Related papers: On the intermediate long wave propagation for inte…
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…
A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the…
The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV…
We continue our study on the convergence issue of the intermediate long wave equation (ILW) on both the real line and the circle. In particular, we establish convergence of the scaled ILW dynamics to that of the Korteweg-de Vries equation…
In this paper, we study the low regularity convergence problem for the intermediate long wave equation (ILW), with respect to the depth parameter $\delta>0$, on the real line and the circle. As a natural bridge between the Korteweg-de Vries…
We study the well-posedness issue of the intermediate long wave equation (ILW) on both the real line and the circle. By applying the gauge transform for the Benjamin-Ono equation (BO) and adapting the $L^2$ well-posedness argument for BO by…
In this paper we derive a higher-order KdV equation (HKdV) as a model to describe the unidirectional propagation of waves on an internal interface separating two fluid layers of varying densities. Our model incorporates underlying currents…
This survey is focused on two asymptotic models for internal waves, the Benjamin-Ono (BO) and Intermediate Long Wave (ILW) equations that are integrable by inverse scattering techniques (IST). After recalling briefly their derivations we…
We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal…
A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface…
A two-layer fluid system separated by a pycnocline in the form of an internal wave is considered. The lower layer is infinitely deep, with a higher density than the upper layer which is bounded above by a flat surface. The fluids are…
We study the effects of an uneven bottom on the internal wave propagation in the presence of stratification and underlying non-uniform currents. Thus, the presented models incorporate vorticity (wave-current interactions), geophysical…
In this manuscript we perform an extensive numerical study of the long wave interaction problem with a fixed partially immersed body into a fluid layer. The incident wave is assumed to be an isolated solitary wave. The body in this study is…
We consider a two-layer fluid with a depth-dependent upper-layer current (e.g. a river inflow, an exchange flow in a strait, or a wind-generated current). In the rigid-lid approximation, we find the necessary singular solution of the…
We investigate regularity properties of the solution map for the intermediate long wave equation (ILW) on the real line. More precisely, we study the scaled ILW which was shown to converge to the Korteweg-de Vries equation (KdV) in…
We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear flow. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive them from the…
(Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here. See the abstract in the paper.) We study convergence problems for the intermediate long wave equation (ILW), with the…
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or…
We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of…
We consider longwave mode of the interface instability in the system comprising of two immiscible fluid layers. The fluids fill out plane horizontal cavity which is subjected to horizontal harmonic vibration. The analysis is performed…