Validity ranges of interfacial wave theories in a two-layer fluid system

作     者：Yutang Yuan Jiachun Li Youliang Cheng 

作者机构：Division of Engineering Sciences Institute of Mechanics Chinese Academy of Sciences Beijing 100080 China Department of Dynamic Engineering North China Electric Power University Baoding 071003 China 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2007年第23卷第6期

页      面：597-607页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

基　　金：the Knowledge Innovation Project of CAS(KJCX-YW-L02) the National 863 Project of China(2006AAO9A103-4) China National Oil Corporation in Beijing(CNOOC) the National Natural Science Foundation of China(10672056) 

主　　题：Validity ranges Two-layer fluid Interfacial waves Interfacial solitary waves Ursell number 

摘      要：In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the available solutions of periodic and solitary waves, we propose a guideline as principle to identify the validity regions of the interfacial wave theories in terms of wave period T, wave height H, upper layer thickness dl, and lower layer thick-ness d2, instead of only one parameter-water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Mehaute＇s plot for free surface waves if water depth ratio r= d1/d2 approaches to infinity and the upper layer water density p1 to zero. On the contrary, the diagram for water surface waves can be used for two-layer interfacial waves if gravity acceleration g in it is replaced by the reduced gravity defined in this study under the condition of σ=（P2 - Pl）/P2 → 1.0 and r 〉 1.0. In the end, several figures of the validity ranges for various interfacial wavetheories in the two-layer fluid are given and compared with the results for surface waves.