Second-Order Analytic Solutions of Nonlinear Interactions of Edge Waves on A Plane Sloping Bottom

Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper. For special ease of slope angle β = π/2, this solution can reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves are also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves are also given. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoreti- cal autocorrelation and spectral density functions of the first and the second orders are derived. The boundary conditions for the determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated.

A Numerical Model for Edge Waves on A Compound Slope

An edge wave is a kind of surface gravity wave basically travelling along a shoaling beach. Based on the periodic assumption in the longshore direction, a second order ordinary differential equation is obtained for numerical simulation of the cross-shore surface elevation. Given parameters at the shoreline, a cross-shore elevation profile is obtained through integration with fourth-order Runge Kutta technique. For a compound slope, a longshore wavenumber is obtained by following a geometrical approach and solving a transcendental equation with an asymptotic method. Numerical results on uniform and compound sloping beaches with different wave periods, slope angles, modes and turning point positions are presented. Some special scenarios, which cannot be predicted by analytical models are also discussed.

Disintegration of Linear Edge Waves

It is demonstrated that offshore wavenumbers of edge waves change from imaginary wavenumbers in deep water to real wavenumbers in shallow water. This finding indicates that edge waves in the offshore direction exist as evanescent waves in deep water and as propagating waves in shallow water. Since evanescent waves can stably exist in a limited region while propagating waves cannot, energy should be released from nearshore regions. In the present study, the instability region is predicted based on both the full water wave solution and the shallow-water wave approximation.

Large-scale edge waves generated by a moving atmospheric pressure

Long waves generated by a moving atmospheric pressure distribution, associated with a storm, in coastal region are investigated numerically. For simplicity the moving atmospheric pressure is assumed to be moving only in the alongshore direction and the beach slope is assumed to be a constant in the on-offshore direction. By solving the linear shallow water equations we obtain numerical solutions for a wide range of physical parameters, including storm size （2a）, storm speed （U）, and beach slope （a）. Based on the numerical results, it is determined that edge wave packets are generated if the storm speed is equal to or greater than the critical velocity, Ucr, which is defined as the phase speed of the fundamental edge wave mode whose wavelength is scaled by the width of the storm size. The length and the location of the positively moving edge wave packet is roughly Ut/2 〈 y 〈 Ut, where y is in the alongshore direction and t is the time. Once the edge wave packet is generated, the wavelength is the same as that of the fundamental edge wave mode corresponding to the storm speed and is independent of the storm size, which can, however, affect the wave amplitude. When the storm speed is less than the critical velocity, the primary surface signature is a depression directly correlated to the atmospheric pressure distribution.

Nonlinear wave-wave interactions and wedge waves

A tetrad mechanism for exciting long waves, for example edge waves, is described based on nonlinear resonant wave-wave interactions. In this mechanism, resonant interactions pass energy to an edge wave, from the three participating gravity waves. The estimated action flux into the edge wave can be orders of magni- tude greater than the transfer fluxes derived from other competing mechanisms, such as triad interactions. More- over, the numerical results show that the actual transfer rates into the edge wave from the three participating gravity waves are two- to three- orders of magnitude greater than bottom friction.

Numerical Study on the Duct Noise Control of Single-Stage Axial Flow Fan with Wave Leading Edge Stator Blade Configurations

This study focuses on a single-stage axial flow fan, investigating the effect of three kinds of wave leading edge stator blades on its noise reduction. The DDES method and the duct acoustic analogy theory based on the penetrable data surface were used for noise prediction. The results showed that the three kinds of wave leading edge blades were effective in reducing the rotor-stator interaction tonal noise and also have a certain inhibitory effect on broadband noise. The A10W15 stator blade can effectively reduce broadband noise in the frequency range of 2200 - 4200 Hz. When the amplitude is increased to 20, the noise reduction effect is further enhanced. However, when the amplitude is increased to 30, the broadband noise reduction effect is no longer significant. Further research shows that the wave leading edge stator blades can significantly change the pressure fluctuation distribution on the leading edge and suction surface, which control the modal energy distribution. Finally, this paper analyzed multiple factors affecting the broadband noise reduction, such as the noise source cut-off and cut-on effect and correlation. The purpose of this paper is to explore the laws of the influence of wave leading edge blades on the duct noise of real fan, and to reveal its noise control mechanism. .

Direct wave and edge waves radiated into a solid medium by a circular thickness-mode transducer

The transient acoustic field radiated by a piezoelectric thickness-mode transducer into a solid medium is theoretically analysed. It is proved that the field consists of the direct wave, the longitudinal edge waves, the shear edge.waves, the head wave and the surface waves. The wavefront approximations of all these waves are given which result in a clear physical picture which is not only simple but also cotains the main features of the field. The theoretical result well describes the experiment.

Poloidal rotation induced by injecting lower hybrid waves in tokamak plasma edge

The poloidal rotation of the magnetized edge plasma in tokamak driven by the ponderomotive force which is generated by injecting lower hybrid wave(LHW) electric field has been studied. The LHW is launched from a waveguide in the plasma edge, and by Brambilla's grill theory, analytic expressions for the wave electric field in the slab model of an inhomogeneous cold plasma have been derived. It is shown that a strong wave electric field will be generated in the plasma edge by injecting LH wave of the power in MW magnitude, and this electric field will induce a poloidal rotation with a sheared poloidal velocity.

Infragravity waves with internal wave characteristics in the south of the Bohai Sea of China

The measurements by using ADCP (500 KH) and CTD were made during August 2000in the south (37?5'N, 120?5'E) of the Bohai Sea, where the water depth was about 16.5 m. The data of horizontal velocity with sampling interval of 2 min in 7 layers were obtained. The power spectrum analysis of these data indicates that there are very energetic infragravity waves with a period of about 6 min. The coherence spectrum analysis and the analysis of temporal variation of shear show that these infragravity waves are mainly the free wave model (properties of edge waves), in the meantime they possess some characteristics of internal waves, which are likely due to the distinctive marine environment in this area. It is speculated on that the instability processes (chiefly shear instability) of sheared stratified tidal flow owing to the effect of sea-floor slope in the coastal area might be the main mechanism generating these infragravity waves.

Key technologies of roll forming automobile components with AHSS

Lightweight design is one of the development trends of the automobile industry. An effective way to achieve lightweight auto bodies is to use AHSS （advanced high strength steel ） for the safety components of automobiles. This study has taken doorsill reinforcements made of martensite AHSS as the object ,and performed research on the AHSS roll forming technologies and prototype development of typical asymmetric open components. By means of finite element analysis （FEA） and simulation,studies have been carried out on the springback and edge wave defects during AHSS roll forming ,and an optimized process design has been achieved. The generation mechanisms of vertical bows ,horizontal cambers, twists,pre-punched hole distortion and cut end flare have been analyzed,and solutions to these defects have been given. In addition,tesing of the roll forming process for AHSS has been conducted and typical samples with required dimensional accuracy have been manufactured. This study has provided technical support for the large-scale application of AHSS.

Numerical Investigations of the Influence of Unsteady Vane Trailing Edge Shock Wave on Film Cooling Effectiveness of Rotor Blade Leading Edge

Unsteady numerical simulations of a high-load transonic turbine stage have been carried out to study the influences of vane trailing edge outer-extending shockwave on rotor blade leading edge film cooling performance. The turbine stage used in this paper is composed of a vane section and a rotor one which are both near the root section of a transonic high-load turbine stage. The Mach number is 0.94 at vane outlet, and the relative Mach number is above 1.10 at rotor outlet. Various positions and oblique angles of film cooling holes were investigated in this research. Results show that the cooling efficiency on the blade surface of rotor near leading edge is significantly affected by vane trailing edge outer-extending shockwave in some cases. In the cases that film holes are close to leading edge, cooling performance suffers more from the sweeping vane trailing edge outer-extending shockwave.In addition, coolant flow ejected from oblique film holes is harder to separate from the blade surface of rotor, and can cover more blade area even under the effects of sweeping vane trailing edge shockwave. As a result, oblique film holes can provide better film cooling performance than vertical film holes do near the leading edge on turbine blade which is swept by shockwaves.

Topological edge state analysis of hexagonal phononic crystals

In this study,we propose valley phononic crystals that consist of a hexagonal aluminum plate with six chiral arrangements of ligaments.Valley phononic crystals were introduced into a topological insulator(TI)system to produce topologically protected edge waves(TPEW s)along the topological interfaces.The implementation of chiral topological edge states is different from the implementation of topological edge states of systems with symmetry.Unlike the conventional breaking of mirror symmetry,a new complete band with topological edge modes gap was opened up at the Dirac point by tuning the difference in lengths of the ligaments in the chiral unit cells.We investigated the dispersion properties in chiral systems and applied the dispersion properties to waveguides on the interfaces to achieve designable route systems.Furthermore,we simulated the robust propagation of TPEWs in different routes and demonstrated their immunity to backscattering at defects.Finally,the existence of the valley Hall effect in chiral systems was demonstrated.The study findings may lead to the further study of the topological states of chiral materials.