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Linear and Nonlinear Solutions of interfacial waves Due to a Doublet

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Journal of Mathematical Research with Applications 2024年第2期44卷 269-284页

作者： Di LIU Zhen WANG School of Mathematics Jilin University School of Mathematical Sciences Beihang University

Steady two-dimensional potential flows of two-layer fluids with a submerged doublet in the lower layer are considered. Both linear analytical solutions and fully nonlinear solutions based on boundary integral equation methods are obtained. Nonlinearity strongly influences the downstream wave height and leads to a slight phase difference. When the Froude number is small, wave height fast gets its maximum as the Froude number increases. While wave-less solutions may be obtained if the Froude number is very large. Afterward, the interfacial waves due to one point vortex or a vortex pair are compared with those due to a doublet. It is found that the nonlinear wave profiles due to a doublet are quite close to those due to a vertical vortex pair if the distance between the vortex pair is set appropriately.

关键词： interfacial waves doublet boundary integral equation method linear solutions

Statistical characteristics of the interfacial waves in horizontal gas-liquid two-phase stratified flow

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Progress in Natural Science:Materials International 1998年第4期 3-5页

作者：李广军郭烈锦陈学俊陈永利 China State Key Laboratory of Multiphase Flow in Power Engineering Xi’an 710049 Xi’an Jiaotong University

The study of the interfacial waves is very important in understanding and grasping the laws of the phase interface exchange dynamics in gas-liquid two-phase flow. Based on a series of experiments and investigations, the statistical characteristics of the interfacial waves in gas-liquid two-phase stratified flow in both time and frequency domains are presented. The statistical parameters with variations of the gas and liquid superficial velocities are analyzed and discussed.

关键词： liquid film thickness gas-liquid two-phase flow interfacial waves statistical analysis.

The Behavior and Characteristics of the interfacialwaves in Gas-Liquid Two-Phase Separated FlowThrough Downward Inclined Rectangular Channel

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Journal of Thermal Science 1998年第1期7卷 29-36页

作者： Guangjun Li Lienjin Guo Xuejun Chen(National Laboratory of Multiphase Flow in Power Engineering,Xi’an Jiaotong University,Xi’an,710049,China) National Laboratory of Multiphase Flow in Power Engineering Xi’an Jiaotong University Xi’an China

An experimental investigation on the behavior and characteristics of interfacial waves in downward inclined rectangular channel was conducted. The interfacial waves were traced and measured by us-ing conductance technique. The wav patterns were distinguished and defined. The characteristics of the interfacial waves, such as time-averaged film thickness, wave height, wave propagation speed,wavlength and wave frequency, were systematically examined in terms of gas and liquid superficial volumetric fiuxes. The effect of the inclination and flow channel geometry of the test section on the interfacial wav was also investigated.

关键词： liquid film thickness gas-liquid two-phase flow interfacial waves experiment study

Validity ranges of interfacial wave theories in a two-layer fluid system

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Acta Mechanica Sinica 2007年第6期23卷 597-607页

作者： Yutang Yuan Jiachun Li Youliang Cheng Division of Engineering Sciences Institute of Mechanics Chinese Academy of Sciences Beijing 100080 China Department of Dynamic Engineering North China Electric Power University Baoding 071003 China

In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the available solutions of periodic and solitary waves, we propose a guideline as principle to identify the validity regions of the interfacial wave theories in terms of wave period T, wave height H, upper layer thickness dl, and lower layer thick-ness d2, instead of only one parameter-water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Mehaute＇s plot for free surface waves if water depth ratio r= d1/d2 approaches to infinity and the upper layer water density p1 to zero. On the contrary, the diagram for water surface waves can be used for two-layer interfacial waves if gravity acceleration g in it is replaced by the reduced gravity defined in this study under the condition of σ=（P2 - Pl）/P2 → 1.0 and r 〉 1.0. In the end, several figures of the validity ranges for various interfacial wavetheories in the two-layer fluid are given and compared with the results for surface waves.

关键词： Validity ranges Two-layer fluid interfacial waves interfacial solitary waves Ursell number

Three-dimensional interfacial wave theory of dendritic growth: (Ⅰ). multiple variables expansion solutions

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Chinese Physics B 2009年第2期18卷 671-685页

作者：陈永强唐熊忻徐鉴君 School of Mathematical Science Nankai University Department of Fundamental Subject Tianjin Institute of Urban Construction School of materials Science and Engineering University of Science and Technology Beijing Department of mathematics and Statistics McGill University

Dendritic pattern formation at the interface between liquid and solid is a commonly observed phenomenon in crystal growth and solidification process. The theoretical investigation of dendritic growth is one of the most profound and highly challenging subjects in the broad areas of interfacial pattern formation, condensed matter physics and materials science, preoccupying many researchers from various areas. Some longstanding key issues on this subject finally gained a breakthrough in the late of last century, via the ＇Interracial Wave （IFW） Theory＇ on the ground of systematical global stability analysis of the basic state of dendritic growth. The original form of the IFW theory mainly focus on the investigation of various axi-symmetric unsteady perturbed modes solutions around the axi-symmetrie basic state of system of dendritic growth. In reality, the system may allow various non-axi-symmetric, unsteady perturbed states. Whether or not the system of dendritic growth allows some growing non-axi-symmetric modes？ Will the stationary dendritic pattern be destroyed by some of such non-axi- symmetric modes？ Or, in one word, what is the stability property of the system, once the non-axi-symmetric modes can be evoked？ The answers for these questions are important for the solid foundation of IFW theory. The present work attempts to settle down these issues and develop a three-dimensional （3D） interfacial wave theory of dendritic growth. Our investigations verify that dendritic growth indeed allows a discrete set of non-axi-symmetric unstable global wave modes, which gives rise to a set of multiple arms spiral waves propagating along the Ivantsov＇s paraboloid.

关键词： Dendritic growth pattern formation interfacial waves selection criterion

Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a two-layer fluid system

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Acta Oceanologica Sinica 2009年第2期28卷 115-120页

作者： SONG Jinbao LIU Yongjun Institute of Oceanology Chinese Academy of Sciences Qingdao 266071 China Key Laboratory of Ocean Circulation and waves （KLOCAW） Chinese Academy of Sciences Qingdao 266071 China Graduate University of Chinese Academy of Sciences Beijing 100039 China

interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a fiat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. （2004. Science in China, Ser. D, 47（12）： 1147-1154） for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth＇s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.

关键词： two-layer fluid interfacial waves wave-induced tangential stress earth rotation

Theoretical Analysis and Symbolic Com putationof Internal Solitary wavesin Stratified Fluids

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Advances in Manufacturing 1999年第1期3卷 84-86页

作者： Doctoral Candidate: Cheng Youliang Advisor: Prof.Dai Shiqiang (Shanghai Institute of Appl.Math.and Mech., Shanghai University) Shanghai Institute of Appl. Math. and Mech. Shanghai University China North China University of Electric Power Baoding

The study of solitary waves has been a subject highly popular and full of interest sinec Russell[1]first observed the solitary waves in a channel and the research on the internal solitary waves in stratified fluids is one of the branches of this *** are extensively internal solitary waves in the atmosphere,*** and *** study them is of academic and practical significance[2].Numerous investigators have made contributions since the theoretical work on internal solitary waves was initiated by Keulegan[3].Nevertheless,some problems remain still to be discussed,for example,the higher-order theories for one-dimensional internal solitary waves in stratified fluids of small depth,the two-dimensional internal solitary waves,the explanation of the experimental and the practical phenomena by means of theoretical *** this thesis,we hope to gain an insight into the above three items by combining of theoretical analysis and symbolic *** following work has been completed.

关键词： ywords stratified fluids two fluid system symbolic computation internal solitary waves interfacial waves shallow water deep water KdV equation BO equation KP equation