Description: Publication date: Available online 27 December 2017 Source: Wave Motion Author(s): S.P. Groth, D.P. Hewett, S. Langdon We present a novel hybrid numerical-asymptotic boundary element method for high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. Our method is based on a standard reformulation of the associated transmission boundary value problem as a direct boundary integral equation for the unknown Cauchy data, but with a nonstandard numerical discretization which efficiently captures the high frequency oscillatory behaviour. The Cauchy data is represented as a sum of the classical geometrical optics approximation, computed by a beam tracing algorithm, plus a contribution due to diffraction, computed by a Galerkin boundary element method using oscillatory basis functions chosen according to the principles of the Geometrical Theory of Diffraction. We demonstrate with a range of numerical experiments that our boundary element method can achieve a fixed accuracy of approximation using only a relatively small, frequency-independent number of degrees of freedom. Moreover, for the scattering scenarios we consider, the inclusion of the diffraction term provides an order of magnitude improvement in accuracy over the geometrical optics approximation alone.

Description: Publication date: Available online 23 December 2017 Source: Wave Motion Author(s): Igor V. Andrianov, Vladyslav V. Danishevskyy, Heiko Topol, Adriaan S. Luyt Biodegradable polymers find an increasing number of applications in different fields of engineering and medicine due to their environmental-friendly degradation. The process of degradation of biodegradable polymer constituents and the bonding quality between the constituents in composites can be identified by the analysis of the phononic band structure. The present article considers a layered composite, in which the matrix degradation is modeled by a multitude of layers with decreasing values of their mechanical properties. Bonding between the inclusion and the degrading matrix is taken into account by a linear elastic bonding model in the first case and by a viscoelastic model in the second case.

Description: Publication date: Available online 20 December 2017 Source: Wave Motion Author(s): K. Terletska, K.T. Jung, V. Maderich, K.O. Kim The dynamics and energetics of a frontal collision of internal solitary waves (ISW) of first mode in a fluid with two homogeneous layers separated by a thin interfacial layer are studied numerically within the framework of the Navier–Stokes equations for stratified fluid. It was shown that the head-on collision of internal solitary waves of small and moderate amplitude results in a small phase shift and in the generation of dispersive wave train travelling behind the transmitted solitary wave. The phase shift grows as amplitudes of the interacting waves increase. The maximum run-up amplitude during the wave collision reaches a value larger than the sum of the amplitudes of the incident solitary waves. The excess of the maximum run-up amplitude over the sum of the amplitudes of the colliding waves grows with the increasing amplitude of interacting waves of small and moderate amplitudes whereas it decreases for colliding waves of large amplitude. Unlike the waves of small and moderate amplitudes collision of ISWs of large amplitude was accompanied by shear instability and the formation of Kelvin—Helmholtz (KH) vortices in the interface layer, however, subsequently waves again become stable. The loss of energy due to the KH instability does not exceed 5%–6%. An interaction of large amplitude ISW with even small amplitude ISW can trigger instability of larger wave and development of KH billows in larger wave. When smaller wave amplitude increases the wave interaction was accompanied by KH instability of both waves.

Description: Publication date: Available online 18 December 2017 Source: Wave Motion Author(s): Wencheng Hu, Wenhua Huang, Zhiming Lu, Yury Stepanyants The interactions of multi-lumps within the Kadomtsev–Petviashvili-1 (KP1) equation are studied analytically and numerically. The dependence of stationary multi-lump structures on free parameters is discussed. The interactions of single lumps with each other and with a more complex objects such as bi-lumps, as well as the interactions of bi-lumps with each other are studied numerically. The results obtained are described and illustrated graphically (the videos are also available).

Description: Publication date: Available online 18 December 2017 Source: Wave Motion Author(s): Carlos Pérez-Arancibia, Eduardo Godoy, Mario Durán This paper presents a mathematical model and a numerical procedure to simulate an acoustic well stimulation (AWS) method for enhancing the permeability of the rock formation surrounding oil and gas wells. The AWS method considered herein aims to exploit the well-known permeability-enhancing effect of mechanical vibrations in acoustically porous materials, by transmitting time-harmonic sound waves from a sound source device—placed inside the well—to the well perforations made into the formation. The efficiency of the AWS is assessed by quantifying the amount of acoustic energy transmitted from the source device to the rock formation in terms of the emission frequency and the well configuration. A simple methodology to find optimal emission frequencies for a given well configuration is presented. The proposed model is based on the Helmholtz equation, a sound-hard boundary condition at the casing, and an impedance boundary condition that effectively accounts for the porous solid-fluid interaction at the interface between the rock formation and the well perforations. Exact non-reflecting boundary conditions derived from Dirichlet-to-Neumann maps are utilized to truncate the circular cylindrical waveguides considered in the model. The resulting boundary value problem is then numerically solved by means of the finite element method. A variety of numerical examples are presented in order to demonstrate the effectiveness of the proposed procedure for finding optimal emission frequencies.

Description: Publication date: Available online 15 December 2017 Source: Wave Motion Author(s): Jan Erik H. Weber Coastally trapped rotational interfacial waves are studied theoretically by using a Lagrangian formulation of fluid motion in a rotating ocean. The waves propagate along the interface between two immiscible inviscid incompressible fluid layers of finite depths and different densities, and are trapped at a straight wall due to the Coriolis force. For layers of finite depth, solutions are sought as series expansions after a small parameter. Comparison is made with the irrotational interfacial Kelvin wave. Both types of waves are identical to first order, having zero vorticity. The second order solution yields a relation between the vorticity and the velocity shear in the wave motion. Requiring that the mean motion in both layers is irrotational, then follows the well-known Stokes drift for interfacial Kelvin waves. On the other hand, if the mean forward drift is identically zero, we obtain the second order vorticity in the Gerstner-type wave. The solutions in both layers for the Gerstner-type interfacial wave are given analytically to second order. It is shown that small density differences and thin upper layers both act to yield a shape of the material interfacial with broader crests and sharper troughs. These effects also tend to make the particle trajectories at the interface in both layers become distorted ellipses which are flatter on the upper side. It is concluded that the effect of air excludes the possibility of observing the exact Gerstner wave in deep water.

Description: Publication date: Available online 15 December 2017 Source: Wave Motion Author(s): A.B. Magan, D.P. Mason, C. Harley The propagation of displacement waves and stress waves for implicit constitutive equations is investigated. This new class of constitutive equations contain Cauchy elastic and hyperelastic bodies as subclasses. We consider a particular subclass where the strain is expressed in terms of a non-invertible function of the stress. This subclass of constitutive equations describe elastic responses where the stress and linearised strain are nonlinearly related. Such a phenomenon cannot be captured in the classical theory. Two constitutive equations are studied. The first constitutive equation is analogous to the constitutive equation for a power-law fluid with an exponent n in the expression for the stress and the second constitutive equation can describe elastic bodies which exhibit limiting strain. The special semi-inverse solution gives a system of nonlinear hyperbolic partial differential equations. These systems can be written as single partial differential equations which describe nonlinear shear stress waves. Solitary wave solutions for each constitutive equation are derived. Perturbation solutions for the system of partial differential equations for displacement and stress are considered and travelling wave and standing wave solutions are found. Although the solutions for both the travelling waves and standing waves contain a secular term, the perturbation expansions break down outside the range of interest. The speed of the solitary wave for both constitutive equations was obtained. The solitary waves develop a shock front and estimates for the time that this will occur are derived. The shock front develops at the back of the wave for the power-law constitutive equation and at the front of the wave for the strain-limiting constitutive equation. For the travelling waves the stress is non-zero at the wave front and the stress waves propagate as shock waves. The speed of propagation and the amplitude of the travelling waves and the period of oscillation of the standing waves are compared for the two constitutive equations.

Description: Publication date: Available online 14 December 2017 Source: Wave Motion Author(s): Yusheng Qi, Guangyu Wu, Yuming Liu, Dick K.P. Yue Our interest is the phase-resolved reconstruction and forecast of multidirectional irregular gravity wave fields based on specific wave measurements. We consider the theoretical predictable zone P in space–time within which the phase-resolved wave field can be fully reconstructed/forecasted based on the given measurements. Using linearized wave theory and reasonable assumptions of the frequency and directional extent of the wave field, we obtain closed-form expressions for P in terms of set theory expressions involving the individual measurement. We derive and illustrate P obtained for measurements at one or more fixed locations over time, for moving probes, for whole-area wave measurements, and combinations of these. We also consider the problem of optimal deployment of these measurements to maximize the volume of P in space–time. For J probes under optimal deployment, we show that the volume of P relative to that of a single probe scales as J 3 for large J .

Description: Publication date: Available online 22 November 2017 Source: Wave Motion Author(s): Yang Liu, Kai Zhang, Wei-Zhong Zhang, Xiu-Yun Meng Large cable net structures have been widely applied in aerospace engineering due to the feature of light-weight, high packaging efficiency, and high thermal stability. Structural vibrations induced by a variety of disturbances are inevitable in the space environment, resulting in the requirement of effective vibration control strategies for large cable net structures. Since the large cable net structures have many closely spaced vibrational modes in the range of low frequencies, traditional modal based control may cause modal truncation and spillover problems. In this paper, a wave-based boundary control strategy is adopted and its effectiveness to control the vibration of cable net structures is investigated, by transfer function analysis and numerical methods. It is found that the structural vibration can be absolutely resisted by applying the wave-based boundary controllers onto all the exterior nodes, when disturbances come from the external boundaries of the cable net. Our results in this paper can provide a theoretical basis for the vibration control of large cable net structures.

Description: Publication date: January 2018 Source: Wave Motion, Volume 76