Interaction of Viscous Wakes With a Free Surface
-
摘要: 解析地研究了无限深不可压粘性流体中运动物体产生层流尾迹与自由表面波的相互作用.以定常的Oseen方程模拟受扰流动,对于小振幅自由表面波则采用线性化的运动学和动力学边界条件.在数学描述上,运动物体以Oseen极子模拟,受扰流场分解成表述粘性尾迹的无界奇异Oseen流和描述自由面效应的有界正则Oseen流之和.通过积分变换法,得到自由表面波的精确解.借助Lighthill的两步格式,导出了自由面波高带有附加校正项的渐近解.所得对称解显示了波动的振幅因粘性和潜深的存在而呈指数衰减.Abstract: The interaction of laminar wakes with free-surface waves generated by a moving body beneath the surface of an incompressible viscous fluid of infinite depth was investigated analytically. The analysis was based on the steady Oseen equations for disturbed flows. The kinematic and dynamic boundary conditions were linearized for the small-amplitude free-surface waves. The effect of the moving body was mathematically modeled as an Oseenlet. The disturbed flow was regarded as the sum of an unbounded singular Oseen flow which represents the effect of the viscous wake and a bounded regular Oseen flow which represents the influence of the free surface. The exact solution for the free-surface waves was obtained by the method of integral transforms. The asymptotic representation with additive corrections for the free-surface waves was derived by means of Lighthill's two-stage scheme. The symmetric solution obtained shows that the amplitudes of the free-surface waves are exponentially damped by the presences of viscosity and submergence depth.
-
Key words:
- free-surface wave /
- viscous wake /
- viscosity /
- submergence depth /
- Oseenlet /
- Lighthill's two-stage ’scheme /
- asymptotic solution
-
[1] Ursell F. On the Kelvin's ship-wave pattern [J].J Fluid Mech, 1960,8:418—431. doi: 10.1017/S0022112060000700 [2] Crapper G D.Surface waves generated by a traveling pressure point[J].Proc Roy Soc A,1964,282:547—558. doi: 10.1098/rspa.1964.0250 [3] Chung Y K, Lim J S. A review of the Kelvin ship wave pattern [J].J Ship Research,1991,35(3):191—197. [4] Reed A M, Milgram J H. Ship wakes and their radar images[J].Annu Rev Fluid Mech,2002,34:469—502. doi: 10.1146/annurev.fluid.34.090101.190252 [5] Cumberbatch E. Effects of viscosity on ship waves[J].J Fluid Mech, 1965,23:471—479. doi: 10.1017/S0022112065001490 [6] Allen R F. The effects of interference and viscosity in the Kelvin ship-wave problem[J].J Fluid Mech,1968,34: 417—421. doi: 10.1017/S0022112068001989 [7] Brard R. Viscosity, wake and ship waves[J].J Ship Research, 1970,14(4): 207—240. [8] Lugt H J. Local flow properties at a viscous free surface[J].Phys Fluids,1987,30(12): 3647—3652. doi: 10.1063/1.866451 [9] Milgram J H. Theory of radar Backscatter from short waves generated by ships, with application to radar (SAR) imagery[J].J Ship Research, 1988,32(1): 54—69. [10] Lyden J D, Hammond R R, Lyzenga D R,et al. Synthetic aperture radar imaging of surface ship waves[J].J Geophysical Research,1988,93(C10): 12293—12303. doi: 10.1029/JC093iC10p12293 [11] Lurye J R. Interaction of free surface waves with viscous wakes[J].Phys Fluids,1968,11(2): 261—265. doi: 10.1063/1.1691899 [12] Lurye J R. Wave height and wave resistance in the presence of a viscous wake[J].Phys Fluids,1973,16(6): 750—760. doi: 10.1063/1.1694424 [13] Chan A T, Chwang A T. Interaction of laminar far wake with a free surface[J].Phys Fluids,1996,8(2):421—429. doi: 10.1063/1.868796 [14] 刘敏嘉, 陶明德.在粘性流体中船行波的速度场[J].应用数学和力学, 2002,23(10):1085—1091. [15] Lu D Q. Free-surface waves and far wakes generated by a floating body in a viscous fluid[J].J Hydrodynamics, Ser B,2003,15(4): 10—16. [16] Chwang A T, Wu T Y. Hydromechanics of low-Reynolds-number flow—Part 2: Singularity method for Stokes flows[J].J Fluid Mech,1975,67:787—815. doi: 10.1017/S0022112075000614 [17] Duffy D G.Transform Methods for Solving Partial Differential Equations[M].Florida:CRC Press,1994:116—117. [18] Happel J,Brenner H.Low Reynolds Number Hydrodynamics[M].Leyden: Noordhoff International Publishing,1973:79—85. [19] Lagerstrom P A.Laminar Flow Theory[M].Princeton: Princeton University Press, 1996,74—75. [20] Lighthill M J.Studies on magneto-hydrodynamic waves and other anisotropic wave motions[J].Phil Trans Roy Soc Lond A,1960,252:397—430. doi: 10.1098/rsta.1960.0010 [21] Wen S L. An extension of Lighthill's result on asymptotic evaluation of multiple Fourier integrals[J].Intl J Eng Sci,1969,7:53—59. doi: 10.1016/0020-7225(69)90022-6
点击查看大图
计量
- 文章访问数: 2962
- HTML全文浏览量: 68
- PDF下载量: 696
- 被引次数: 0