Open AccessSecond-order Stokes solutions for internal waves in three-layer density-stratified fluid
Author(s) -
Xiaogang Chen,
Song Jin-bao,
Qun Sun
Publication year - 2005
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.54.5699
Subject(s) - internal wave , physics , amplitude , order (exchange) , mechanics , stratified flow , perturbation (astronomy) , perturbation theory (quantum mechanics) , stratified flows , work (physics) , mathematical analysis , first order , classical mechanics , optics , mathematics , quantum mechanics , turbulence , finance , economics
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.