Numerical Modelling of Standing Waves with Three-Dimensional Non-Linear Wave Propagation Model

Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate the wave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth (d/lambda(0), ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, And the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions possess good adaptability.

Existence and Stability of Standing Waves for the Nonlinear Schrödinger Equation with Combined Nonlinearities and a Partial Harmonic Potential

In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L2-supercritical case, we obtain the existence and stability of standing waves. Our results are complements to the results of Carles and Il’yasov’s artical, where orbital stability of standing waves have been studied for the 2D Schrödinger equation with combined nonlinearities and harmonic potential.

Contact Analysis and Modeling of Standing Wave Linear Ultrasonic Motor

A contact model for describing the contact mechanics between the stator and slider of the standing wave linear ultrasonic motor was presented. The proposed model starts from the assumption that the vibration characteristics of the stator is not affected by the contact process. A modified friction models was used to analyze the contact problems. Firstly, the dynamic normal contact force, interface friction force, and steady-state characteristics were analyzed. Secondly, the influences of the contact layer material, the dynamic characteristics of the stator, and the pre-load on motor performance were simulated. Finally, to validate the contact model, a linear ultrasonic motor based on in-plane modes was used as an example. The corresponding results show that a set of simulation of motor performances based on the proposed contact mechanism is in good agreement with experimental results. This model is helpful to understanding the operation principle of the standing wave linear motor and thus contributes to the design of these types of motor.

The characteristic and prediction of scour in front of breakwaters by standing waves

In this paper bottom scours in front of vertical breakwaters by standing waves are systematically investigated, the scouring patterns, criterion for differentiating the scouring patterns and scouring mechanism are discussed ; a formula of maximum depth of scouring trough considering sediment size is given; and influence of mound foundation on bottom scours is investigated.

Physical design and cooling test of C-band standing wave accelerating tube

The physical design and cooling test of a C-band 2MeV standing wave （SW） accelerating tube are described in this paper. The designed accelerating structure consists of 3-cell buncher and 4-cell accelerating section with a total length of about 163mm, excited with 1MW magnetron. Dynamic simulation presents that about 150mA beam pulse current and 30% capture efficiency can be achieved. By means of nonlinear Gauss fit on electron transverse distribution, the diameter of beam spot FWHM （full width at half maximum of density distribution） is about 0.55mm. Cooling test results of the accelerating tube show that frequencies of cavities are tuned to 5527MHz and the field distribution of bunching section is about 3：9：10.

Influence of the Phase of the Antenna Current Standing Wave on the Power Flux in Ion Cyclotron Heating

For ion cyclotron resonance heating, the current on the antenna surface exists in a form of standing wave, and the phase of the poloidal current standing wave affects significantly on the performance of the coupling. In this paper, a coupling calculation is carried out based on a practical model for the loop antenna. The ion cyclotron wave coupling performance depends greatly on the antenna current propagation constant and the phase of standing wave. For a small antenna-current-propagation constant, the antenna coupling performance is more sensitive to a π/2 change in the phase of standing wave.

Experimental study of freak waves due to three-dimensional island terrain in random wave

An experimental study is carried out for waves passing an isolated reef terrain in a wave tank. A three-dimensional model of a representative and isolated reef terrain in the West Pacific is built. Random wave trains with various periods and wave heights are generated by a wave maker using the improved JONSWAP spectrum. It is observed that there are different kinds of generation processes and waveforms of freak waves. The freak wave factor Hm/Hs (where Hm is the maximum wave height of wave series, and Hs is significant wave height) is analyzed in detail, in terms of the skewness, kurtosis and water depth, as well as the relationship between freak wave height H& and skewness. The freak wave factor Hm/Hs is found to be in positive correlation with the kurtosis, while larger H[x tends to be related with bigger skewness. The rapid variation of water depth, such as slope and seamount, contributes to the occurrence probability of freak waves.

Numerical simulation of standing waves for ultrasonic purification of magnesium alloy melt

It was attempted to enhance and accelerate the separation of oxidation inclusions from magnesium alloy melt by virtue of ultrasonic agglomeration technology.In order to investigate the feasibility and effectiveness of standing waves for ultrasonic purification of magnesium alloy melt,numerical simulation and relevant experiment were carried out.The numerical simulation was broken into two main aspects.On one hand,the ultrasonic field propagations within the cells with various shapes were characterized by numerical solutions of the wave equation and with a careful choice of geometry a nearly idealized standing wave field was finally obtained.On the other hand,within such a standing wave field the agglomeration behavior of oxidation inclusions in magnesium alloy melt was analyzed and discussed.The agglomeration time and agglomeration position of oxidation inclusions were predicted with numerical simulation method.The results show that the oxidation inclusions whose apparent densities are close to the density of the melt can agglomerate at wave nodes in a short time which to a great extent enhances and accelerates the separation of oxidation inclusions from magnesium alloy melt.

Numerical study of three-dimensional wave-induced longshore current's effects on sediment spreading of the Huanghe River mouth

A three-dimensional wave radiation stress is introduced into the hydrodynamic sediment coupled model COHERENS-SED, which has been developed through introducing wave-enhanced bottom shear stress, wave dependent surface drag coefficient, wave-induced surface mixing, SWAN, damping function of sediment on turbulence, sediment model and depth-dependent wave radiation stress to COHERENS. The COHERENS-SED is adopted to study the effects induced by wave-induced three-dimensional longshore current on suspended sediment spreading of the Huanghe River （Yellow River） mouth. Several different cases divided by setting different wave parameters of inputting boundary waves are carried out. The modeling results agree with measurement data. In terms of simulation results, it is easy to know that three-dimensional wave radiation stress plays an obvious role when inputting boundary wave height is stronger than 3 m. Moreover, wave direction also affects the sediment spreading rules of the mouth strongly too.

A third-order asymptotic solution of nonlinear standing water waves in Lagrangian coordinates

Asymptotic solutions up to third-order which describe irrotational finite amplitude standing waves are derived in Lagrangian coordinates. The analytical Lagrangian solution that is uniformly valid for large times satisfies the irrotational condition and the pressure p = 0 at the free surface, which is in contrast with the Eulerian solution existing under a residual pressure at the free surface due to Taylor＇s series expansion. In the third-order Lagrangian approximation, the explicit parametric equation and the Lagrangian wave frequency of water particles could be obtained. In particular, the Lagrangian mean level of a particle motion that is a function of vertical label is found as a part of the solution which is different from that in an Eulerian description. The dynamic properties of nonlinear standing waves in water of a finite depth, including particle trajectory, surface profile and wave pressure are investigated. It is also shown that the Lagrangian solution is superior to an Eulerian solution of the same order for describing the wave shape and the kinematics above the mean water level.

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.

A Three-dimensional Wave Activity Flux of Inertia–Gravity Waves and Its Application to a Rainstorm Event

A three-dimensional transformed Eulerian-mean(3D TEM) equation under a non-hydrostatic and non-geostrophic assumption is deduced in this study. The vertical component of the 3D wave activity flux deduced here is the primary difference from previous studies, which is suitable to mesoscale systems. Using the 3D TEM equation, the energy propagation of the inertia–gravity waves and how the generation and dissipation of the inertia–gravity waves drive the mean flow can be examined. During the mature stage of a heavy precipitation event, the maximum of the Eliassen–Palm(EP) flux divergence is primarily concentrated at the height of 10–14 km, where the energy of the inertia–gravity waves propagates forward(eastward) and upward. Examining the contribution of each term of the 3D TEM equation shows that the EP flux divergence is the primary contributor to the mean flow tendency. The EP flux divergence decelerates the zonal wind above and below the high-level jet at the height of 10 km and 15 km, and accelerates the high-level jet at the height of 12–14 km. This structure enhances the vertical wind shear of the environment and promotes the development of the rainstorm.

EXISTENCE AND STABILITY OF STANDING WAVES FOR A COUPLED NONLINEAR SCHRDINGER SYSTEM

We study the existence and stability of the standing waves of two coupled SchrSdinger equations with potentials ｜x｜bi（bi ∈ R,i = 1, 2）. Under suitable conditions on the growth of the nonlinear terms, we first establish the existence of standing waves of the SchrSdinger system by solving a L2-normalized minimization problem, then prove that the set of all minimizers of this minimization problem is stable. Finally, we obtain the least energy solutions by the Nehari method and prove that the orbit sets of these least energy solutions are unstable, which generalizes the results of [11] where b1 = b2 = 2.

Poleward-moving recurrent auroral arcs associated with impulse-excited standing hydromagnetic waves

In Earth's high-latitude ionosphere, the poleward motion of east–west elongated auroral arcs has been attributed to standing hydromagnetic waves, especially when the auroral arcs appear quasi-periodically with a recurrence time of a few minutes. The validation of this scenario requires spacecraft observations of ultra-low-frequency hydromagnetic waves in the magnetosphere and simultaneous observations of poleward-moving auroral arcs near the spacecraft footprints. Here we present the first observational evidence from the multi-spacecraft THEMIS (Time History of Events and Macroscale Interactions during Substorms) mission and the conjugated all-sky imager to support the scenario that standing hydromagnetic waves can generate the quasi-periodic appearance of poleward-moving auroral arcs. In this specific event, the observed waves were toroidal branches of the standing hydromagnetic waves, which were excited by a pulse in the solar wind dynamic pressure. Multi-spacecraft measurements from THEMIS also suggest higher wave frequencies at lower L shells (consistent with the distribution of magnetic field line eigenfrequencies), which indicates that the phase difference across latitudes would increase with time. As time proceeds, the enlarged phase difference corresponds to a lower propagation speed of the auroral arcs, which agrees very well with the ground-based optical data.

Relationship of mode transitions and standing waves in helicon plasmas

Helicon wave plasma sources have the well-known advantages of high efficiency and high plasma density, with broad applications in many areas. The crucial mechanism lies with mode transitions, which has been an outstanding issue for years. We have built a fluid simulation model and further developed the Peking University Helicon Discharge code. The mode transitions, also known as density jumps, of a single-loop antenna discharge are reproduced in simulations for the first time. It is found that large-amplitude standing helicon waves(SHWs) are responsible for the mode transitions, similar to those of a resonant cavity for laser generation.This paper intends to give a complete and quantitative SHW resonance theory to explain the relationship of the mode transitions and the SHWs. The SHW resonance theory reasonably explains several key questions in helicon plasmas, such as mode transition and efficient power absorption, and helps to improve future plasma generation methods.

Reflection of three-dimensional plane waves at the free surface of a rotating triclinic half-space under the context of generalized thermoelasticity

The reflection of three-dimensional(3D) plane waves in a highly anisotropic(triclinic) medium under the context of generalized thermoelasticity is studied. The thermoelastic nature of the 3D plane waves in an anisotropic medium is investigated in the perspective of the three-phase-lag(TPL), dual-phase-lag(DPL), Green-Naghdi-III(GNIII), Lord-Shulman(LS), and classical coupled(CL) theories. The reflection coefficients and energy ratios for all the reflected waves are obtained in a mathematical form. The rotational effects on the reflection characteristics of the 3D waves are discussed under the context of generalized thermoelasticity. Comparative analyses for the reflection coefficients of the waves among these generalized thermoelastic theories are performed. The energy ratios for each of the reflected waves establish the energy conservation law in the reflection phenomena of the plane waves. The highly anisotropic materials along with the rotation may have a significant role in the phenomenon of the reflection behavior of the 3D waves. Numerical computations are performed for the graphical representation of the study.

A study on the Antarctic circumpolar wave mode-A coexistence system of standing and traveling wave

The Antarctic circumpolar wave （ACW） has become a focus of the air-sea coupled Southern Ocean study since 1996, when it was discovered as an air-sea coupled interannual signal propagating eastward in the region of the Antarctic Circumpolar Current （ACC）. In order to analyze the mechanism of discontinuity along the latitudinal propagation, a new idea that ACW is a system with a traveling wave in the Southern Pacific and Atlantic Ocean and with a concurrent standing wave in the southern Indian Ocean is proposed in this paper. Based on the ideal wave principle, the average wave parameters of ACW is achieved using a non-linear approximation method, by which we find that the standing part and the traveling part possess similar radius frequency, proving their belonging to an integral system. We also give the latitudinal distribution of wave speed with which we could tell the reason for steady propagation during the same period. The spatial distribution of the propagation reveals complex process with variant spatial and temporal scales--The ENSO scale oscillation greatly impacts on the traveling process, while the result at the south of Australia indicates little connection between the Indian Ocean and the Pacific, which may be blocked by the vibration at the west of the Pacific. The advective effect of ACC on the propagation process should be examined clearly through dynamical method.

Three-Dimensional Model Test for Port Engineering with Multi-Directional Waves

-The necessity of using irregular waves, especially multi- directional waves to conduct three-dimensional model tests for port engineering and the test method are described in this paper through an example of model test for a port. The test results show that a deep navigation channel has a large effect on the waves in front of the breakwater near the port entrance and on the wave condition in the port.

Numerical study on wave loads and motions of two ships advancing in waves by using three-dimensional translating-pulsating source

A frequency domain analysis method based on the three-dimensional translating-pulsating （3DTP） source Green function is developed to investigate wave loads and free motions of two ships advancing on parallel course in waves. Two experiments are carried out respectively to mea- sure the wave loads and the free motions for a pair of side-by- side arranged ship models advancing with an identical speed in head regular waves. For comparison, each model is also tested alone. Predictions obtained by the present solution are found in favorable agreement with the model tests and are more accurate than the traditional method based on the three dimensional pulsating （3DP） source Green function. Numer- ical resonances and peak shift can be found in the 3DP pre- dictions, which result from the wave energy trapped in the gap between two ships and the extremely inhomogeneous wave load distribution on each hull. However, they can be eliminated by 3DTP, in which the speed affects the free sur- face and most of the wave energy can be escaped from the gap. Both the experiment and the present prediction show that hydrodynamic interaction effects on wave loads and free motions are significant. The present solver may serve as a validated tool to predict wave loads and motions of two ves- sels under replenishment at sea, and may help to evaluate the hydrodynamic interaction effects on the ships safety in replenishment operation.

Helical streamers guided by surface electromagnetic standing waves

The streamer that is driven by the specific pulse DC discharge parameters can stably form a three-dimensional helical plasma channel in a long dielectric tube in the low-temperature plasma experiment,in cases when there were neither external background magnetic field or other factors that destroyed the poloidal symmetry of the tube.The formation mechanism and chirality of helical streamers are discussed according to the surface electromagnetic standing wave theory.The shape of the helical streamers and the characteristics of helical branches are quantitatively analyzed to further expand the application of plasma and streamer theory in the helix problem and chiral catalytic synthesis.