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

Abstract

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 d 1, and lower layer thickness d 2, instead of only one parameter–water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Méhauté’s plot for free surface waves if water depth ratio r = d 1/d 2 approaches to infinity and the upper layer water density ρ 1 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 = (ρ 2 − ρ 1)/ρ 2 → 1.0 and r > 1.0. In the end, several 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.