arXiv subjects
Publications and source records attributed to S. B. Kozitskiy.
An adiabatic mode Helmholtz equation for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the crosswedge benchmark and proved an excellent agreement with the source images method.
A pure analytic one-way coupled mode propagation model for resonant interacting modes is obtained by the multiscale expansion method. It is proved that the acoustic energy flux is conserved in this model up to the first degree of the corresponding small parameter. The test calculations with the COUPLE program give an excellent agreement.
A mode parabolic equation method for resonantly interacted modes was developed. The flow of acoustic energy is conserved for the derived equations with an accuracy adequate to the used approximation. The testing calculations were done for ASA wedge benchmark and proved excellent agreement with COUPLE program.
The paper deals with electromagnetic effects associated with a radially symmetric system of progressive surface waves in the deep sea, induced by underwater oscillating sources or by dispersive decay of the initial localized perturbations of the sea surface.
Three-dimensional double-diffusive convection in a horizontally infinite layer of an uncompressible fluid interacting with horizontal vorticity field is considered in the neighborhood of Hopf bifurcation points. A family of amplitude equations for variations of convective cells amplitude is derived by multiple-scaled method. Shape of the cells is given as a superposition of a finite number of convective rolls with different wave vectors. For numerical simulation of the obtained systems of amplitude equations a few numerical schemes based on modern ETD (exponential time differencing) pseudo-spectral methods were developed. The software packages were written for simulation of roll-type convection and convection with square and hexagonal type cells. Numerical simulation has showed that the convection takes the form of elongated "clouds", "spots" or "filaments". It was noted that in the system quite rapidly a state of diffusive chaos is developed, where the initial symmetric state is destroyed and the convection becomes irregular both in space and time. The obtained results may be the basis for the construction of more advanced models of multi-component convection, for instance, model of Saturn's polar hexagon.
Three dimensional roll-type double-diffusive convection in a horizontally infinite layer of an uncompressible liquid is considered in the neighborhood of Hopf bifurcation points. A system of amplitude equations for the variations of convective rolls amplitude is derived by multiple-scaled method. An attention is paid to an interaction of convection and horizontal vortex. Different cases of the derived equations are discussed.
A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The results of numerical experiments on propagation of an incident plane wave over a circular-type shoal are presented in comparison with the analytical result, based on Born approximation.
The multiple scale expansion method is used to derive amplitude equations for a system with thermohaline convection in the neighborhood of Hopf and Taylor bifurcation points and at the double zero point of the dispersion relation. A complex Ginzburg-Landau equation, a Newell-Whitehead-type equation, and an equation of the $ϕ^4$ type, respectively, were obtained. Analytic expressions for the coefficients of these equations and their various asymptotic forms are presented. In the case of Hopf bifurcation for low and high frequencies, the amplitude equation reduces to a perturbed nonlinear Schrödinger equation. In the high-frequency limit, structures of the type of "dark" solitons are characteristic of the examined physical system.
Double-diffusive convection in a horizontally infinite layer of a unit height in a large Rayleigh numbers limit is considered. From linear stability analysis it is shown, that the convection tends to have a form of travelling tall thin rolls with height 10-30 times larger than width. Amplitude equations of ABC type for vertical variations of amplitude of these rolls and mean values of diffusive components are derived. As a result of its numerical simulation it is shown, that for a wide variety of parameters considered ABC system have solutions, known as diffusive chaos, which can be useful for explanation of fine structure generation in some important oceanographical systems like thermohaline staircases.