SURFACE EFFECTS OF INTERNAL WAVE GENERATED BY A MOVING SOURCE IN A TWO-LAYER FLUID OF FINITE DEPTH

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (9): 1025-1040.

SURFACE EFFECTS OF INTERNAL WAVE GENERATED BY A MOVING SOURCE IN A TWO-LAYER FLUID OF FINITE DEPTH

魏岗^1,2, 乐嘉春¹, 戴世强¹

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
2. Institute of Science, University of Science and Technology, PLA, Nanjing 211101, P. R. China

收稿日期:2002-02-01 修回日期:2003-03-21 出版日期:2003-09-18 发布日期:2003-09-18
基金资助:
the National Natural Science Foundation of China (69925307, 60274001);the National Key Basic Reasearch and Development Program (2002CB312200);the Postdoctoral Program Foundation of China

SURFACE EFFECTS OF INTERNAL WAVE GENERATED BY A MOVING SOURCE IN A TWO-LAYER FLUID OF FINITE DEPTH

WEI Gang^1,2, LE Jia-Chun¹, DAI Shi-qiang ¹

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
2. Institute of Science, University of Science and Technology, PLA, Nanjing 211101, P. R. China

Received:2002-02-01 Revised:2003-03-21 Online:2003-09-18 Published:2003-09-18
Supported by:
the National Natural Science Foundation of China (69925307, 60274001);the National Key Basic Reasearch and Development Program (2002CB312200);the Postdoctoral Program Foundation of China

摘要/Abstract

摘要： Based on the potential flow theory of water waves, the interaction mechanism between the free-surface and internal waves generated by a moving point source in the lower layer of a two-layer fluid was studied. By virtue of the method of Green's function, the properties of the divergence field at the free surface were obtained, which plays an important role in the SAR (Synthetic Aperture Radar) image. It is shown that the coupling interaction between the surface-wave mode and internal-wave mode must be taken into account for the cases of large density difference between two layers, the source approaching to the pynocline and the total Froude number Fr close to the critical number Fr. The theoretical analysis is qualitatively consistent with the experimental results presented by Ma Hui-yang.

Abstract: Based on the potential flow theory of water waves, the interaction mechanism between the free-surface and internal waves generated by a moving point source in the lower layer of a two-layer fluid was studied. By virtue of the method of Green's function, the properties of the divergence field at the free surface were obtained, which plays an important role in the SAR (Synthetic Aperture Radar) image. It is shown that the coupling interaction between the surface-wave mode and internal-wave mode must be taken into account for the cases of large density difference between two layers, the source approaching to the pynocline and the total Froude number Fr close to the critical number Fr. The theoretical analysis is qualitatively consistent with the experimental results presented by Ma Hui-yang.

中图分类号:

O353
76B20

魏岗;乐嘉春;戴世强. SURFACE EFFECTS OF INTERNAL WAVE GENERATED BY A MOVING SOURCE IN A TWO-LAYER FLUID OF FINITE DEPTH[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(9): 1025-1040.

WEI Gang;LE Jia-Chun;DAI Shi-qiang . SURFACE EFFECTS OF INTERNAL WAVE GENERATED BY A MOVING SOURCE IN A TWO-LAYER FLUID OF FINITE DEPTH[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(9): 1025-1040.

参考文献

[1] MENG Jun-min. The simulation of the SAR image of internal solitary waves in Alboram seas[J]. J Hydrodynamics, Ser B, 2001, 3:88-92.
[2] DAI Shi-qiang. Interactions between two pairs of the solitary waves in a two-layer fluid [J].Science in China, Ser A, 1983, (11):1007-1017. (in Chinese).
[3] Lamb H. Hydrodynamics[M]. Sixth Edition. Cambridge:Cambridge University Press, 1932.
[4] Wehausen J V, Laitone E V. Surface Wave [M]. Handbuch der Physik, Berlin:Springcr-Verlag, 9, 1960.
[5] Chomaz J M. The structure of the near wake of a sphere moving horizontally in a stratified fluid[J]. J Fluid Mech, 1993, 254:1-21.
[6] MA Hui-yang. Experimental study on Interactions between free surface and a moving object in stratified fluid[J]. Experiment and Measurement in Fluid Mechanics, 2000, 14 (3):7-11. (in Chinese).
[7] Lighthill J. Waves in Fluid[M]. Cambridge:Cambridge University Press, 1978.
[8] Keller J B, Munk W H. Internal wave wakes of a body moving in a stratified fluid[J]. Phys Fluids, 1970, 13:1452-1431.
[9] Miles J W. Intemal waves generated by a horizontally moving source [J]. Physical Fluid Dynamics, 1970, 2:63-87.
[10] Sharman R D, Wurtele M D. Ship waves and Lee waves[J]. J Atmos Sci, 1983, 40:396- 427.
[11] Phillips O M. The Dynamatics of the Dynamics of Upper Ocean [M]. Second Edition, Cambridge:Cambridge University Press, 1977.
[12] YIH Chia-shun, ZHU Song-ping. Pattem of ship waves[J]. QuarAppl Math, 1989, 47(1):17 -33.
[13] Hudimac A A. Ship waves in a stratified ocean[J]. J Fluid Mech, 1961, 11:229-243.
[14] Crapper G D. Ship waves in a stratified ocean[J]. J Fluid Mech, 1967, 29:667-672.
[15] Yeung R W, Nguyen T C. Waves generated by a moving source in a two-layer ocean of finite depth[J]. J Eng Math, 1999, 35:85-107.
[16] Alpers W, Hennings I. A theory of the imaging mechanism of underwater bottom topography by real and synthetic aperture radar[J]. J Geophysical Research, 1984, 89(C6):10529-10546.
[17] Alpers W. On the detectability of ocean surface waves by real and synthetic aperture radar[J]. J Geophys Res, 1981, 86:6481-6498.
[18] Stefanick T. The nonacoustic detection of submarine[J]. Scientific American, 1988, 258:41-47.
[19] Stewart R H. Methods of Satellite Oceanography [M]. California:University of California Press, 1985.
[20] GUO Hua-dong. Theory and Application for Radar Observation [M]. Beijing:Science Press, 2001. (in Chinese).
[21] Lin J T, Pao Y H. Wakes in stratified fluid[J]. Ann Rev Fluid Mech, 1979, 11:317-338.
[22] Kallen E. Surface effects of vertically propagating gravity waves in a stratified fluid [J]. J Fluid Mech, 1986, 182:111-125.

SURFACE EFFECTS OF INTERNAL WAVE GENERATED BY A MOVING SOURCE IN A TWO-LAYER FLUID OF FINITE DEPTH

SURFACE EFFECTS OF INTERNAL WAVE GENERATED BY A MOVING SOURCE IN A TWO-LAYER FLUID OF FINITE DEPTH

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 13

编辑推荐

Metrics

本文评价

[1]	陈志敏;W. G. PRICE. Dissipative free-surface solver for potential flow around hydrofoil distributed with doublets[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(11): 1467-1480.
[2]	S. TARIVERDILO;J. MIRZAPOUR;M. SHAHMARDANI;G. REZAZADEH. Free vibration of membrane/bounded incompressible fluid[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(9): 1167-1178.
[3]	张殿新;陶建华. 一种改善了非线性和色散性的Boussinesq方程模型[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(7): 897-908 .
[4]	黄振华. Reflection and transmission of regular waves at a surface-pitching slotted barrier[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(9): 1153-1162 .
[5]	赵存宝;张嘉钟;黄文虎. Vibration reduction of floating elastic plates in surface waves[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(8): 1037-1047 .
[6]	余延生;马兴瑞;王本利. Multidimensional modal analysis of liquid nonlinear sloshing in right circular cylindrical tank[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(8): 1007-1018 .
[7]	菅永军;鄂学全;张杰. DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(3): 417-424 .
[8]	菅永军;鄂学全;张杰. CAPILLARY EFFECT ON VERTICALLY EXCITED SURFACE WAVE IN CIRCULAR CYLINDRICAL VESSEL[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(2): 227-234 .
[9]	苏晓冰;魏岗;戴世强. TWO-DIMENSIONAL ALGEBRAIC SOLITARY WAVE AND ITS VERTICAL STRUCTURE IN STRATIFIED FLUID[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(10): 1255-1265 .
[10]	王忠民;张战午;赵凤群. STABILITY ANALYSIS OF VISCOELASTIC CURVED PIPES CONVEYING FLUID[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(6): 807-813 .
[11]	王本龙;刘桦. HIGHER ORDER BOUSSINESQ-TYPE EQUATIONS FOR WATER WAVES ON UNEVEN BOTTOM[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(6): 774-784 .
[12]	菅永军;鄂学全;柏威. NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(10): 1194-1207.
[13]	周显初;芮燚. NUMERICAL SIMULATION OF STANDING SOLITONS AND THEIR INTERACTION[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(12): 1371-1380.