A new mathematical integral representation including five integrals about the far field wave shape fimction of Havelock form translating-pulsating source is obtained by performing variable substitution. Constant-phase...A new mathematical integral representation including five integrals about the far field wave shape fimction of Havelock form translating-pulsating source is obtained by performing variable substitution. Constant-phase curves and propagation wave patterns are investigated by applying stationary phase analysis method to the new representation. Some findings are summarized as follows： （1） when 0〈r 〈0.25 （where r is the Strouhal number）, three types of stationary phase curves corresponding to three propagation wave patterns such as fan wave pattern, inner V and outer V wave patterns, are found in the integral representation. （2） When r 〉0.25, besides three types of wave patterns such as a ring-faning wave pattern, a fan wave pattern and an inner V wave pattern, a new one called parallel wave pattern is also found which not only exists in the integrals about the ring-fan wave and fan wave, but also in the integrals whose interval is [0, 7＇] ~ In addition, Characteristics about these parallel waves such as mathematical expressions, existence conditions, propagation directions and wave lengths are obtained, and cancellation relationships between these parallel waves are stated, which certificates the fact that there are no parallel waves existing in the far field.展开更多
In order to interpret the physical feature of Bessho form translating-pulsating source Green function, the phase function is extracted from the integral representation and stationary-phase analysis is carried out in t...In order to interpret the physical feature of Bessho form translating-pulsating source Green function, the phase function is extracted from the integral representation and stationary-phase analysis is carried out in this paper. The complex characteristics of the integral variable and segmentation of the integral intervals are discussed in m complex plane. In θ space, the interval [-π/2+φ,-π/2+φ-iε] is dominant in the near-field flow, and there is a one-to-one correspondence between the real intervals in m space and the unsteady wave patterns in far field. If 4τ>1(τ is the Brard number), there are three kinds of propagation wave patterns such as ring-fan wave pattern, fan wave pattern and inner V wave pattern, and if 0<4τ<1, a ring wave pattern, an outer V and inner V wave pattern are presented in far field. The ring-fan or ring wave pattern corresponds to the interval [-π+α,-π/2+φ] for integral terms about k2, and the fan or outer V wave pattern and inner V wave pattern correspond to [-π+α,-π/2) and(-π/2,-π/2+φ] respectively for terms about k1. Numerical result shows that it is beneficial to decompose the unsteady wave patterns under the condition of τ≠0 by converting the integral variable θ to m. In addition, the constant-phase curve equations are derived when the source is performing only pulsating or translating.展开更多
Ship wave pattern is a fascinating research topic in the fields of marine hydrodynamics and water waves. Within the pure-gravity wave theory, the ship wave pattern composed of transverse waves and divergent waves appe...Ship wave pattern is a fascinating research topic in the fields of marine hydrodynamics and water waves. Within the pure-gravity wave theory, the ship wave pattern composed of transverse waves and divergent waves appearing on the downstream is confined within a sector symmetrical about the ship track with a half-angle 19°28＇. However, when the surface tension is accounted for, the wave pattern is greatly modified especially at a low translating speed. Besides the minimum speed of capillary waves c_（min）= 0.23 m/s below which waves cannot be generated, there is another critical speed c_（div）= 0.45 m/s associated with the disappearance of divergent waves. In the present paper, the wave patterns created by a steadily translating source are studied, and they are examined with the crestlines obtained from the asymptotic analysis.展开更多
Air-layer drag reduction (ALDR) technology for ship energy saving is getting more and more attention in recent years because of the outstanding drag reduction effect. In order to promote practical application, it is n...Air-layer drag reduction (ALDR) technology for ship energy saving is getting more and more attention in recent years because of the outstanding drag reduction effect. In order to promote practical application, it is necessary to fully understand the two phase flow characteristics of the air layer. Recent experimental studies have shown that the surface of the air layer presents wave pattern, which has an important influence on its damage risk. However, it is difficult to measure the wave pattern quantificationally due to the interference of equipment. The main goal of the present paper is to investigate the wave pattern characteristic of air layer in cavity using numerical simulation method. On this basis, the effect of flow and geometric influence factors are discussed to understand the key control conditions. A computational fluid dynamics (CFD) numerical method based on Reynolds averaged Navier-Stokes (RANS) equations and volume of fluid (VOF) interface capturing method is established, and has been successfully applied in the simulation of air layer wave pattern. Both 2-D and 3-D simulations are carried out, aiming at analyzing air-water interface flow and vortex flow directly. Based on the simulation results, several important conclusions about the mechanism of air layer wave pattern can be obtained. Firstly, it is found to be an inherent characteristic that the wave height of the upstream air layer is higher than that of the downstream. The extremely high wave peak is easy to contact with the flat plate, leading to the breakup of air layer and a “central blank area” phenomenon. With the help of flow analysis, it is found that this characteristic is mainly caused by the strong counterclockwise vortex behind the bow wedge block. Secondly, the air layer stability is reduced with the increase of water flow velocity by affecting the wave height. There is a saturation point of air flow rate to reach maximum thickness of air layer. Thirdly, cavity configuration has obvious influence on air layer stability by influencing vortex flow field. The increase of cavity depth and width can aggravate the unsteady and nonlinear characteristics of air layer. Finally, comprehensive design criteria are concluded from the view of geometrical configuration and flow conditions. A cavity with the moderate depth and width can avoid the upstream damage of air layer. Longitudinal position of air nozzles should be set within the low pressure zone behind the wedge block for stable air layer formation.展开更多
The formation of spatial patterns is an important issue in reaction–diffusion systems.Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion(such ...The formation of spatial patterns is an important issue in reaction–diffusion systems.Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion(such as normal or fractional Laplace diffusion),namely,assuming that spatial environments of the systems are homogeneous.However,the complexity and heterogeneity of spatial environments of biochemical reactions in vivo can lead to asymmetric diffusion of reactants.Naturally,there arises an open question of how the asymmetric diffusion affects dynamical behaviors of biochemical reaction systems.To answer this,we build a general asymmetric L´evy diffusion model based on the theory of a continuous time random walk.In addition,we investigate the two-species Brusselator model with asymmetric L´evy diffusion,and obtain a general condition for the formation of Turing and wave patterns.More interestingly,we find that even though the Brusselator model with symmetric diffusion cannot produce steady spatial patterns for some parameters,the asymmetry of L´evy diffusion for this model can produce wave patterns.This is different from the previous result that wave instability requires at least a three-species model.In addition,the asymmetry of L´evy diffusion can significantly affect the amplitude and frequency of the spatial patterns.Our results enrich our knowledge of the mechanisms of pattern formation.展开更多
Propagation of the surface waves along a two-dimensional plasma column and the far-field radiation patterns are studied in thin column approximation. Wave phase and attenuation coefficients are calculated for various ...Propagation of the surface waves along a two-dimensional plasma column and the far-field radiation patterns are studied in thin column approximation. Wave phase and attenuation coefficients are calculated for various plasma parameters. The radiation patterns are shown. Results show that the radiation patterns are controllable by flexibly changing the plasma length and other parameters in comparison to the metal monopole antenna. It is meaningful and instructional for the optimization of the plasma antenna design.展开更多
By using a linear baroclinic model(LBM),this study investigates the different Rossby wave train(RWT)patterns associated with the Tibetan Plateau(TP)upper-atmospheric heat source(TPUHS)that is anomalously shallower and...By using a linear baroclinic model(LBM),this study investigates the different Rossby wave train(RWT)patterns associated with the Tibetan Plateau(TP)upper-atmospheric heat source(TPUHS)that is anomalously shallower and deeper in boreal summer.Observational results indicate the different RWT patterns between the developing and decaying periods of synoptic TPUHS events,when the anomalous TPUHS develops from a relatively shallower to a deeper TP heat source.Based on the different vertical heating profiles between these two periods in observation,this study forces the LBM with prescribed TPUHS profiles to mimic a shallower and deeper summer TP heat source.The results show that the atmospheric responses to a shallower and deeper TPUHS do exhibit different RWT patterns that largely resemble those in observation.Namely,corresponding RWT pattern to a shallower TPUHS stretches from the TP to the west coast of America,while that to a deeper TPUHS extends from the TP region to Alaska.展开更多
Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with...Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV展开更多
A fully three-dimensional surface gravitycapillary short-crested wave system is studied as two progressive wave-trains of equal amplitude and frequency, which are collinear with uniform currents and doubly-periodic in...A fully three-dimensional surface gravitycapillary short-crested wave system is studied as two progressive wave-trains of equal amplitude and frequency, which are collinear with uniform currents and doubly-periodic in the horizontal plane, are propagating at an angle to each other. The first- and second-order asymptotic analytical solutions of the short-crested wave system are obtained via a perturbation expansion in a small parameter associated with the wave steepness, therefore depicting a series of typical three-dimensional wave patterns involving currents, shallow and deep water, and surface capillary waves, and comparing them with each other.展开更多
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 n...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.展开更多
Based on the cluster model for wave-like motions of a 2D vertically vibrated granular system we established previously (Chin Phys Lett,2010,27:124501),a generalization of the cluster model for a 3D granular system is ...Based on the cluster model for wave-like motions of a 2D vertically vibrated granular system we established previously (Chin Phys Lett,2010,27:124501),a generalization of the cluster model for a 3D granular system is presented in this paper.The 3D cluster model proposes frustums of pyramids as clusters of the 3D granular system,and explains wave patterns as the result of the cluster-boundary and cluster-plate collisions.By analyzing the movement of one cluster in a collision period,we derive a basic equation,which relates the internal characteristic parameter to the external driving parameters.The theoretical results reproduce the behaviors of wave patterns as changes in the driving parameters,and the 3D dispersion relation,which agree with the experimental results.展开更多
In this paper, the evolution of the pattern transition induced by the vortical electric field （VEF） is investigated. Firstly, a scheme is suggested to generate the VEF by changing the spatial magnetic field. Secondl...In this paper, the evolution of the pattern transition induced by the vortical electric field （VEF） is investigated. Firstly, a scheme is suggested to generate the VEF by changing the spatial magnetic field. Secondly, the VEF is imposed on the whole medium, and the evolutions of the spiral wave and the spatiotemporal chaos are investigated by using the numerical simulation. The result confirms that the drift and the breakup of the spiral wave and the new net-like pattern are observed when different polarized fields are imposed on the whole medium respectively. Finally, the pattern transition induced by the polarized field is discussed theoretically.展开更多
In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inver...In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inverse scattering problems by Tikhonov regularization method.展开更多
This paper is ttie continuation of part （Ⅰ）, which completes the derivations of the 3D global wave modes solutions, yields the stability criterion and, on the basis of the results obtained, demonstrates the selecti...This paper is ttie continuation of part （Ⅰ）, which completes the derivations of the 3D global wave modes solutions, yields the stability criterion and, on the basis of the results obtained, demonstrates the selection criterion of pattern formation.展开更多
基金financially supported by the National Natural Science Foundation of China (Grant No. 50879090)Key Research Program of Hydrodynamics of China (Grant No. 9140A14030712JB11044)
文摘A new mathematical integral representation including five integrals about the far field wave shape fimction of Havelock form translating-pulsating source is obtained by performing variable substitution. Constant-phase curves and propagation wave patterns are investigated by applying stationary phase analysis method to the new representation. Some findings are summarized as follows： （1） when 0〈r 〈0.25 （where r is the Strouhal number）, three types of stationary phase curves corresponding to three propagation wave patterns such as fan wave pattern, inner V and outer V wave patterns, are found in the integral representation. （2） When r 〉0.25, besides three types of wave patterns such as a ring-faning wave pattern, a fan wave pattern and an inner V wave pattern, a new one called parallel wave pattern is also found which not only exists in the integrals about the ring-fan wave and fan wave, but also in the integrals whose interval is [0, 7＇] ~ In addition, Characteristics about these parallel waves such as mathematical expressions, existence conditions, propagation directions and wave lengths are obtained, and cancellation relationships between these parallel waves are stated, which certificates the fact that there are no parallel waves existing in the far field.
基金financial support from the National Natural Science Foundation of China under Grant No. 50879090the Key Program of Hydrodynamics of China under Grant No.9140A14030712JB11044
文摘In order to interpret the physical feature of Bessho form translating-pulsating source Green function, the phase function is extracted from the integral representation and stationary-phase analysis is carried out in this paper. The complex characteristics of the integral variable and segmentation of the integral intervals are discussed in m complex plane. In θ space, the interval [-π/2+φ,-π/2+φ-iε] is dominant in the near-field flow, and there is a one-to-one correspondence between the real intervals in m space and the unsteady wave patterns in far field. If 4τ>1(τ is the Brard number), there are three kinds of propagation wave patterns such as ring-fan wave pattern, fan wave pattern and inner V wave pattern, and if 0<4τ<1, a ring wave pattern, an outer V and inner V wave pattern are presented in far field. The ring-fan or ring wave pattern corresponds to the interval [-π+α,-π/2+φ] for integral terms about k2, and the fan or outer V wave pattern and inner V wave pattern correspond to [-π+α,-π/2) and(-π/2,-π/2+φ] respectively for terms about k1. Numerical result shows that it is beneficial to decompose the unsteady wave patterns under the condition of τ≠0 by converting the integral variable θ to m. In addition, the constant-phase curve equations are derived when the source is performing only pulsating or translating.
文摘Ship wave pattern is a fascinating research topic in the fields of marine hydrodynamics and water waves. Within the pure-gravity wave theory, the ship wave pattern composed of transverse waves and divergent waves appearing on the downstream is confined within a sector symmetrical about the ship track with a half-angle 19°28＇. However, when the surface tension is accounted for, the wave pattern is greatly modified especially at a low translating speed. Besides the minimum speed of capillary waves c_（min）= 0.23 m/s below which waves cannot be generated, there is another critical speed c_（div）= 0.45 m/s associated with the disappearance of divergent waves. In the present paper, the wave patterns created by a steadily translating source are studied, and they are examined with the crestlines obtained from the asymptotic analysis.
基金Project supported by the Ministry of Industry and Information Technology of China(Project No.CB01N20-05).
文摘Air-layer drag reduction (ALDR) technology for ship energy saving is getting more and more attention in recent years because of the outstanding drag reduction effect. In order to promote practical application, it is necessary to fully understand the two phase flow characteristics of the air layer. Recent experimental studies have shown that the surface of the air layer presents wave pattern, which has an important influence on its damage risk. However, it is difficult to measure the wave pattern quantificationally due to the interference of equipment. The main goal of the present paper is to investigate the wave pattern characteristic of air layer in cavity using numerical simulation method. On this basis, the effect of flow and geometric influence factors are discussed to understand the key control conditions. A computational fluid dynamics (CFD) numerical method based on Reynolds averaged Navier-Stokes (RANS) equations and volume of fluid (VOF) interface capturing method is established, and has been successfully applied in the simulation of air layer wave pattern. Both 2-D and 3-D simulations are carried out, aiming at analyzing air-water interface flow and vortex flow directly. Based on the simulation results, several important conclusions about the mechanism of air layer wave pattern can be obtained. Firstly, it is found to be an inherent characteristic that the wave height of the upstream air layer is higher than that of the downstream. The extremely high wave peak is easy to contact with the flat plate, leading to the breakup of air layer and a “central blank area” phenomenon. With the help of flow analysis, it is found that this characteristic is mainly caused by the strong counterclockwise vortex behind the bow wedge block. Secondly, the air layer stability is reduced with the increase of water flow velocity by affecting the wave height. There is a saturation point of air flow rate to reach maximum thickness of air layer. Thirdly, cavity configuration has obvious influence on air layer stability by influencing vortex flow field. The increase of cavity depth and width can aggravate the unsteady and nonlinear characteristics of air layer. Finally, comprehensive design criteria are concluded from the view of geometrical configuration and flow conditions. A cavity with the moderate depth and width can avoid the upstream damage of air layer. Longitudinal position of air nozzles should be set within the low pressure zone behind the wedge block for stable air layer formation.
基金supported by the National Natural Science Foundation of China(Grant Nos.62066026,62363027,and 12071408)PhD program of Entrepreneurship and Innovation of Jiangsu Province,Jiangsu University’Blue Project’,the Natural Science Foundation of Jiangxi Province(Grant No.20224BAB202026)the Science and Technology Research Project of Jiangxi Provincial Department of Education(Grant No.GJJ2203316).
文摘The formation of spatial patterns is an important issue in reaction–diffusion systems.Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion(such as normal or fractional Laplace diffusion),namely,assuming that spatial environments of the systems are homogeneous.However,the complexity and heterogeneity of spatial environments of biochemical reactions in vivo can lead to asymmetric diffusion of reactants.Naturally,there arises an open question of how the asymmetric diffusion affects dynamical behaviors of biochemical reaction systems.To answer this,we build a general asymmetric L´evy diffusion model based on the theory of a continuous time random walk.In addition,we investigate the two-species Brusselator model with asymmetric L´evy diffusion,and obtain a general condition for the formation of Turing and wave patterns.More interestingly,we find that even though the Brusselator model with symmetric diffusion cannot produce steady spatial patterns for some parameters,the asymmetry of L´evy diffusion for this model can produce wave patterns.This is different from the previous result that wave instability requires at least a three-species model.In addition,the asymmetry of L´evy diffusion can significantly affect the amplitude and frequency of the spatial patterns.Our results enrich our knowledge of the mechanisms of pattern formation.
文摘Propagation of the surface waves along a two-dimensional plasma column and the far-field radiation patterns are studied in thin column approximation. Wave phase and attenuation coefficients are calculated for various plasma parameters. The radiation patterns are shown. Results show that the radiation patterns are controllable by flexibly changing the plasma length and other parameters in comparison to the metal monopole antenna. It is meaningful and instructional for the optimization of the plasma antenna design.
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences [grant number XDA17010105]the National Natural Science Foundation of China [grant numbers 91437105,41430533,and 41575041]the Key Research Program of Frontier Sciences [grant number QYZDY-SSW-DQC018]
文摘By using a linear baroclinic model(LBM),this study investigates the different Rossby wave train(RWT)patterns associated with the Tibetan Plateau(TP)upper-atmospheric heat source(TPUHS)that is anomalously shallower and deeper in boreal summer.Observational results indicate the different RWT patterns between the developing and decaying periods of synoptic TPUHS events,when the anomalous TPUHS develops from a relatively shallower to a deeper TP heat source.Based on the different vertical heating profiles between these two periods in observation,this study forces the LBM with prescribed TPUHS profiles to mimic a shallower and deeper summer TP heat source.The results show that the atmospheric responses to a shallower and deeper TPUHS do exhibit different RWT patterns that largely resemble those in observation.Namely,corresponding RWT pattern to a shallower TPUHS stretches from the TP to the west coast of America,while that to a deeper TPUHS extends from the TP region to Alaska.
基金Project supported by the National Natural Science Foundation of China （Grant No 10172056）, the Natural Science Foundation of Zhejiang Province, China （Grant No Y604106）, the Foundation of New Century 151 Talent Engineering of Zhejiang Province, the Scientific Research Foundation of Zhejiang Provincial Education Department of China （Grant No 20070568） and the Natural Science Foundation of Zhejiang Lishui University （Grant No KZ04008）.
文摘Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV
基金The project supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (200428)the National Natural Science Foundation of China (10272072and 50424913)the Shanghai Natural Science Foundation(05ZR14048)
文摘A fully three-dimensional surface gravitycapillary short-crested wave system is studied as two progressive wave-trains of equal amplitude and frequency, which are collinear with uniform currents and doubly-periodic in the horizontal plane, are propagating at an angle to each other. The first- and second-order asymptotic analytical solutions of the short-crested wave system are obtained via a perturbation expansion in a small parameter associated with the wave steepness, therefore depicting a series of typical three-dimensional wave patterns involving currents, shallow and deep water, and surface capillary waves, and comparing them with each other.
基金support of the Hong Kong Research Grants Council through contracts 711807E and 712008E
文摘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.
基金supported by the National Natural Science Foundation of China (10674067)
文摘Based on the cluster model for wave-like motions of a 2D vertically vibrated granular system we established previously (Chin Phys Lett,2010,27:124501),a generalization of the cluster model for a 3D granular system is presented in this paper.The 3D cluster model proposes frustums of pyramids as clusters of the 3D granular system,and explains wave patterns as the result of the cluster-boundary and cluster-plate collisions.By analyzing the movement of one cluster in a collision period,we derive a basic equation,which relates the internal characteristic parameter to the external driving parameters.The theoretical results reproduce the behaviors of wave patterns as changes in the driving parameters,and the 3D dispersion relation,which agree with the experimental results.
基金supported by the National Natural Science Foundation of China (Grant Nos 10747005,10572056 and30670529)the Fund of Lanzhou University of Technology of China (Grant No Q200706)
文摘In this paper, the evolution of the pattern transition induced by the vortical electric field （VEF） is investigated. Firstly, a scheme is suggested to generate the VEF by changing the spatial magnetic field. Secondly, the VEF is imposed on the whole medium, and the evolutions of the spiral wave and the spatiotemporal chaos are investigated by using the numerical simulation. The result confirms that the drift and the breakup of the spiral wave and the new net-like pattern are observed when different polarized fields are imposed on the whole medium respectively. Finally, the pattern transition induced by the polarized field is discussed theoretically.
基金Shanghai Youth Science FoundationSupported in Part by Shanghai ScienceTechnology Development Foundation
文摘In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inverse scattering problems by Tikhonov regularization method.
基金supported by the Nankai University, China and in part by NSERC Grant of Canada
文摘This paper is ttie continuation of part （Ⅰ）, which completes the derivations of the 3D global wave modes solutions, yields the stability criterion and, on the basis of the results obtained, demonstrates the selection criterion of pattern formation.
