Nonlinear and chaotic ice ages: data vs speculations

It is shown that, the wavelet regression detrended fluctuations of the reconstructed temperature for the past 400,000 years (Antarctic ice cores data) are completely dominated by one-third subharmonic resonance, presumably related to Earth precession effect on the energy that the intertropical regions receive from the Sun. Effects of Galactic turbulence on the temperature fluctuations are also discussed. Direct evidence of chaotic response of the atmospheric CO_2 dynamics to obliquity periodic forcing has been found in a reconstruction of atmospheric CO_2 data (deep sea proxies), for the past 650,000 years

Distributed chaos tuned to large scale coherent motions in turbulence

It is shown, using direct numerical simulations and laboratory experiments data, that distributed chaos is often tuned to large scale coherent motions in anisotropic inhomogeneous turbulence. The examples considered are: fully developed turbulent boundary layer (range of coherence: $14 < y^{+} < 80$), turbulent thermal convection (in a horizontal cylinder), and Cuette-Taylor flow. Two ways of the tuning have been described: one via fundamental frequency (wavenumber) and another via subharmonic (period doubling). For the second way the large scale coherent motions are a natural component of distributed chaos. In all considered cases spontaneous breaking of space translational symmetry is accompanied by reflexional symmetry breaking

Distributed chaos and turbulence in B\'{e}nard-Marangoni and Rayleigh-B\'{e}nard convection

Temporal and spatio-temporal (turbulence) distributed chaos in B\'{e}nard-Marangoni and Rayleigh-B\'{e}nard convection have been studied using results of laboratory experiments and direct numerical simulations in the terms of effective chaotic diffusivity (viscosity) and action. It is shown that for the both cases decaying part of the power spectra has stretched exponential form - for temporal spectrum $E(f) \propto \exp-(f/f_{\beta})^{1/2}$ and for spatial spectrum $E(k) \propto \exp-(k/k_{\beta})^{2/3}$, where the $f_{\beta}$ and $k_{\beta}$ represent low-frequency (large-scale) coherent oscillations

Distributed chaos and helicity in turbulence

The distributed chaos driven by Levich-Tsinober (helicity) integral: $I=\int \langle h({\bf x},t)~h({\bf x}+{\bf r}, t)\rangle d{\bf r}$ has been studied. It is shown that the helical distributed chaos can be considered as basis for complex turbulent flows with interplay between large-scale coherent structures and small-scale turbulence, such as Cuette-Taylor flow, wake behind cylinder and turbulent flow in the Large Plasma Device (LAPD) with inserted limiters. In the last case appearance of the helical distributed chaos, caused by the limiters, results in improvement of radial particle confinement

Distributed chaos in turbulent wakes

Soft and hard spontaneous breaking of space translational symmetry (homogeneity) have been studied in turbulent wakes by means of distributed chaos. In the case of the soft translational symmetry breaking the vorticity correlation integral $\int_{V} \langle {\boldsymbol \omega} ({\bf x},t) \cdot {\boldsymbol \omega} ({\bf x} + {\bf r},t) \rangle_{V} d{\bf r}$ dominates the distributed chaos and the chaotic spectra $\exp-(k/k_{\beta})^{\beta }$ have $\beta =1/2$. In the case of the hard translational symmetry breaking, control on the distributed chaos is switched from one type of fundamental symmetry to another (in this case to Lagrangian relabeling symmetry). Due to the Noether's theorem the relabeling symmetry results in the inviscid helicity conservation and helicity correlation integral $I=\int \langle h({\bf x},t)~h({\bf x}+{\bf r}, t)\rangle d{\bf r}$ (Levich-Tsinober invariant) dominates the distributed chaos with $\beta =1/3$. Good agreement with the experimental data has been established for turbulent wakes behind a cylinder, behind grids (for normal and super-fluids) and for bubbling flows. In the last case even small concentration of bubbles leads to a drastic change of the turbulent velocity spectra due to the hard spontaneous symmetry breaking in the bubbles' wakes.Comment: extended version (some experimental data have been added

Lagrangian chaos and turbulent diffusivity

Passive scalar mixing, produced by Lagrangian chaos generated a) by quasi-periodic (integrable) motion of three quasi-point vortices and b) by chaotic motion of three and six quasi-point vortices, has been studied and compared with turbulent mixing of passive scalar in 2D and 3D steady isotropic homogeneous turbulence and in turbulent wakes behind grid and behind cylinder. Results of numerical and laboratory experiments have been used and effective diffusivity approximation as well as distributed chaos approach have been applied to this problem

Turbulence and distributed chaos with spontaneously broken symmetry

It is shown that in turbulent flows the distributed chaos with spontaneously broken translational space symmetry (homogeneity) has a stretched exponential spectrum $\exp-(k/k_{\beta})^{\beta }$ with $\beta =1/2$. Good agreement has been established between the theory and the data of direct numerical simulations of isotropic homogeneous turbulence (energy dissipation rate field), of a channel flow (velocity field), of a fully developed boundary layer flow (velocity field), and the experimental data at the plasma edges of different fusion devices (stellarators and tokamaks). An astrophysical application to the large-scale galaxies distribution has been briefly discussed and good agreement with the data of recent Sloan Digital Sky Survey SDSS-III has been established.Comment: extended version (experimental data have been added

Magnetic field gradients in solar wind plasma and geophysics periods

Using recent data obtained by Advanced Composition Explorer (ACE) the pumping scale of the magnetic field gradients of the solar wind plasma has been calculated. This pumping scale is found to be equal to 24h $\pm$ 2h. The ACE spacecraft orbits at the L1 libration point which is a point of Earth-Sun gravitational equilibrium about 1.5 million km from Earth. Since the Earth's magnetosphere extends into the vacuum of space from approximately 80 to 60,000 kilometers on the side toward the Sun the pumping scale cannot be a consequence of the 24h-period of the Earth's rotation. Vise versa, a speculation is suggested that for the very long time of the coexistence of Earth and of the solar wind the weak interaction between the solar wind and Earth could lead to stochastic synchronization between the Earth's rotation and the pumping scale of the solar wind magnetic field gradients. This synchronization could transform an original period of the Earth's rotation to the period close to the pumping scale of the solar wind magnetic field gradients

Gaussian paradox and clustering in intermittent turbulent signals

A relation between intermittency and clustering phenomena in velocity field has been revealed for homogeneous fluid turbulence. It is described how the intermittency exponent can be split into sum of two other exponents. One of these exponents (cluster-exponent) characterizes clustering of the 'zero'-crossing points in nearly Gaussian velocity field and another exponent is related to the tails of the velocity probability distribution. The cluster-exponent is uniquely determined by the energy spectrum of the nearly Gaussian velocity field and entire dependence of the intermittency exponent on Reynolds number is determined by the cluster-exponent

Prime numbers: periodicity, chaos, noise

Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). The recovered period for the sequence of the first 10000 prime numbers is equal to 8\pm1 (subject to the prime number theorem). For small and moderate values of the prime numbers (first 2000 prime numbers) this result has been directly checked using the twin prime killing method.Comment: extende