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Second-order random interfacial wave solutions for two-layer fluid with a free surface

Second-order random interfacial wave solutions for two-layer fluid with a free surface

作     者:SONG Jinbao SUN Qun 

作者机构:Institute of Oceanology Chinese Academy of Sciences Qingdao 266071 China 

出 版 物:《Acta Oceanologica Sinica》 (海洋学报(英文版))

年 卷 期:2006年第25卷第1期

页      面:15-20页

核心收录:

学科分类:07[理学] 0707[理学-海洋科学] 

基  金:supported by the National Science Foundation for Distinguished Young Scholars of China under contract No.40425015 the Cooperative Project of Chinese Academy Sciences and the China National 0ffshore 0il Corporation("Behaviours of internal waves and their roles on the marine stuctures") 

主  题:two-layer fluid free surface random interracial waves second-order solutions 

摘      要:A previous study (Song. 2004. Geophys Res Lett, 31 (15):L15302) of the second-order solutions for random interracial waves is extended in a constant depth, two-layer fluid system with a rigid lid is extended into a more general case of two-layer fluid with a top free surface. The rigid boundary condition on the upper surface is replaced by the kinematical and dynamical boundary conditions of a free surface, and the equations describing the random displacements of free surface, density-interface and the associated velocity potentials in the two-layer fluid are solved to the second order using the same expansion technology as that of Song (2004. Geophys Res Lett, 31 (15):L15302). The results show that the interface and the surface will oscillate synchronously, and the wave fields to the first-order both at the free surface and at the density-interface are made up of a linear superposition of many waves with different amplitudes, wave numbers and frequencies. The second-order solutions describe the second-order wave-wave interactions of the surface wave components, the interface wave components and among the surface and the interface wave components. The extended solutions also include special cases obtained by Thorpe for progressive interracial waves (Thorpe. *** R Soc London, 263A:563~614) and standing interracial waves (Thorpe. 1968b. J Fluid Mech, 32:489-528) for the two-layer fluid with a top free surface. Moreover, the solutions reduce to those derived for random surface waves by Sharma and Dean (*** Engineering Rep 20) if the density of the upper layer is much smaller than that of the lower layer.

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