Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one soliton solution for the initial depth.Comment: 18 pages, 6 figures, 1 tabl

Hamiltonian approach to modelling interfacial internal waves over variable bottom

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 effects (Coriolis force) and a variable bathymetry. An example of the physical situation described above is well illustrated by the equatorial internal waves in the presence of the Equatorial Undercurrent (EUC). We find that the interface (physically coinciding with the thermocline and the pycnocline) satisfies in the long wave approximation a KdV–mKdV type equation with variable coefficients. The soliton propagation over variable depth leads to effects such as soliton fission, which is analysed and studied numerically as well

Photo- and Thermo-Induced Changes in Optical Constants and Structure of Thin Films from GeSe2-GeTe-ZnTe System

AbstractWe examined the condition of preparation of thin films from GeSe2-GeTe-ZnTe system by thermal evaporation and changes in their optical properties after exposure to light and thermal annealing. The results for composition analysis of thin films showed absence of Zn independently of the composition of the bulk glass. By X-ray diffraction (XRD) analysis it was found that a reduction of ZnTe in ZnSe in bulk materials takes of place during the film deposition. A residual from ZnSe was observed in the boat after thin film deposition. Optical constants (refractive index, n and absorption coefficient, α) and thickness, d as well as the optical band gap, Eg, depending of the content of Te in ternary Ge-Se-Te system are determined from specrophotometric measurements in the spectral range 400-2500nm applying the Swanepoel's envelope method and Tauc's procedure. With the increase of Te content in the layers the absorption edge is shifted to the longer wavelengths, refractive index increases while the optical band gap decreases from 2.02eV for GeSe2 to 1.26eV for Ge34Se42Te24. The values of the refractive index decrease after annealing of all composition and Eg increase, respectively. Thin films with composition of Ge27Se47Te9Zn17 and Ge28Se49Te10Zn13 were prepared by co-evaporation of (GeSe2)78(GeTe)22 and Zn from a boat and a crucible and their optical properties, surface morphology and structure were investigated. The existence of a correlation between the optical band gap and the copostion of thin films from the system studied was demonstrated

Surface waves over currents and uneven bottom

The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution for the initial depth. Emergence of new solitons is observed as a result of the wave interaction with the uneven bottom