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非线性海洋内波的理论、模型与计算

王展 朱玉可

王展, 朱玉可. 非线性海洋内波的理论、模型与计算[J]. 力学学报, 2019, 51(6): 1589-1604. doi: 10.6052/0459-1879-19-326
引用本文: 王展, 朱玉可. 非线性海洋内波的理论、模型与计算[J]. 力学学报, 2019, 51(6): 1589-1604. doi: 10.6052/0459-1879-19-326
Wang Zhan, Zhu Yuke. THEORY, MODELLING AND COMPUTATION OF NONLINEAR OCEAN INTERNAL WAVES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1589-1604. doi: 10.6052/0459-1879-19-326
Citation: Wang Zhan, Zhu Yuke. THEORY, MODELLING AND COMPUTATION OF NONLINEAR OCEAN INTERNAL WAVES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1589-1604. doi: 10.6052/0459-1879-19-326

非线性海洋内波的理论、模型与计算

doi: 10.6052/0459-1879-19-326
基金项目: 1) 国家自然科学基金资助项目(11772341);国家自然科学基金资助项目(11911530171)
详细信息
    通讯作者:

    王展

  • 中图分类号: O352

THEORY, MODELLING AND COMPUTATION OF NONLINEAR OCEAN INTERNAL WAVES

  • 摘要: 海水因盐度与温度的垂向差异造成密度层结现象, 进而由于海洋系统的内部扰动(如海潮流过局部隆起的海底地形)与外部扰动(如死水现象)造成等密面的波动, 这一现象称为“内波”. 内波在全球范围内大量存在, 尤其是在海峡入海口等密度层结现象较为明显和稳定的区域会有内波频繁活动. 海洋通常呈现“三明治”状的结构: 密度相对稳定的混合层与深水层, 以及位于中间密度连续过渡的密跃层. 密跃层的整体脉动对于海洋工程和海洋生态环境有重大的影响; 而密跃层内部的波动对于潜艇的非声探测(反过来说, 对于潜艇的隐身作战)具有潜在的应用价值. 而造成这些重大影响的根源在于内波在水平和垂直方向都具备传播能力, 这是有别于海洋表面波浪的关键之处.本文针对两类海洋密度模型-连续分层模型与间断分层模型, 从理论研究、数值模拟、实验室机理实验等方面论述了研究海洋内波的各类非线性模型(包括弱非线性的Korteweg-de Vries方程、Benjamin-Ono方程, Kadomtsev-Petviashvili方程等著名模型以及强非线性Miyata-Choi-Camassa方程、非线性势流理论、带密度变化的不可压缩Navier-Stokes方程等), 讨论各自的适用范围, 并借此探讨内波在海洋质量动量能量输运中所起的至关重要的作用.

     

  • 1 Mercier MJ, Vasseur R, Dauxois T . Resurrecting dead-water phenomenon. Nonlinear Processes in Geophysics, 2011,18:193-208
    2 Perry RB, Schimke GR . Large-amplitude internal waves observed off the northwest coast of Sumatra. Journal of Geophysical Research, 1965,70(10):2319-2324
    3 Osborne AR, Burch TL . Internal solitons in the Andaman Sea. Science, 1980,208(4443):451-460
    4 Duda TF, Lynch JF, Irish JD , et al. Internal tide and nonlinear internal wave behavior at the continental slope in the northern South China Sea. IEEE Journal of Oceanic Engineering, 2005,29(4):1105-1130
    5 5种劲松, 周晓中 . 合成孔径雷达图像海洋内波探测研究综述. 雷达学报, 2013,2(4):406-421
    5 ( Chong Jinsong, Zhou Xiaozhong . Survey of study on internal waves detection in synthetic aperture radar image. Journal of Radars, 2013,2(4):406-421 (in Chinese))
    6 Caponi EA, Crawford DR, Yuen HC , et al. Modulation of radar backscatter from the ocean by a variable surface current. Journal of Geophysical Research Oceans, 1988,93(C10):12249-12263
    7 Alpers W . Theory of radar imaging of internal waves. Nature, 1985,314(6008):245-247
    8 Jackson C . Internal wave detection using the moderate resolution imaging spectroradiometer (modis). Journal of Geophysical Research: Oceans, 2007,112:C11012
    9 李家春 . 水面下的波浪--海洋内波. 力学与实践, 2005,27(2):3-8
    9 ( Li Jiachun . Billow under the sea surface-Internal waves in the ocean. Mechanics in Engineering, 2005,27(2):3-8 (in Chinese))
    10 蔡树群, 何建玲, 谢皆烁 . 近10年来南海孤立内波的研究进展. 地球科学进展, 2011,26(7):703-710
    10 ( Cai Shuqun, He Jianling, Xie Jieshuo . Recent decadal progress of the study on internal solitons in the South China Sea. Advances in Earth Science, 2011,26(7):703-710 (in Chinese))
    11 蔡树群, 甘子钧 . 南海北部孤立子内波的研究进展. 地球科学进展, 2001,16(2):215-219
    11 ( Cai Shuqun, Gan Zijun . Progress in the study of the internal soliton in the northern South China Sea. Advances in Earth Science, 2001,16(2):215-219 (in Chinese))
    12 李家春, 程友良, 范平 . 海洋内波与海洋工程. 庆祝郑哲敏先生八十华诞应用力学报告会--应用力学进展论文集. 北京: 科学出版社, 2004: 41-45
    13 Apel JR, Ostrovsky LA, Stepanyants YA , et al. Internal solitons in the ocean and their effect on underwater sound. The Journal of the Acoustical Society of America, 2007,121:695-722
    14 Joseph RI . Solitary waves in a finite depth fluid. Journal of Physics A General Physics, 1977,10(12):L225-L227
    15 Kubota T . Weakly-nonlinear, long internal gravity waves in stratified fluids of finite depth. Journal of Hydronautics, 1978,12(4):157-165
    16 Benjamin, Brooke T . Internal waves of permanent form in fluids of great depth. Journal of Fluid Mechanics, 1967,29(3):559-592
    17 Davis RE, Acrivos A . Solitary internal waves in deep water. Journal of Fluid Mechanics, 2006,29(3):593-607
    18 Ono H . Algebraic solitary waves in stratified fluids. Journal of the Physical Society of Japan, 1975,39(4):1082-1091
    19 Matsuno Y . A unified theory of nonlinear wave propagation in two-layer fluid systems. Journal of the Physical Society of Japan, 2007,62(6):1902-1916
    20 Choi W, Camassa R . Weakly nonlinear internal waves in a two-fluid system. Journal of Fluid Mechanics, 1996,313:83-103
    21 Grue J, Jensen A , Rus$\mathring{a}$s PO. Properties of large-amplitude internal waves. Journal of Fluid Mechanics, 2000,380:257-278
    22 Koop CG, Butler G . An investigation of internal solitary waves in a two-fluid system. Journal of Fluid Mechanics, 1981,112:225-251
    23 Michallet H , Barth$\acute{e}$lemy E. Experimental study of interfacial solitary waves. Journal of Fluid Mechanics, 1998,366:159-177
    24 Lee CY, Beardsley RC . The generation of long nonlinear internal waves in a weakly stratified shear flow. Journal of Geophysical Research, 1974,79(3):453-462
    25 Helfrich KR, Melville WK . Long nonlinear internal waves. Annual Review of Fluid Mechanics, 2006,38:395-425
    26 Miyata M . Long internal waves of large amplitude. IUTAM Symposinm of Nonlinear Water Waves, Tokyo, Janpan, Aug. 25-28, 1987-1988
    27 Choi W, Camassa R . Fully nonlinear internal waves in a two-fluid system. Journal of Fluid Mechanics, 1999,396:1-36
    28 Jo TC, Choi W . Dynamics of strongly nonlinear internal solitary waves in shallow water. Studies in Applied Mathematics, 2010,109(3):205-227
    29 Ostrovsky Lev A, Grue J . Evolution equations for strongly nonlinear internal waves. Physics of Fluids, 2003,15(10):2934-2948
    30 Turner REL, Vanden-Broeck JM . Broadening of interfacial solitary waves. Physics of Fluids, 1988,31(9):2486-2490
    31 Laget O, Dias F . Numerical computation of capillary-gravity interfacial solitary waves. Journal of Fluid Mechanics, 1997,349:221-251
    32 Kataoka T . The stability of finite-amplitude interfacial solitary waves. Fluid Dynamics Research, 2006,38(12):831-867
    33 Vanden-Broeck J-M . Numerical calculation of gravity-capillary interfaical waves of finite amplitude. Physics of Fluids, 1980,23:1723-1726
    34 Turner REL, Vanden-Broeck J-M . The limiting configuration of interfacial gravity waves. Physics of Fluids, 1986,29:372-375
    35 Dias F, Vanden-Broeck J-M . On internal fronts. Journal of Fluid Mechanics, 2003,479:145-154
    36 Sha H, Vanden-Broeck JM . Two-layer flows past a semicircular obstruction. Physics of Fluids, 1993,5:2661-2668
    37 Dias F, Vanden-Broeck JM . Steady two-layer flows over an obstacle. Philosophical Transactions of the Royal Society A, 2002,360:2137-2154
    38 Dias F, Vanden-Broeck JM . Two-layer hydraulic falls over an obstacle. European Journal of Mechanics B/Fluids, 2004,23:879-898
    39 Baker GR. Generalized vortex methods for free-surface flows//Waves on Fluid Interfaces, Wisconsin-Madison: Academic Press, 1983: 53-81
    40 Hou TY, John SL, Michael JS . Removing the stiffness from interfacial flows with surface tension. Journal of Computational Physics, 1994,114(2):312-338
    41 Meiron DI, Saffman PG . Oerhanging interfacial gravity waves of large amplitude. Journal of Fluid Mechanics, 1983,129:213-218
    42 Grimshaw RHJ, Pullin DI . Extreme interfacial waves. Physics of Fluids, 1986,29:2802-2807
    43 Akers B, Ambrose DM, Wright JD . Traveling waves from the arclength parameterization: Vortex sheets with surface tension. Interfaces and Free Boundaries, 2013,15:359-380
    44 Wilkening J . Breakdown of self-similarity at the crests of large amplitude standing water waves. Physical Review Letters, 2011,107:184501
    45 Ambrose DM, Wilkening J . Computation of symmetric, time-periodic solutions of the vortex sheet with surface tension. Proceedings of the National Academy of Sciences of the United States of America, 2010,108(8):3361-3366
    46 Wang Z, Guan X . Mass transport by fully nonlinear internal waves in two-layer fluids. Preprint, 2019
    47 Kodaira T, Waseda T, Miyata M , et al. Internal solitary waves in a two-fluid system with a free surface. Journal of Fluid Mechanics, 2016,804:201-223
    48 Forgia G. la, Sciortino G . The role of the free surface on interfacial solitary waves. Physics of Fluids, 2019,31:106601
    49 Craig W, Guyenne D, Kalisch H . Hamiltonian long wave expansions for free surfaces and interfaces. Communication on Pure and Applied Mathematics, 2005,58:1587-1641
    50 Haut TS, Ablowitz MJ . A reformulation and applications of interfacial fluids with a free surface. Journal of Fluid Mechanics, 2009,631:375-396
    51 Barros R, Gavrilyuk SL, Teshukov VM . Dispersive nonlinear waves in two-layer flows with free surface. i. Model derivation and general properties. Studies in Applied Mathematics, 2007,119(3):191-211
    52 Fochesato C, Dias F, Grimshaw R . Generalized solitary waves and fronts in coupled korteweg-de vries systems. Physica D, 2005,210:96-117
    53 Dias F, Il’ichev A . Interfacial waves with free-surface boundary conditions: An approach via a model equation. Physica D, 2001,150:278-300
    54 Moni JN, King AC . Guided and unguided interfacial solitary waves. Quarterly Journal of Mechanics and Applied Mathematics, 1995,48:21-38
    55 Michallet H, Dias F . Numerical study of generalized interfacial solitary waves. Physics of Fluids, 1999,11(6):1502-1511
    56 P$\breve{a}$r$\breve{a}$u EI, Dias F . Interfacial periodic waves of permanent form with free-surface boundary conditions. Journal of Fluid Mechanics, 2001,437:325-336
    57 Wang Z, P$\breve{a}$r$\breve{a}$u EI, Milewski PA , et al. Numerical study of interfacial solitary waves propagating under an elastic sheet. Proceedings of the Royal Society A, 2014,470(2168):20140111
    58 Rusas P-O, Grue J . Solitary waves and conjugate flows in a three-layer fluid. European Journal of Mechanics B/Fluids, 2002,21:185-206
    59 Fructus D, Grue J . Fully nonlinear solitary waves in a layered stratified fluid. Journal of Fluid Mechanics, 2004,505:323-347
    60 Vanden-Broeck JM, Turner REL . Long periodic internal waves. Physics of Fluids, 1992,4:1929-1935
    61 Sha H, Vanden-Broeck JM . Internal solitary waves with stratification in density. Journal of the Australian Mathematical Society Series B, 1997,38:563-580
    62 Carr M, Davies PA, Hoebers RP . Experiments on the structure andstability of mode-2 internal solitary-like waves propagating on an offset pycnocline. Physics of Fluids, 2015,27:046602
    63 Deepwell D, Stastna M, Carr M , et al. Interaction of a mode-2 internal solitary wave with narrow isolated topography. Physics of Fluids, 2017,29:076601
    64 Carr M, Stastna M, Davies PA , et al. Shoaling mode-2 internal solitary-like waves. Journal of Fluid Mechanics, 2019,879:604-632
    65 Ambrose DM . Well-posedness of vortex sheets with surface tension. SIAM Journal of Mathematical Analysis, 2003,35(1):211-244
    66 Benney DJ . Long non-linear waves in fluid flows. Journal of Mathematical Physics, 1966,45:52-63
    67 Lee CY, Beardsley RC . The generation of long nonlinear internal waves in a weakly stratified shear flow. Journal of Geophysical Research, 1974,79:453-462
    68 Dubreil-Jacotin ML . Sur la d$\acute{e}$termination rigoureuse des ondes permanentes p$\acute{e}$riodiques d’ampleur finie. [PhD Thesis]. Gauthier-Villars, 1934
    69 Long RR . Some aspects of the flow of stratified fluds I. A theoretical investigation. Tellus, 1953,5:42-58
    70 Stastna M, Lamb KG . Large fully nonlinear internal solitary waves: The effect of background current. Physics of Fluids, 2002,14(9):2987-2999
    71 Mowbray DE, Rarity BSH . A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. Journal of Fluid Mechanics, 1967,56(1):1-16
    72 Lighthill MJ. Waves in Fluids. Cambridge University Press, 1978
    73 Haynes PH, Marks CJ, Mclntyre ME , et al. On the “downward control” of extratropical diabatic circulations by eddy-induced mean zonal forces. Journal of the Atmospheric Sciences, 1991,48:651-678
    74 Fovell R, Durran D, Holton JR . Numerical simulations of convectively generated stratospheric gravity waves. Journal of the Atmospheric Sciences, 1992,49(16):1427-1442
    75 Alexander MJ, Holton JR, Durran DR . The gravity wave response above deep convection in a squall line simulation. Journal of the Atmospheric Sciences, 1995,52:2212-2226
    76 Li Z . A high-order numerical scheme for St. Andrew’s cross in stratified fluids. Zhejiang University, 2018
    77 Thomas NH, Stevenson TN . A similarity solution for viscous internal waves. Journal of Fluid Mechanics, 1972,54(3):495-506
    78 Gordon D, Klement UR, Stevenson TN . A viscous internal wave in a stratified fluid whose buoyancy frequency varies with altitude. Journal of Fluid Mechanics, 1975,69(3):615-624
    79 Hurley DG, Keady G . The generation of internal waves by vibrating elliptic cylinders. Part 2. Approximate viscous solution. Journal of Fluid Mechanics, 2000,351:119-138
    80 Sutherland BR, Linden PF . Internal wave excitation by a vertically oscillating elliptical cylinder. Physics of Fluids, 2002,14(2):721-731
    81 Tabaei A, Akylas TR . Nonlinear internal gravity wave beams. Journal of Fluid Mechanics, 2003,482:141-161
    82 Tabaei A, Akylas TR, Lamb KG . Nonlinear effects in reflecting and colliding internal wave beams. Journal of Fluid Mechanics, 2005,526:217-243
    83 Diamessis PJ, Wunsch S, Delwiche I , et al. Nonlinear generation of harmonics through the interaction of an internal wave beam with a model oceanic pycnocline. Dynamics of Atmospheres and Oceans, 2014,66(2):110-137
    84 Javam A, Imberger J, Armfield SW . Numerical study of internal wave reflection from sloping boundaries. Journal of Fluid Mechanics, 1999,396:183-201
    85 Javam A, Imberger J, Armfield SW . Numerical study of internal wave-wave interactions in a stratified fluid. Journal of Fluid Mechanics, 2000,415:89-116
    86 Slinn DN, Riley JJ . A model for the simulation of turbulent boundary layers in an incompressible stratified flow. Journal of Computational Physics, 1998,144:550-602
    87 Liu R . A numerical and analytic study of internal waves in stratified fluids. [PhD Thesis]. University of Manchester, 1989
    88 Diamessis P, Domaradzki J, Hesthaven J . A spectral multidomain penalty method model for the simulation of high Reynolds number localized stratified turbulence. Journal of Computational Physics, 2005,202:298-322
    89 Pal A, Stadler MBD, Sarkar S . The spatial evolution of fluctuations in a self-propelled wake compared to a patch of turbulence. Physics of Fluids, 2013,25(9):317-338
    90 Stadler MBD, Sarkar S . Simulation of a propelled wake with moderate excess momentum in a stratified fluid. Journal of Fluid Mechanics, 2012,692(2):28-52
    91 Abdilghanie AM, Diamessis PJ . The internal gravity wave field emitted by a stably stratified turbulent wake. Journal of Fluid Mechanics, 2013,720(4):104-139
    92 Gilreath HE, Brandt A . Experiments on the generation of internal waves in a stratified fluid. AIAA Journal, 1983,23(5):693-700
    93 Hopfinger EJ, Flor JB, Chomaz JM, Bonneton P . Internal waves generated by a moving sphere and its wake in a stratified fluid. Experiments in Fluids, 1991,11(4):255-261
    94 Bonneton P, Chomaz JM, Hopfinger EJ . Internal waves produced by the turbulent wake of a sphere moving horizontally in a stratified fluid. Journal of Fluid Mechanics, 1993,254:23-40
    95 Meunier P . Stratified wake of a tilted cylinder. Part 2. lee internal waves. Journal of Fluid Mechanics, 2012,699(5):198-215
    96 Spedding GR, Browand FK, Bell R, Chen J . Internal waves from intermediate, or late-wake vortices. Stratified Flows I//Proceedings of the 5th International Symposium on Stratified Flows, 2000, 113-118
    97 Spedding GR . The evolution of initially turbulent bluff-body wakes at high internal froude number. Journal of Fluid Mechanics, 1997,337:283-301
    98 Kops SMDB, Riley JJ, Winters KB . Dynamics of turbulence strongly influenced by buoyancy. Physics of Fluids, 2003,15(7):2047-2059
    99 Diamessis PJ, Spedding GR, Domaradzki JA . Similarity scaling and vorticity structure in high-Reynolds-number stably stratified turbulent wakes. Journal of Fluid Mechanics, 2011,671(3):52-95
    100 Taylor JR, Sarkar S . Internal gravity waves generated by a turbulent bottom ekman layer. Journal of Fluid Mechanics, 2007,590:331-354
    101 Linden PF . Internal wave excitation from stratified flow over a thin barrier. Journal of Fluid Mechanics, 1998,377:223-252
    102 Donato AN, Peregrine DH, Stocker JR . The focusing of surface waves by internal waves. Journal of Fluid Mechanics, 1999,384:27-58
    103 Yuan C, Grimshaw R, Johnson E . The evolution of second mode internal solitary waves over variable topography. Journal of Fluid Mechanics, 2018,836:238-259
    104 Yuan C, Grimshaw R, Johnson E , et al. Topographic effect on oblique internal wave-wave interactions. Journal of Fluid Mechanics, 2018,856:36-60
    105 Yuan C, Grimshaw R, Johnson E , et al. The propagation of internal solitary waves over variable topography in a horizontally two-dimensional framework. Journal of Physical Oceanography, 2018,48:283-300
    106 Tunaley JKE . Simulation of internal wave wakes and comparison with observations. ESA Living Planet Symposium, 2013
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  • 收稿日期:  2019-10-25
  • 刊出日期:  2019-11-18

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