Nonlinear problems of complex natural systems: Sun and climate dynamics.

The universal role of the nonlinear one-third subharmonic resonance mechanism in generation of strong fluctuations in complex natural dynamical systems related to global climate is discussed using wavelet regression detrended data. The role of the oceanic Rossby waves in the year-scale global temperature fluctuations and the nonlinear resonance contribution to the El Niño phenomenon have been discussed in detail. The large fluctuations in the reconstructed temperature on millennial time scales (Antarctic ice core data for the past 400,000 years) are also shown to be dominated by the one-third subharmonic resonance, presumably related to the Earth's precession effect on the energy that the intertropical regions receive from the Sun.

Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers.

It is shown that the correlation function of the mean wind velocity generated by a turbulent thermal convection (Rayleigh number Ra ∼ 10(11)) exhibits exponential decay with a very long correlation time, while the corresponding largest Lyapunov exponent is certainly positive. These results together with the reconstructed phase portrait indicate the possible presence of chaotic component in the examined mean wind. Telegraph approximation is also used to study the relative contribution of the chaotic and stochastic components to the mean wind fluctuations and an equilibrium between these components has been studied in detail.

Fluctuations of temperature gradients in turbulent thermal convection.

Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature fluctuation T , except that the velocity field in the new equation is substantially smoothed. This smoothed field leads to a -1 scaling of the spectrum of G in the same range of scales for which the spectral exponent of T lies between -7/5 and -5/3 . This result is confirmed by measurements in a confined container with cryogenic helium gas as the working fluid for Rayleigh number Ra=1.

Intermittency and the passive nature of the magnitude of the magnetic field.

It is shown that the statistical properties of the magnitude of the magnetic field in turbulent electrically conducting media resemble, in the inertial range, those of passive scalars in fully developed three-dimensional fluid turbulence. This conclusion, suggested by the data from the Advanced Composition Explorer, is supported by a brief analysis of the appropriate magnetohydrodynamic equations.

"Clusterization" and intermittency of temperature fluctuations in turbulent convection.

Temperature time traces are obtained in turbulent thermal convection at high Rayleigh numbers. Measurements are made in the midplane of the apparatus, near the sidewall but outside the boundary layer. A telegraph approximation for temperature traces is generated by setting the fluctuation amplitude to 1 or 0 depending on whether or not it exceeds the mean value.