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

摘要

In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfa-cial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the avail-able 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 d1, and lower layer thick-ness d2, instead of only one parameter-water depth d as in the water surface wave circumstance. The diagram proposed 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 ofσ = (P2 - P1)/P2→1.0 and r ＞ 1.0. In the end, sev-eral figures of the validity ranges for various interfacial wave theories in the two-layer fluid are given and compared with the results for surface waves.