47 3 Vol.47, No.3 016 5 OCEANOLOGIA ET LIMNOLOGIA SINICA May, 016 * 1 1 1 1 (1. 66100;. 66590) KdVmKdV, Fluent,,,,, :, ;,, ;,, Fluent; ; ; ; P751 doi: 10.11693/hyhz0150600165,,,, (, 001), (Osborne et al, 1980), KdVmKdV (Choi et al, 1999;Helfrich et al, 006), Liu (014) SAR, 005 5 Xu (010) KdVmKdV,, ekdv (009),, Michallet (1998), KdV, KdV-mKdV ; Buick (003), PIV,, (CFD) Zhang (01) CFD, KdV, (009) Fluent,, ; (01) MCC,,, CFD CFD, Fluent,, VOF (, 009),, *, 5179187 ;, 015ZDZX04003,, E-mail: vanilla_ 103@163.com :,,, E-mail: hyguo@ouc.edu.cn : 015-06-15, : 015-09-04
3 : 503,,,, 1, Navier-Stokes : 1500cm, 58cm, 9.5cm, 48.5cm, x, ; y, 1, 80cm, 15cm Fig.1 1 The sketch of numerical wave tank :, (wall) (, 005),, (wall) :, UDF,,, Navier-Stokes,, KdVmKdV : h1 1 h, ( x, t) KdV (Michallet et al, 1998): : x ct, sec ( ) (1) L xt a h ac1 c c0, 3 1 c L () ( ac ) 3c0 1h h1 c0 1h1hhh 1 1, c ( 6 ( 1hh 1 h1 h) 1h h1) c (3) mkdv (Michallet et al,1998): : sec h [ ( x cmt)] ( xt, ) a 1tanh [ ( x c t)] m 1 (4) 1 3hh h 3 3 ( h hc ) ( hhc) hc 1/ h hc, 1/, h h hc, 1 (5) h / h h 0 ( ) h / h ( h 0) (6) h h h a, h h h a (7) c m 1 h H c0 1 h h c 1 1 (8) gh 4(1 ) hc( hhc) c0 1 1 h (9) a, L KdVmKdV (a/h), KdV mkdv UDF v(t)( c ( x, t), 01): vt (), D, c D :,, x, :, x ct : vtd () t ( Dt,) x (10)
504 47 c ( x, t) vt () (11) D :,,, y= 8.5cm y=0.5cm, 0.5cm,,,,, 1.0 x, x cm : Fig. The gridding of the numerical flume : Fluent, 1 =1035kg/m 3, =1054kg/m 3 Fluent k, VOF,, PISO,,,, (, 000;, 009): 1,,, : Tab.1 表 1 数值模拟工况设置 Setting of amplitude for the numerical simulation a(cm) 4.060 5.877 7.378 8.108 KdVmKdV (a/h), 1 a/h<0.1, KdV ; a/h>0.1, mkdv (, 013) :, 0.01s, 0.1,, : 15m 0.35m 0.7m(), 0.6m Oster, h 1 =9.5cm, ρ 1 =1035kg/m 3 ; h =48.5cm, ρ =1054kg/m 3 3 PIV(Wang et al, 015),,,
3 : 505 3 Fig.3 Experimental wave generation CCD, 50Hz, 190 1080,,.,, : 5,,,,,,,,,,, Fig.4 4 Comparison in shape of the waves generated between numerical simulation (red lines) and experiment (black lines) in different amplitudes
506 47 3 3.1,, : (1)y=5cm, ; ()y= 4cm,, : Fig.5 5 Comparison in horizontal velocity magnitude induced by generated internal solitary waves between numerical simulation (red lines) and experiment (black lines) at different depth 6,,,, ;,,, :,,, : 6,,, ; ;,, :, Tab. 表 内孤立波波致水平流速的最大值 The maximum horizontal velocity induced by internal solitary waves y=5cm (cm/s) 4.00 5.30 6.4 6.95 y= 4cm (cm/s) 1.4 1.94.59.85 3. 7,, ;
3 : 507,,, : (1) ; (),,,, ; (3) ; (4),, (5),, Fig.6 6 Profiles of magnitude of the horizontal velocity induced by internal solitary waves 4 Fluent,,, UDF, KdVmKdV,, : (1), (),,,,, (3),,,, (4),,, (5),,,, 005.. :
508 47, 58 81,, 000.., 18(): 46 50,,, 001.., 5(4): 5 8,, 009. Fluent., 8(4): 7 75, 100,,, 009.., 40(3): 69 74, 01.. :, 3 34,,, 01. MCC., 30(4): 9 36,,, 013.., 6(8): 084705,, 009. VOF., 4(1): 15 1,,, 009. VOF., 30(1): 9 13 Buick J M, Martin A J, Cosgrove J A et al, 003. Comparison of a lattice Boltzmann simulation of steep internal waves and laboratory measurements using particle image velocimetry. European Journal of Mechanics-B/Fluids, (1): 7 38 Choi W, Camassa R, 1999. Fully nonlinear internal waves in a two-fluid system. Journal of Fluid Mechanics, 396: 1 36 Helfrich K R, Melville W K, 006. Long nonlinear internal waves. Annual Review of Fluid Mechanics, 38(1): 395 45 Liu B Q, Yang H, Zhao Z X et al, 014. Internal solitary wave propagation observed by tandem satellites. Geophysical Research Letters, 41(6): 077 085 Michallet H, Barthélemy E, 1998. Experimental study of interfacial solitary waves. Journal of Fluid Mechanics, 366: 159 177 Osborne A R, Burch T L, 1980. Internal solitons in the Andaman Sea. Science, 08(4443): 451 460 Wang F, Wu K F, Guo H Y et al, 015. Experimental study on internal solitary wave induced flow field. In: Xie L Q ed. Advanced Engineering and Technology II. Hong Kong, China: CRC Press, 111 Xu Z H, Yin B S, Hou Y J, 010. Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea. Chinese Journal of Oceanology and Limnology, 8(5): 1049 1054 Zhang L, Wang L L, Yu Z Z et al, 01. Characteristics of nonlinear internal waves in a three-dimensional numerical wave tank. Applied Mechanics and Materials, 1 13: 113 1130 A NUMERICAL SIMULATION ON FLOW FIELD INDUCED BY INTERNAL SOLITARY WAVES WANG Wei 1, GUO Hai-Yan 1, WANG Fei, MIAO De-Sheng 1, MA Dong 1 (1. Engineering College, Ocean University of China, Qingdao 66100, China;. College of Architecture and Civil Engineering, Shandong University of Science and Technology, Qingdao 66590, China) Abstract Based on KdV and mkdv theories, we simulated internal solitary waves generated in flat slapping piston wave-making technology with software Fluent. We then verified the the flow characteristics against experimental data. The results show that the wave-induced horizontal velocities are opposite in direction between upper and lower layers of fluid, showing a trend of going up first, reaching the maximum when passing the trough of the internal wave, and then going down. Across the trough, the wave-induced velocities in vertical distribution in upper layer did not change remarkably; and they decayed slightly in the lower layer. A transitional zone was observed between the interface of the two layers and the wave trough surface, in which the wave-induced velocities weakened obviously. With the increase in amplitude of internal solitary wave, the range of the transitional zone increased too. Key words Software Fluent; internal solitary wave; numerical simulation; flow characteristics; physical experiment