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Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

Song Jin-Bao Sun Qun Chen Xiao-Gang

Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

Song Jin-Bao, Sun Qun, Chen Xiao-Gang
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  • Received Date:  04 March 2005
  • Accepted Date:  30 June 2005
  • Published Online:  20 December 2005

Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

  • 1. (1)中国科学院海洋研究所,青岛 266071; (2)中国科学院海洋研究所,青岛 266071;内蒙古工业大学理学院,呼和浩特 010062;中国科学院研究生院,北京 100039

Abstract: In this paper, internal waves in three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the first-order solutions are consistent with ordinary linear theoretical results, and the second-order solutions describe the second-order modification on the linear theory and the interactions between the two interfacial waves. Both the first-order and second-order solutions derived depend on the depths and densities of the three-layer fluid. It is also noted that the solutions obtained from the present work include the theoretical results derived by Umeyama as special cases.

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