in a closed basin. Further, a staggered finite volume method is implemented to solve the model numerically. The numerical

A finite volume full-wave method is used to simulate nonlinear dissipative acoustic propagation in ducts with a circular cross-section. Thermoviscous dissipative effects, due to bulk viscosity and shear viscosity in the boundary layer adjacent to the duct walls, are also considered. The propagation is assumed to be axisymmetric, and two different geometries are considered: a straight cylindrical tube

The method of transfer matrices of orders n=2 and n=4 is known from the theory of the propagation of light and elastic waves in layered media. The development of this matrix method is presented for cases n>4. The transfer matrix T of waves through a homogeneous layer of thickness d is defined as the matrix exponential T=exp(Wd). The elements of the matrix W depend on the physical properties of the

We study the canonical problem of wave scattering by periodic arrays, either of infinite or finite extent, of Neumann scatterers in the plane; the characteristic lengthscale of the scatterers is considered small relative to the lattice period. We utilise the method of matched asymptotic expansions, together with Fourier series representations, to create an efficient and accurate numerical approach

In engineering practice, the microcracks usually generate during the initial period of fatigue, and randomly distribute in the metallic structure. It is great challenge for linear non-destructive testing methods to detect those microscopic damages. In this work, the numerical simulations on nonlinear interaction between Lamb wave and microcracks are performed to investigate the behavior of frequency

In this paper, experimental and numerical studies were performed to investigate the characteristics of longshore current under two mild slopes, the results of which may complement the existing studies, which have mainly focused on steep slopes. The experimental results revealed that the average velocity distribution of the longshore current was significantly different under the two different mild slopes

We provide a theoretical analysis to support the presence of both slow and fast compression waves in an unconsolidated, fully saturated, granular material. We derive the constitutive relation for such an aggregate based upon a micro-mechanics analysis. In doing this, we take in account the coupling between the solid particles and fluid. As a consequence of this coupling, the lubrication layer provides

The solution of wave problems using Domain Decomposition (DD) requires that the subdomain boundaries should be virtually non-existent, so that waves are not affected by the boundaries. This is a primary problem in DD, and it intensifies in the case of cross-points at which three or more subdomains meet. This topic has received a lot of attention in recent years, with special treatment of cross-points

In this paper, we describe a continuum model that accurately reproduces the experimentally measured structure of physical shocks in a perfect gas. We begin by presenting a history of shock structure research, theoretical, experimental and numerical, to quantify the significant discrepancies between Navier–Stokes predictions and laboratory measurements. In our first main result, we discuss modifications

The paper shows how to use a genetic algorithm to design quasi one-dimensional structures with given properties. The superlattices were surrounded by water and made of epoxy resin and glass, with a layer thicknesses selected in such a way that a phononic bandgap occurs in the frequency range of acoustic waves. Multilayer transmission was calculated using the Transfer Matrix Method algorithm. In order

Thin plates with attached concentrated masses are considered. Time-harmonic flexural waves are generated by a force applied over a finite region of the plate. The problem of calculating the resulting plate response reduces to calculating the displacement of the masses, and this is done by solving a finite system of linear algebraic equations in the manner of previous work by Evans and Porter. Numerical

We study the solutions of a generalized Allen–Cahn equation deduced from a Landau energy functional, endowed with a non-constant higher order stiffness. We assume the stiffness to be a positive function of the field and we discuss the stability of the stationary solutions proving both linear and local non-linear stability.

We review work of Jordan on a hyperbolic variant of the Fisher–KPP equation, where a shock solution is found and the amplitude is calculated exactly. The Jordan procedure is extended to a hyperbolic variant of the Chafee–Infante equation. Extension of Jordan’s ideas to a model for traffic flow are also mentioned. We also examine a diffusive susceptible–infected (SI) model, and generalizations of diffusive

A new generalized complex modified Korteweg–de Vries equation associated with a 3 × 3 matrix spectral problem is proposed by resorting to the zero-curvature equation. Based on the gauge transformations between the Lax pairs, a Darboux transformation for the generalized complex modified Korteweg–de Vries equation is constructed, from which the corresponding N-fold Darboux transformations are derived

The discontinuous Lagrangian approach, allowing for a variational description of irreversible phenomena in continuum theory such as viscosity and thermal conductivity, is utilised for the analysis of damped acoustic waves. Starting from a Lagrangian for general viscous flow theory, by linearisation of the resulting Euler–Lagrange equations and performing an ensemble average, a single wave equation

Finite difference is a well-suited technique for modeling acoustic wave propagation in heterogeneous media as well as for imaging and inversion. Typically, the method aims at solving a set of partial differential equations for the unknown pressure field by using a regularly spaced grid. Although finite differences can be fast and cheap to implement, the accuracy of the solution is always restricted

By using the Hamilton principle of stationary action, we derive the governing equations and Rankine–Hugoniot conditions for continuous media where the specific energy depends on the space and time density derivatives. The governing system of equations is a time reversible dispersive system of conservation laws for the mass, momentum and energy. We obtain additional relations to the Rankine–Hugoniot

In this work, formulas for the reflection and transmission coefficients of one-dimensional linear water waves propagating over a submerged structure with a cycloidal cross section in presence of a sloping beach are determined. In the specialized literature, the previous coefficients are obtained mainly for the limit of linear water waves, considering that the water depth upstream and downstream of

In this paper we proposed the kinetic framework based fifth-order adaptive finite difference WENO schemes abbreviated as WENO-AO-K schemes to solve the compressible Euler equations, which are quasi-linear hyperbolic equations that can admit discontinuous solutions like shock and contact waves. The formulation of the proposed schemes is based on the kinetic theory where one can recover the Euler equations

We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the literature for the existence of solitary wave solutions. We then apply two numerical algorithms based on the Petviashvili method for solving the Rosenau equation with single or double power law nonlinearity. Numerical calculations

Speed of sound is a key parameter for the compressibility effects in multiphase flow. We present a new approach to do direct numerical simulations on the speed of sound in compressible two-phase flow, based on the stratified flow model (Chang and Liou, 2007). In this method, each face is divided into gas–gas, gas–liquid, and liquid–liquid parts via reconstruction of volume fraction. The numerical fluxes

Asymptotic homogenisation of an elastic metamaterial consisting of a series of plates interspaced by a fluid is considered. It is shown that the usual method must be extended by the inclusion of a second macroscale, the “emergent scale”, in order to correctly capture the behaviour of this metamaterial at low frequency. The leading order solutions for plane wave propagation are found and the effective

In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a finite number of Helmholtz resonators in a unit cell and that unit cell is repeated periodically. To solve the scattering problem, the mathematical framework elaborated

Conventional plane harmonic waves decay in direction of propagation, but unconventional harmonic waves grow in the direction of propagation. While a single unconventional wave cannot be a solution to a physically meaningful boundary value problem, these waves may have an essential contribution to the overall solution of a problem as long as this is a superposition of unconventional and conventional

The viscosity of water induces a vorticity near the free surface boundary. The resulting rotational component of the fluid velocity vector greatly complicates the water wave system. Several approaches to close this system have been proposed. Our analysis compares three common sets of model equations. The first set has a rotational kinematic boundary condition at the surface. In the second set, a gauge

The paper examines the model problem of high-frequency diffraction by a convex surface consisting of two parts. One is soft, the other is hard. The incident wave falls at a small angle to the line which separates soft and hard parts of the surface. The change in the boundary condition provokes the field in the Fock zone to have a rapid transverse variation. This causes a special boundary-layer to be

Analytical solutions are reported for the scattering coefficients of a solid elastic sphere suspended in a viscous fluid for arbitrary partial wave order. Expressions are derived for incident compressional and shear wave modes, taking into account the viscosity of the surrounding fluid and resultant wave mode conversion. The long compressional wavelength limit is employed to simplify the derivation

Three problems for a discrete analog of the Helmholtz equation are studied analytically using the plane wave decomposition and the Sommerfeld integral approach. They are: (1) the problem with a point source on an entire plane; (2) the problem of diffraction by a Dirichlet half-line; (3) the problem of diffraction by a Dirichlet right angle. It is shown that the total field can be represented as an

We systematically employ the method of matched asymptotic expansions to model Helmholtz resonators, with thermoviscous effects incorporated starting from first principles and with the lumped parameters characterizing the neck and cavity geometries precisely defined and provided explicitly for a wide range of geometries. With an eye towards modeling acoustic metasurfaces, we consider resonators embedded

To solve scattering problems with multi-transmitting boundary, we present an improved wave motion input method based on the idea that error caused by the difference between incident wave field used in calculation and waves propagating in finite element grids can be eliminated to suppress drift instability. In this method, a calculation scheme is proposed to obtain the numerical solution of incident

Based on the linear three-dimensional elastic theory and the mechanics theory of incremental deformation, using the Legendre orthogonal polynomial expansion (LOPE) method, the wave equations of Lamb wave propagation in the non-principal symmetry axes direction of anisotropic composite lamina was firstly derived when the initial stresses were applied in the horizontal and vertical directions. Subsequently

In this article we study the time evolution of broad banded, random inhomogeneous fields of deep water waves. Our study is based on solutions of the equation derived by Crawford, Saffman and Yuen in 1980, (Crawford et al., 1980). Our main result is that there is a significant increase in the probability of freak wave occurrence than that predicted from the Rayleigh distribution. This result follows

We study the model formulations of wave–current interactions in the framework of Euler equations. This work is intrigued by a recent paper from Wang et al. (2018) (hereafter WMY), which proposes such a model for the evolution of nonlinear broadband surface waves under the influence of a prescribed steady and irrotational current without vertical shear. We show that WMY’s model can be derived from a

The article describes an experimental study, which aims to detect signs of jump-like inelasticity in sandstone and to establish their influence on the P-wave attenuation. The measurements were taken in a sandstone sample using the reflection method at a pulse frequency of 1 MHz and with the strain amplitudes ε1 ≈ 0.1 microstrain and ε2 ≈ 0.24 microstrain at a hydrostatic pressure of 10 MPa. Using the

At long lapse times in randomly fluctuating media with macroscopic isotropy (texture-less media), the energy of elastic waves is equipartitioned between compressional (P) and shear (S) waves. This property is independent of the local isotropy or anisotropy of the heterogeneous constitutive tensor and of the type of source. However the local symmetry of the constitutive tensor does influence the rate

An apparent increase in the frequency and intensity of natural disturbances and anthropogenic activities accelerates the global degradation of coral reefs. The emergency planning for coastal erosion and flooding along the low-lying coasts fronted by coral reefs underscores the need to predict and evaluate reasonably the hydrodynamic consequences of reef degradation. Here the ability of the well validated

A systematic boundary-layer approach is for the first time applied to diffraction of a high-frequency plane wave by a contour with a jump of curvature. Assuming that the incident wave is non-tangent, we present a detailed description of the outgoing wavefield within a boundary layer surrounding the point of non-smoothness of the contour. This allows us to describe the wavefield within a transition

In this study, a 2-D infinite flexible waveguide is considered. The waveguide carries a weakly nonlinear acoustic fluid. It is bounded on one side by a weakly nonlinear flexible membrane and the other side is rigid. The infinite waveguide is driven at the origin by a piston oscillating at a single frequency. However, we focus only on the positive side of the piston. As the coupled waves propagate in