Manipulating Backward Propagation of Acoustic Waves by a Periodical Structure

In the backward propagation of acoustic waves, the direction of phase velocity is anti-parallel to that of group velocity. We propose a scheme to manipulate the backward propagation using a periodicM structure. The dynamic backward propagation process is further experimentally observed. It is demonstrated that the oblique incident plane wave moves backward when it travels through the periodical structure and the backward shift can be controlled within a certain range.

Applicability evaluation of ERA5 wind and wave reanalysis data in the South China Sea

Wind and wave data are essential in climatological and engineering design applications.In this study,data from 15 buoys located throughout the South China Sea(SCS)were used to evaluate the ERA5 wind and wave data.Applicability assessment are beneficial for gaining insight into the reliability of the ERA5 data in the SCS.The bias range between the ERA5 and observed wind-speed data was-0.78-0.99 m/s.The result indicates that,while the ERA5 wind-speed data underestimation was dominate,the overestimation of such data existed as well.Additionally,the ERA5 data underestimated annual maximum wind-speed by up to 38%,with a correlation coefficient>0.87.The bias between the ERA5 and observed significant wave height(SWH)data varied from-0.24 to 0.28 m.And the ERA5 data showed positive SWH bias,which implied a general underestimation at all locations,except those in the Beibu Gulf and centralwestern SCS,where overestimation was observed.Under extreme conditions,annual maximum SWH in the ERA5 data was underestimated by up to 30%.The correlation coefficients between the ERA5 and observed SWH data at all locations were greater than 0.92,except in the central-western SCS(0.84).The bias between the ERA5 and observed mean wave period(MWP)data varied from-0.74 to 0.57 s.The ERA5 data showed negative MWP biases implying a general overestimation at all locations,except for B1(the Beibu Gulf)and B7(the northeastern SCS),where underestimation was observed.The correlation coefficient between the ERA5 and observed MWP data in the Beibu Gulf was the smallest(0.56),and those of other locations fluctuated within a narrow range from 0.82 to 0.90.The intercomparison indicates that during the analyzed time-span,the ERA5 data generally underestimated wind-speed and SWH,but overestimated MWP.Under non-extreme conditions,the ERA5 wind-speed and SWH data can be used with confidence in most regions of the SCS,except in the central-western SCS.

NONLINEAR TRAVELING WAVES IN A COMPRESSIBLE MOONEY-RIVLIN ROD I.LONG FINITE-AMPLITUDE WAVES

In literature,nonlinear traveling waves in elastic circular rods have only been studied based on single partial differential equation(pde)models,and here we consider such a problem by using a more accurate coupled-pde model.We derive the Hamiltonian from the model equations for the long finite-amplitude wave approximation,analyze how the number of singular points of the system changes with the parameters,and study the features of these singular points qualitatively.Various physically acceptable nonlinear traveling waves are also discussed,and corresponding examples are given.In particular,we find that certain waves,which cannot be counted by the single-equation model,can arise.

A Maximum-Entropy Compound Distribution Model for Extreme Wave Heights of Typhoon-Affected Sea Areas

A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.

Evaluating the Accuracy of ERA5 Wave Reanalysis in the Water Around China

Wave parameters, such as wave height and wave period, are important for human activities, such as navigation, ocean engineering and sediment transport, etc. In this study, wave data from six buoys around Chinese waters, are used to assess the quality of wave height and wave period in the ERA5 reanalysis of the European Centre for Medium-Range Weather Forecasts. Annual hourly data with temporal resolution are used. The difference between the significant wave height(SWH) of ERA 5 and that of the buoy varies from-0.35 m to 0.30 m for the three shallow locations;for the three deep locations, the variation ranges from-0.09 m to 0.09 m. The ERA5 SWH data show positive biases, indicating an overall overestimation for all locations, except for E2 and S1 where underestimation is observed. During the tropical cyclone period, a large(about 32%) underestimation of the maximum SWH in the ERA5 data is observed. Hence, the ERA5 SWH data cannot be used for design applications without site-specific validation. The difference between the annual wave period from ERA5 and the mean wave period from the buoys varies from-1.31 s to 0.4 s. Inter-comparisons suggest that the ERA5 dataset is consistent with the annual mean SWH. However, for the average period, the performance is not good, and half of the correlation coefficients in the four points are less 50%. Overall, the deep water area simulation effect is better than that in the shallow water.

The difference between the joint probability distributions of apparent wave heights and periods and individual wave heights and periods

The joint distribution of wave heights and periods of individual waves is usually approximated by the joint distribution of apparent wave heights and periods. However there is difference between them. This difference is addressed and the theoretical joint distributions of apparent wave heights and periods due to Longuet-Higgins and Sun are modified to give more reasonable representations of the joint distribution of wave heights and periods of individual waves. The modification has overcome an inherent drawback of these joint PDFs that the mean wave period is infinite. A comparison is made between the modified formulae and the field data of Goda, which shows that the new formulae consist with the measurement better than their original counterparts.

BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED DODD-BULLOUGH-MIKHAILOV EQUATION

In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.Some exact explicit parametric representations of the above travelling solutions are obtained.

New exact periodic solutions to (2+1)-dimensional dispersive long wave equations

In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions （m → 1）. This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.

ORBITAL STABILITY OF PERIODIC TRAVELING WAVE SOLUTIONS TO THE GENERALIZED ZAKHAROV EQUATIONS

This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].

The comparison of altimeter retrieval algorithms of the wind speed and the wave period

With the launch of altimeter,much effort has been made to develop algorithms on the wind speed and the wave period.By using a large data set of collocated altimeter and buoy measurements,the typical wind speed and wave period algorithms are validated.Based on theoretical argument and the concept of wave age,a semi-empirical algorithm for the wave period is also proposed,which has the wave-period dimension,and explicitly demonstrates the relationships between the wave period and the other variables.It is found that Ku and C band data should be applied simultaneously in order to improve either wind speed or wave period algorithms.The dual-band algorithms proposed by Chen et al.(2002) for the wind speed and Quilfen et al.(2004) for the wave period perform best in terms of a root mean square error in the practical applications.

Riemann theta function periodic wave solutions for the variable-coefficient mKdV equation

In this paper, a variable-coefficient modified Korteweg-de Vries （vc-mKdV） equation is considered. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function, then the one and two periodic wave solutions are presented~ and it is also shown that the soliton solutions can be reduced from the periodic wave solutions.

Development and validation of an ocean wave retrieval algorithm for VV-polarization Sentinel-1 SAR data

The purpose is to study the accuracy of ocean wave parameters retrieved from C-band VV-polarization Sentinel-1Synthetic Aperture Radar（SAR） images, including both significant wave height（SWH） and mean wave period（MWP）, which are both calculated from a SAR-derived wave spectrum. The wind direction from in situ buoys is used and then the wind speed is retrieved by using a new C-band geophysical model function（GMF） model,denoted as C-SARMOD. Continuously, an algorithm parameterized first-guess spectra method（PFSM） is employed to retrieve the SWH and the MWP by using the SAR-derived wind speed. Forty-five VV-polarization Sentinel-1 SAR images are collected, which cover the in situ buoys around US coastal waters. A total of 52 subscenes are selected from those images. The retrieval results are compared with the measurements from in situ buoys. The comparison performs good for a wind retrieval, showing a 1.6 m/s standard deviation（STD） of the wind speed, while a 0.54 m STD of the SWH and a 2.14 s STD of the MWP are exhibited with an acceptable error.Additional 50 images taken in China＇s seas were also implemented by using the algorithm PFSM, showing a 0.67 m STD of the SWH and a 2.21 s STD of the MWP compared with European Centre for Medium-range Weather Forecasts（ECMWF） reanalysis grids wave data. The results indicate that the algorithm PFSM works for the wave retrieval from VV-polarization Sentinel-1 SAR image through SAR-derived wind speed by using the new GMF C-SARMOD.

Estimation of JONSWAP Spectral Parameters by Using Measured Wave Data

- This paper presents the method of determining JONSWAP spectrum by using measured wave data. If Hs, Tz and Tc are the measured significant wave height, average zero-up crossing wave period and average period between wave crests respectively and let y = T Z / TC; this paper provides equation to solve y fromf(y,y) = 0. From the solutions of this equation and by using LSM, the expression relating y as a function of y (for 2.54<y< 15.34 and 1.6 <y < 1,79) may be written as y -5546.721 - 9586.533y + 5568.168/- 1089/+ 2/, for other intervals the related formulas are also given. When y is known, the rest of parameters in JONSWAP spectrum can be obtained. In addition, this paper also provides alternatives for determining JONSWAP spectral parameters by using Hs, Tz and (, or Hs, Tz and S(w0) or other three given data. The JONSWAP spectra given in this paper satisfy the following formulas HS= 4.0 = 2 Tc = 2

Periodic folded waves for a (2+1)-dimensional modified dispersive water wave equation

A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.

A new type of internal solitary waves with a re-appearance period of 23 h observed in the South China Sea

The South China Sea （SCS）, in particular the northern SCS, is one of ocean areas where energetic internal solitary waves （ISWs）occur most frequently （Cai et al., 2012; Zheng, 2017）. Based on the re-appearance period （RP） at an observation station, Ramp et al.（2004） divided the ISWs into two types：Type-a and Type-b. Type-a ISWs arrive regularly at the same time every day, i.e., the RP is about 24 h, and Type-b ISWs arrive about one hour late every day, i.e., the RP is about 25 h.

Diversity of New Three-Wave Solutions and New Periodic Waves for the (3 + 1)-Dimensional Kadomtsev-Petviashvili-Boussinesq-Like Equation

Based on the generalized bilinear method, diversity of exact solutions of the (3 + 1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation is successfully derived by using symbolic computation with Maple. These new solutions, named three-wave solutions and periodic wave have greatly enriched the existing literature. Via the three-dimensional images, density images and contour plots, the physical characteristics of these waves are well described. The new three-wave solutions and periodic solitary wave solutions obtained in this paper, will have a wide range of applications in the fields of physics and mechanics.

Application of MEP Method to the Study of statistical Properties of Random Waves

The maximum entropy principle (MEP) method and the corresponding probability evaluation method are introduced, and the maximum entropy probability distribution expression is deduced in moment of the second order. Fully developed wave height distribution in deep water and wave height and period distribution for different depths in wind wave channel experiment are obtained from the MEP method, and the results are compared with the distribution and the experimental histogram. The wave height and period distribution for the Lianyungang port is also obtained by the MEP method, and the results are compared with the Weibull distribution and the field histogram.

Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized exp(-Φ(ξ))-Expansion Method

In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering.

Doubly periodic patterns of modulated hydrodynamic waves:exact solutions of the Davey-Stewartson system

Exact doubly periodic standing wave patterns of the Davey-Stewartson （DS） equations are derived in terms of rational expressions of elliptic functions.In fluid mechanics,DS equations govern the evolution of weakly nonlinear,free surface wave packets when long wavelength modulations in two mutually perpendicular,horizontal directions are incorporated.Elliptic functions with two different moduli （periods） are necessary in the two directions.The relation between the moduli and the wave numbers constitutes the dispersion relation of such waves.In the long wave limit,localized pulses are recovered.

Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma

The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated.The existence of the travelling wave solutions is discussed.The modulation stability of linear waves and the modulation instability of weakly nonlinear waves are presented.Both suggest that the Korteweg-de Vries(KdV)system is modulationally stable.Besides,the wave interactions including the periodic wave interaction and the solitary wave interaction are captured and presented.It is shown that these interacting waves alternately exchange their energy during propagation.The Fourier spectrum analysis is used to depict the energy transformation between the primary and harmonic waves.It is known that the wave interactions in magnetized plasma play an important role in various processes of heating and energy transportation in space and astrophysical plasma.However,few researchers have considered such magnetohydrodynamic(MHD)wave interactions in plasma.It is expected that this work can provide additional insight into understanding of behaviors of MHD wave interactions.