ORCID
- Rossen Ivanov: 0000-0003-1008-8272
Abstract
A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that the upper layer is considerably deeper with a lower density than the lower layer. The fluid dynamics is presented in Hamiltonian form with appropriate Dirichlet–Neumann operators for the two fluid domains, and the depth-dependent current is taken into account. The well known integrable Intermediate Long Wave Equation (ILWE) is derived as an asymptotic internal waves model in the case of flat bottom. For a non-flat bottom the ILWE is with variable coefficients. Two limits of the ILWE lead to the integrable Benjamin–Ono and Korteweg-de Vries equations. Higher-order ILWE is obtained as well.
Keywords
Dirichlet–Neumann operator, Intermediate long-wave equation, Internal waves, Shear current
DOI Link
Publication Date
2026-01-01
Publication Title
Nonlinear Analysis: Real World Applications
Volume
87
ISSN
1468-1218
Deposit Date
2026-01-27
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Additional Links
Recommended Citation
Ivanov, R., & Ivanova, L. (2026) 'Modelling intermediate internal waves with currents and variable bottom', Nonlinear Analysis: Real World Applications, 87. Available at: 10.1016/j.nonrwa.2025.104451