Real-time nonlinear cylinder wave force reconstruction in stochastic wave field considering second-order wave effects

This study provides a novel method for reconstructing real-time nonlinear wave forces on a large-scale circular cylinder by considering second-order wave effects. Potential theory is utilized for deriving the expression of wave forces with the measured data of wave elevation. Approximate expressions of quadratic transfer functions are built with undetermined coefficients, which are resolved by using the historical data of measured wave elevation. Two different algorithms, including fast Fourier transform (FFT) and recursive least squares (RLS), are adopted for real-time reconstruction. Hydrodynamic tests are conducted in the wave flume on a circular cylinder to examine the effectiveness of the nonlinear reconstruction method. Comparative results demonstrate that the accuracy of real-time reconstructed wave forces is significantly enhanced by the present method. The over-prediction errors at force crests and the under-prediction errors at force troughs have been reduced. Furthermore, comparative results show that the nonlinear method implemented by the FFT algorithm provides more accurate results, whereas the RLS algorithm is more time cost efficient.     

Interaction between a stokes wave packet and a solitary wave

This paper is a theoretical and experimental study of the propagation of a short gravity wave packet (modulated Stokes wave) over a solitary wave. The theoretical approach used here relies on a nonlinear WKB-type perturbation method. This method yields a theory of gravity waves that can describe both short and long waves simultaneously. We obtain explicit analytical solutions describing the interaction between the soliton and the short wave packet: phase shifts, variations of wavelengths and of frequencies (Doppler effects). In the experimental part of this work the phase shift experienced by the Stokes wave is measured. The theoretical conclusions are confirmed.     

Solitary wave interaction

The interaction between solitary wave solutions to a double sine-Gordon equation is examined numerically. Depending on the velocity, formation of breather-like modes or quasi solitonic behaviour are observed when a 2δ-kink interact with a 2π-antikink. As a result of collision between a (2π-2δ)-kink and a (2π-2δ)-antikink two 2δ-kink-antikink pairs always appear.     

Shock wave trapping

This paper presents a two-dimensional investigation into the effectiveness of trapping shock and blast waves in a duct in order to enhance attenuation, by placing an array of opposing wedges in the channel. The concept of the wedge arrangement in the trap is to allow easy shock wave entry, with weak reflected shocks, into the trap, but stronger internal reflected shocks if a wave is re-emering. The internal reflections, including those of vortices shed from earlier shock passage, result in strong shock attenuation. Different wedge placements, wedge angles, and area blockages are investigated numerically, as well as experimentally for a particular case, using pressure measurement and schlieren photography. Received 4 August 1995 / Accepted 12 December 1995     

Pulses in binary wave guide arrays and long wave PDE approximations

Binary waveguide arrays are linear arrays of optical waveguides with binary alternation of parameters, and have been of recent interest. They can be modeled by systems of nonlinear ODEs with forms related to the discrete nonlinear Schrödinger equation. Such equations can also arise in semi-classical molecular models of polymers with excitable states in each monomer, and coupling between these.An important class of solutions arises from an initially highly localized signal, such as input to a single element of the array. Simulations show that for a wide array of parameter values and of such initial data, a pulse is generated that travels approximately as a traveling wave. After a suitable phase shift in the variables, this pulse quickly develops a slow spatial variation, leading to a long-wave approximation by a system of coupled third order PDEs; one each for nodes of even and odd indices.This system of PDEs is presented, and verified to quite accurately reproduce the pulse propagation seen in the ODE system; further there is often a strong tendency for the behavior of the two PDE components to converge, with a corresponding convergence of the even and odd index parts of the ODE system solution. The PDE model gives some indication of why this occurs.     

Non-linear wave interactions

Non-linear wave interactions in physical systems are considered and analytical solutions of the governing equations obtained. Stability criteria are developed by obtaining general solutions for the first-order perturbations of the solutions. The problems discussed include various wave resonance interactions including Davydov's alpha-helix and Langmuir waves in a plasma.     

Interference between a centered rarefaction wave and an inclined shock wave

The gas flow in the zone of interaction between an oblique shock and a centered isentropic rarefaction wave is studied using the direct statistical simulation method for solving the Boltzmann equation. The data of calculations of the shock and rarefaction wave structures, flow fields, and streamlines are given for the free-stream Mach number M_∞ = 6, 4 and 2. The formation of the interaction zone is simulated by a gas flow past a double-plane wedge in which the break of the generating line leads to formation of the centered isentropic rarefaction wave. The results of calculations of this flow in solving the Boltzmann equation are given in the Euler approximation.     

Bifurcations of travelling wave solutions for a coupled nonlinear wave system

Introduction FangShaomeiandGuoBoling[1]consideredthefollowingtimeperiodicproblemof dampedcouplednonlinearwaveequations:ut f(u)x-αuxx βuxxx 2vvx=G1(u,v) h1(x),vt-γvxx 2(uv)x g(v)x=G2(u,v) h2(x),(1)whereα,β,γareconstants,andγ>0,β≠0.Undertheperiodicboundaryconditions,the authorsobtainedtheuniqueexistenceofstrongsolutionsfortheabovesystem.InthispaperweshallconsiderbifurcationbehaviorofthetravellingwavesolutionsofEq.(1)inthecaseGi(u,v)≡0,hi(u,v)≡0(i=1,2).Letξ=x-ct,u=u(x-ct),where cis…     

A non-reflective spectral wave maker for SPH modeling of nonlinear wave motion

A momentum source function derived from the linear wave theory is introduced into the weakly compressible smoothed particle hydrodynamic (SPH) model for the long-time simulation of regular and irregular wave generation problems. Wave absorption is realized by adding a velocity attenuation term into the governing momentum equation. The performances of the wave maker are tested under different wave conditions. The wave maker is then applied to the study of the challenging processes, such as random wave breaking on the reef-face or the reef-crest, wave setup and spectral transfer of wave energy from the peak frequency to lower frequencies over the reef-flat. The predicted results are compared with the experimental data and a good agreement is obtained. The SPH model with a non-reflective spectral wave maker can be used as a practical tool for studying wave interaction with coastal structures.     

Travelling wave solutions for a second order wave equation of KdV type

The theory of planar dynamical systems is used to study the dynamical behaviours of travelling wave solutions of a nonlinear wave equations of KdV type.In different regions of the parametric space,sufficient conditions to guarantee the existence of solitary wave solutions,periodic wave solutions,kink and anti-kink wave solutions are given.All possible exact explicit parametric representations are obtained for these waves.     

Shock wave triple-point morphology

The existence and characteristics of shock wave triple points are examined. The analysis utilizes a single flow plane for the three shocks and is local to the triple point. It applies when the flow is unsteady, three-dimensional, and the upstream flow is nonuniform. Under more restrictive conditions, a relation is also derived for the ratio of the curvature of the Mach stem to that of the reflected shock. For given values of the ratio of specific heats, γ, and the upstream Mach number, M ₁, a solution window is established. A parametric set of solutions is generated within the window for γ = 1, 1.4, and 5/3 and for 16 values of M ₁ ranging from solution onset to M ₁ = 6.A solution can be one of three types, these stem from the velocity tangency condition along the slip stream. Topics are addressed such as solution multiplicity, shock wave and slip stream orientation, the nature of the reflected wave (weak, strong, inverted, normal), the nature of the Mach stem (weak, strong, normal), and differences due to changes in γ and M ₁.     

Numerical simulations of wave interactions with vertical wave barriers using the SPH method

This paper focuses on the fluid boundary separation problem of the conventional dynamic solid boundary treatment (DSBT) and proposes a modified DSBT (MDSBT). Classic 2D free dam break flows and 3D dam break flows against a rectangular box are used to assess the performance of this MDSBT in free surface flow and violent fluid–structure interaction, respectively. Another test, water column oscillations in a U‐tube, is specially designed to reveal the applicability of dealing with two types of particular boundaries: the wet–dry solid boundary and the large‐curvature solid boundary. A comparison between the numerical results and the experimental data shows that the MDSBT is capable of eliminating the fluid boundary separation, improving the accuracy of the solid boundary pressure calculations and preventing the unphysical penetration of fluid particles. Using a 2D SPH numerical wave tank with MDSBT, the interactions between regular waves and a simplified vertical wave barrier are simulated. The numerical results reveal that the maximum horizontal force occurs at the endpoint of the vertical board, and with the enlargement of the relative submerged board length, the maximum moment grows linearly; furthermore, the relative average mass transportation under the breakwater initially increases to 11.14 per wave strike but is later reduced. The numerical simulation of a full‐scale 3D wave barrier with two vertical boards shows that the wave and structure interactions in the practical project are far more complicated than in the simplified 2D models. The SPH model using the MDSBT is capable of providing a reference for engineering designs. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiple rogue wave,breather wave and interaction solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation

Nonlinear Dynamics - Based on a direct variable transformation, we obtain multiple rogue wave solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation, including...     

Quasi-kinematic flood wave propagation

Summary In the flood waves of natural streams, the plot of discharge versus simultaneous water level values at a river station usually show a little shift from the socalled steady rating curve. In other terms, natural flood waves normally have small loops and may be considered to be quasi-kinematic. Very often, on the basis of the steady rating curve and of the observed hydrograph at an upstream gage station, we can quickly and easily forecast the values and time of flood peaks at one or more downstream channel sections. This article describes a set of very simple formulas first to check whether the flood wave may be considered to be quasi-kinematic, and then to estimate the speed and the attenuation with which it moves downstream. For a number of prismatic channels, the results were compared with those obtained with equally simple, currently used formulas (Jones, Henderson) and with the exact solutions. The comparisons showed that the formulas proposed in this article are more general and accurate than the other known simple formulas and that, for flood loops of less than 10%, give results that are very near to being exact.

---

Sommario Nei fenomeni di piena dei corsi d'acqua naturali la successions nel tempo dei valori di portata e livello idrometrico in una sezione d'alveo presenta, nella gran parte dei casi, modesti scostamenti dalla cosiddetta scala di deflusso di moto permanente: in altri termini normalmente le onde naturali di piena hanno cappi modesti e possono ritenersi quasi cinematiche. Molto spesso, data una stazione di monte in cui sia nota la scala di deflusso el'drogrammadei livelli, occorre prevedere semplicemente e rapidamente i valori e gli istanti dei colmi di portata e livello in una o più sezioni a valle. In questo articolo vengono presentate formule molto semplici per verificare dapprima che l'onda di piena possa ritenersi quasi cinematica, e stimare quindi la velocità e l'attenuazione con cui i colmi si propagano verso valle. I confronti fatti, per alcuni alvei cilindrici, con la soluzione esatta e con i risultati ottenibili con formule altrettanto semplici e di uso corrente (Jones, Henderson), mostrano che le formule proposte sono più generali e corrette di queste ultime, e danno risultati quasi esatti finchè i cappi di piena relativi sono inferiori al 10%.

---

List of symbols P(x, z) steady rating curve - Q volumetric rate of discharge - q=Q-P flood loop - g gravitational acceleration - I water surface slope - c=dP/dA kinematic wave velocity - y water depth - p, s time and space steps - x, t channel distance starting upstream; time - z water surface height above datum - A, B channel cross section area and surface width - F=B Q ²/gA ³ Froude number - L,L ₀,L ₁,L ₂,L ₃ characteristic lengths of the channel - T=L/c characteristic time of the channel - f _x =f/x, f _f =f/t etc for the partial derivatives - Df/Dt,Df/Dx for the derivatives of functionf following the discharge peak     

Transformation method and wave control

Transformation method provides an efficient way to control wave propagation by materials.The transformed relations for field and material during a transformation are essential to fulfill this method.We propose a systematic method to derive the transformed relations for a general physic process,the constraint conditions are obtained by considering geometrical and physical constraint during a mapping. The proposed method is applied to Navier＇s equation for elastodynamics,Helmholtz＇s equation for acoustic wave and Maxwell＇s equation for electromagnetic wave,the corresponding transformed relations are derived,which can be used in the framework of transformation method for wave control.We show that contrary to electromagnetic wave,the transformed relations are not uniquely determined for elastic wave and acoustic wave,so we have a freedom to choose them differently.Using the obtained transformed relations,we also provide some examples for device design,a concentrator for elastic wave,devices for illusion acoustic and illusion optics are conceived and validated by numerical simulations.     

Development of a numerical wave tank for analysis of nonlinear and irregular wave field

A numerical wave-absorption filter has been developed for an open boundary condition in the analysis of nonlinear and irregular wave evolution. The filter is composed of a simulated sponge layer and Sommerfeld's radiation condition at the outer edge of the layer. The wave-absorption characteristics of the filter have been investigated by applying the linear potential theory and a two-dimensional nonlinear boundary element model. In both cases, the filter is found to he applicable for a wide range of wave parameters. In order to realize an idealized “numerical wave tank”, the present model also incorporates a nonreflective wave generator in the computational domain composed of a series of vertically aligned point sources. Numerous numerical experiments demonstrate that the present approach is effective in generating an arbitrary wave profile without reflection not only at the open boundaries but also at the wave generator.     

Computation of wave interference and relaxation of particles after passing of a shock wave

Interaction of a shock wave with a system of motionless or relaxing particles is numerically simulated. Regimes of the gas flow around these particles are described, and the influence of the initial parameters of the examined phenomenon on the flow pattern is analyzed. The drag coefficient of particles is calculated as a function of the Mach number behind the shock wave at a fixed Reynolds number. The dynamics of heat exchange for particles of different sizes (10 μm–1 mm) is determined, and the laws of thermal relaxation after passing of a shock wave over the system of particles are found. The times of thermal and velocity relaxation of particles are estimated as functions of the Reynolds number, and the predicted relaxation time is compared with the corresponding empirical dependences.     

An interfacial Gerstner-type trapped wave

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.