Equations for the wave perturbations of velocity and pressure in a nonisothermal atmosphere are considered. It is noted that the pressure perturbation has singularities near the altitude where the equality of the horizontal phase velocity of the perturbation and sound velocity in the medium is fulfilled. At this altitude, a thin atmospheric layer with finite mass is concentrated. The wave perturbations do not penetrate to a higher level. The presence of a singularity in the wave perturbation of pressure was numerically confirmed for the actual altitude temperature profiles of the atmosphere.
We consider the problem on the existence of discrete Lorenz attractors in a nonholonomic Celtic stone model. To this end, in two-parameter families of such models of certain types, the main local and global bifurcations leading to both the appearance and destruction of the attractors are studied. In the plane of governing parameters (one of them is the angle of dynamical asymmetry of the stone, and the other is the total energy) , we construct the corresponding bifurcation diagram, where the region of existence of the discrete Lorenz attractor is shown and its boundaries are explained. We point out the similarities and differences in the scenarios of the emergence of the discrete Lorenz attractor in the nonholonomic model of Celtic stone and the attractor from the classical Lorenz model.
In this paper, a new scenario of the appearance of mixed dynamics in two-dimensional reversible diffeomorphisms is proposed. The key point of the scenario is a sharp increase of the sizes of both strange attractor and strange repeller which appears due to heteroclinic bifurcations of the invariant manifolds of saddle fixed points belonging to these attractor and repeller. Due to such bifurcations, a strange attractor collides with the boundary of its absorbing domain, while a strange repeller collides with the boundary of it's ``repulsion'' domain and, as a result, the intersections between these two sets appear immediately. As a result of the scenario, the dissipative dynamics associated with the existence of strange attractor and strange repeller (which are separated from each other) sharply becomes mixed, when attractors and repellers are principally inseparable. The possibility of implementing the proposed scenario is demonstrated on the example of such a well-known problem from rigid body dynamics as a nonholonomic model of Suslov top.
It is shown that the discrete frequency spectrum of the plane hydrodynamic flow of an ideal incompressible liquid with localized trajectories of liquid particles can contain only one harmonic, two harmonics, or an infinite number of the latter.
We study the statistical moments of the soliton gas (mean field, variance, skewness, and kurtosis), which is described within the framework of the Gardner equation with negative cubic nonlinearity. The influence of the limiting (thick or table-like) soliton on the statistical moments of the soliton gas is considered. It is shown to be substantial if the thick-soliton intensity is comparable with that of the moderate-amplitude solitons.
Evolution of solitons is addressed in the framework of an extended nonlinear Schrödinger equation (NLSE), including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term which is well known as an ingredient of the temporal-domain NLSE in optics. In the present context, it is induced by the underlying interaction of the high-frequency envelope wave with a damped low-frequency wave mode. Also included is spatial inhomogeneity of self-phase modulation (SPM). It is shown that the wavenumber downshift of solitons, caused by the pseudo-SRS, may be compensated by an upshift provided by the increasing SPM coefficient. An analytical solution for solitons is obtained in an approximate form. Analytical and numerical results agree well.
We study dynamical properties of a Celtic stone moving along the plane. Both one- and two-parameter families of the corresponding nonholonomic models are considered, in which bifurcations are studied that lead to changing types of stable motions of the stone as well as to the onset of chaotic dynamics. It is shown that multistability phenomena are observed in such models when stable regimes of various types (regular and chaotic) can coexist in the phase space of the system. In the parameter space, the regions are constructed in which multistability is observed, and its types are described. We also show that chaotic dynamics of the nonholonomic model of Celtic stone can be very diverse. Here, in the corresponding parameter regions, there are observed both spiral strange attractors of various types, including the so-called discrete Shilnikov attractors, and mixed dynamics, when attractor and repeller intersect and almost coincide.
In quiet low-latitude Earth's ionosphere, a rather developed current system that is responsible for the Sq magnetic-field variations is formed in quiet sunny days under the action of tidal streams. The density of the corresponding currents is maximal at the equatorial latitudes in the midday hours, where the so-called equatorial current jet is formed. In this work, we discuss the nature of the equatorial current jet. The original part of this paper is dedicated to the study of the value of its response to external effects. First of all, it is related to estimating the possibility of using the equatorial current jet for generating the low-frequency electromagnetic signals during periodic heating of the ionosphere by the heating-facility radiation. The equatorial current jet can also produce electrodynamic response to the natural atmospheric processes, e.g., an acoustic-gravitational wave.