arXiv subjects

Lyudmila Ivanova

Publications and source records attributed to Lyudmila Ivanova.

2 recordsLinked to original sources

arXiv2026

Benjamin-Ono dynamics of internal waves with currents

Internal water waves arise when there is a change in density stratification in a fluid, which may occur in an oceanographical context due to variations in temperature, salinity, or other fluctuations in the equations of state. We present a derivation of nonlinear integrable models for the propagation of interfacial internal waves arising between two fluid layers of different densities (at the so called pycnocline). We examine the integrable Benjamin-Ono (BO) equation as an internal wave model, incorporating underlying currents by permitting a sheared current in both fluid layers. The BO equation arises for a specific small-amplitude asymptotic regime. We show that the BO soliton characteristics are strongly affected by the shear current parameters.

nlin.PS↗

arXiv2025

Modelling intermediate internal waves with currents and variable bottom

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.

nlin.PS↗