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Based on the small steepness parameter assumption, the three-layer incompressible, inviscid and irrotational fluid system of arbitrary depth is discussed by using the perturbation method, and a unified theory of nonlinear interfacial-internal wave propagation and the approximate nonlinear evolution equations (NEEs) for interfacial-internal elevations are given on the basis of the rigid upper boundary and the flat impermeable bottom. At last we also discuss on NEEs arising from various limiting cases of fluid depth. It is also noted that the theories obtained from the present work include the theoretical results derived by Yoshimasa Matsuno (1993) as special cases.
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Keywords:
- nonlinear evolution equations(NEEs) /
- perturbation method /
- three-layer fluid systems /
- unified theory
[1] Djordjevic V D, Redekopp L G 1978 J. Phys. Oceanogr. 8 1016
[2] Benjamin T B 1967 J. Fluid Mech. 29 559
[3] Ono H 1975 J. Phys. Soc. Jpn. 39 1082
[4] Segur H, Hammack J L 1982 J. Fluid Mech. 118 285
[5] Joseph R I 1977 J. Phys. A: Math. Gen. 10 L225
[6] Kakutani T, Yamasaki N 1978 J. Phys. Soc. Jpn. 45 674
[7] Choi W 1999 J. Fluid Mech. 396 1
[8] Matsuno Y 1993 J. Phys. Soc. Jpn. 62 1902
[9] Chen X G, Song J B, Sun Q 2005 Acta Phys. Sin. 54 5699 (in Chinese)[陈小刚、 宋金宝、 孙 群 2005 54 5699]
[10] Hu D M 1985 Acta Oceanol. Sin. 7 540 (in Chinese)[胡定明 1985 海洋学报 7 540]
[11] Chen X G, Song J B 2006 Chin. Phys. 15 756
[12] Chen X G, Guo Z P, Song J B 2008 Chin. Phys. B 17 3387
[13] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese)[范恩贵、 张鸿庆 1998 47 353]
[14] Fan E G 2000 Acta Phys. Sin. 49 1409 (in Chinese) [范恩贵 2000 49 1409]
[15] Liu S K, Fu Z T, Liu S D, Zhao Q 2001 Acta Phys. Sin. 50 2068 (in Chinese)[刘式适、 付遵涛、 刘式达、 赵 强 2001 50 2068]
[16] Fu Z T, Liu S K, Liu S D 2004 Acta Phys. Sin. 53 343 (in Chinese) [付遵涛、 刘式适、 刘式达 2004 53 343]
[17] Lü K P, Shi Y R, Duan W S, Zhao J B 2001 Acta Phys. Sin. 50 2074 (in Chinese)[吕克璞、 石玉仁、 段文山、 赵金保 2001 50 2074]
[18] Yan Z Y, Zhang H Q, Fan E G 1999 Acta Phys. Sin. 48 1 (in Chinese)[闫振亚、 张鸿庆、 范恩贵 1999 48 1]
[19] Yan Z Y, Zhang H Q 1999 Acta Phys. Sin. 48 1962 (in Chinese)[闫振亚、 张鸿庆 1999 48 1962]
[20] Naranmandula, Wunenboyn, Wang K X 2004 Acta Phys. Sin. 53 11(in Chinese)[那仁满都拉、 乌恩宝音、 王克协 2004 53 11]
[21] Matsuno Y 1992 Phys. Rev. Lett. 69 609
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[1] Djordjevic V D, Redekopp L G 1978 J. Phys. Oceanogr. 8 1016
[2] Benjamin T B 1967 J. Fluid Mech. 29 559
[3] Ono H 1975 J. Phys. Soc. Jpn. 39 1082
[4] Segur H, Hammack J L 1982 J. Fluid Mech. 118 285
[5] Joseph R I 1977 J. Phys. A: Math. Gen. 10 L225
[6] Kakutani T, Yamasaki N 1978 J. Phys. Soc. Jpn. 45 674
[7] Choi W 1999 J. Fluid Mech. 396 1
[8] Matsuno Y 1993 J. Phys. Soc. Jpn. 62 1902
[9] Chen X G, Song J B, Sun Q 2005 Acta Phys. Sin. 54 5699 (in Chinese)[陈小刚、 宋金宝、 孙 群 2005 54 5699]
[10] Hu D M 1985 Acta Oceanol. Sin. 7 540 (in Chinese)[胡定明 1985 海洋学报 7 540]
[11] Chen X G, Song J B 2006 Chin. Phys. 15 756
[12] Chen X G, Guo Z P, Song J B 2008 Chin. Phys. B 17 3387
[13] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese)[范恩贵、 张鸿庆 1998 47 353]
[14] Fan E G 2000 Acta Phys. Sin. 49 1409 (in Chinese) [范恩贵 2000 49 1409]
[15] Liu S K, Fu Z T, Liu S D, Zhao Q 2001 Acta Phys. Sin. 50 2068 (in Chinese)[刘式适、 付遵涛、 刘式达、 赵 强 2001 50 2068]
[16] Fu Z T, Liu S K, Liu S D 2004 Acta Phys. Sin. 53 343 (in Chinese) [付遵涛、 刘式适、 刘式达 2004 53 343]
[17] Lü K P, Shi Y R, Duan W S, Zhao J B 2001 Acta Phys. Sin. 50 2074 (in Chinese)[吕克璞、 石玉仁、 段文山、 赵金保 2001 50 2074]
[18] Yan Z Y, Zhang H Q, Fan E G 1999 Acta Phys. Sin. 48 1 (in Chinese)[闫振亚、 张鸿庆、 范恩贵 1999 48 1]
[19] Yan Z Y, Zhang H Q 1999 Acta Phys. Sin. 48 1962 (in Chinese)[闫振亚、 张鸿庆 1999 48 1962]
[20] Naranmandula, Wunenboyn, Wang K X 2004 Acta Phys. Sin. 53 11(in Chinese)[那仁满都拉、 乌恩宝音、 王克协 2004 53 11]
[21] Matsuno Y 1992 Phys. Rev. Lett. 69 609
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