Alexey Gledzer

Passive particles advection is considered in the vicinity of hyperbolic stationary point of the separatrix destroyed by insteady perturbations. For different frequencies of the disturbancies the trajectories of advected particles are investigated analytically and numerically. The approximate criteria of capture and release of particles are obtained. The results are linked with known law for the stochastic layer width near separatrix. The obtained criteria are connected with analytical Melnikov’s integral.

The oscillatory types of motion in frame of 6-modes model of convection are considered into nearly axially symmetrical ellipsoidal volume. The pseudo-Prandtl, Rayleigh numbers and vertical aspect ratio are changed in large ranges. The regimes with different types of vorticity oscillations are determined, that are connected with the turning of the fluid rotation axis or with the alteration of rotation. For some of the regimes the analytical solution and formulae of oscillation periods were obtained.

The interaction of various climatic zones (northern, temperate and southern) as circulation cells of large-scale atmospheric currents is represented in the form of a superposition of six-dimensional systems that describe the motion of stratified fluids in the space of linear velocity and temperature fields. The effect of each of the zones on neighboring zones occurs only through temperature gradients along the meridional direction which are due to sources and sinks of heat (short-wave radiation, downcoming long-wave radiation, outgoing long-wave radiation). The resulting nonlinear system, in which each of the blocks contains vortex and temperature components of the fields, is discretized by an implicit scheme. Long-period nonlinear oscillations are modeled, showing the natural “breath” of the climate of the atmosphere, in which the amplitudes of vortex intensity and temperature differences of various zones change with characteristic times of decades. In this case, the transition between quasi-stationary states of the system can occur over several years. A comparison is made between various numerical methods that show long-term oscillations in convective systems.