arXiv subjects
Publications and source records attributed to A. Bershadskii.
It is shown that the periodic alteration of night and day provides a chaotic dissipation mechanism for the North Atlantic (NAO) and Southern (SOI) climate oscillations. The wavelet regression detrended daily NAO index for last 60 years and daily SOI for last 20 years as well as an analytical continuation in the complex time domain were used for this purpose.
The wavelet regression detrended fluctuations of the reconstructed temperature for the past three ice ages: approximately 340000 years (Antarctic ice cores isotopic data), exhibit clear evidences of the galactic turbulence modulation up to 2500 years time-scales. The observed strictly Kolmogorov turbulence features indicates the Kolmogorov nature of galactic turbulence, and provide explanation to random-like fluctuations of the global temperature on the millennial time scales.
It is shown that, the wavelet regression detrended fluctuations of the monthly sunspot number for 1749-2009 years exhibit strong periodicity with a period approximately equal to 3.7 years. The wavelet regression method detrends the data from the approximately 11-years period. Therefore, it is suggested that the one-third subharmonic resonance can be considered as a background for the 11-years solar cycle. It is also shown that the broad-band part of the wavelet regression detrended fluctuations spectrum exhibits an exponential decay that, together with the positive largest Lyapunov exponent, are the hallmarks of chaos. Using a complex-time analytic approach the rate of the exponential decay of the broad-band part of the spectrum has been theoretically related to the Carrington solar rotation period. Relation of the driving period of the subharmonic resonance (3.7-years) to the active longitude flip-flop phenomenon, in which the dominant part of the sunspot activity changes the longitude every 3.7 years on average, has been briefly discussed.
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.
It is shown that, the wavelet regression detrended fluctuations of the monthly global temperature data (land and ocean combined) for the period 1880-2009yy, are completely dominated by one-third subharmonic resonance to annual forcing (both natural and anthropogenically induced). Role of the oceanic Rossby waves and the resonance contribution to the El Nino phenomenon have been discussed in detail.
It is shown that correlation function of the mean wind velocity in a turbulent thermal convection (Rayleigh number $Ra \sim 10^{11}$) exhibits exponential decay with a very long correlation time, while corresponding largest Lyapunov exponent is certainly positive. These results together with the reconstructed phase portrait indicate presence of a chaotic component in the examined mean wind. Telegraph approximation is also used to study relative contribution of the chaotic and stochastic components to the mean wind fluctuations and an equilibrium between these components has been studied. Since solar activity is based on the thermal convection processes, it is reasoned that the observed solar activity long-term correlations can be an imprint of the mean wind chaotic properties. In particular, correlation function of the daily sunspots number exhibits exponential decay with a very long correlation time and corresponding largest Lyapunov exponent is certainly positive, also relative contribution of the chaotic and stochastic components follows the same pattern as for the convection mean wind.
It is shown that correlation function of the mean wind velocity generated by a turbulent thermal convection (Rayleigh number $Ra \sim 10^{11}$) exhibits exponential decay with a very long correlation time, while corresponding largest Lyapunov exponent is certainly positive. These results together with the reconstructed phase portrait indicate presence of chaotic component in the examined mean wind. Telegraph approximation is also used to study relative contribution of the chaotic and stochastic components to the mean wind fluctuations and an equilibrium between these components has been studied in detail.
It is shown that global climate exhibits chaotic response to solar forcing variability in a vast range of timescales: from annual to multi-millennium. Unlike linear systems, where periodic forcing leads to periodic response, nonlinear chaotic response to periodic forcing can result in exponentially decaying broad-band power spectrum with decay rate T_e equal to the period of the forcing. It is shown that power spectrum of a reconstructed time series of Northern Hemisphere temperature anomaly for the past 2,000 years has an exponentially decaying broad-band part with T_e = 11 yr, i.e. the observed decay rate T_e equals the mean period of the solar activity. It is also shown that power spectrum of a reconstruction of atmospheric CO_2 time fluctuations for the past 650,000 years, has an exponentially decaying broad-band part with T_e = 41,000 years, i.e. the observed decay rate T_e equals the period of the obliquity periodic forcing. A possibility of a chaotic solar forcing of the climate has been also discussed. These results clarify role of solar forcing variability in long-term global climate dynamics (in particular in the unsolved problem of the glaciation cycles) and help in construction of adequate dynamic models of the global climate.
Solar activity is studied using a cluster analysis of the time-fluctuations of sunspot number. In the historic period (1850-1932) the cluster exponent was approximately equal to 0.37 (strong clustering) for the high activity components of the solar cycles. In the modern period (last seven solar cycles: 1933-2007) the cluster exponent was approximately equal to 0.50 (random, white noise-like). Comparing these results with the corresponding data from laboratory experiments on convection it is shown, that in the historic period emergence of sunspots in the solar photosphere was dominated by turbulent photospheric convection. In the modern period, this domination was broken by a new more active dynamics of the inner layers of the convection zone. Cluster properties of the solar wind magnetic field and the aa-geomagnetic-index also support this result. Long-range chaotic dynamics in the solar activity is briefly discussed.
Solar activity is studied using a cluster analysis of the time-fluctuations of the sunspot number. It is shown that in an Historic period the high activity components of the solar cycles exhibit strong clustering, whereas in a Modern period (last seven solar cycles: 1933-2007) they exhibit a white-noise (non-)clustering behavior. Using this observation it is shown that in the Historic period, emergence of the sunspots in the solar photosphere was strongly dominated by turbulent photospheric convection. In the Modern period, this domination was broken by a new more active dynamics of the inner layers of the convection zone. Then, it is shown that the dramatic change of the sun dynamics at the transitional period (between the Historic and Modern periods, solar cycle 1933-1944yy) had a clear detectable impact on Earth climate. A scenario of a chain of transitions in the solar convective zone is suggested in order to explain the observations, and a forecast for the global warming is suggested on the basis of this scenario. A relation between the recent transitions and solar long-period chaotic dynamics has been found. Contribution of the galactic turbulence (due to galactic cosmic rays) has been discussed. These results are also considered in a content of chaotic climate dynamics at millennial timescales.
It is shown that a mechanism of energy redistribution and dissipation by the inertial waves can be effectively utilized in isotropic turbulence at small Reynolds numbers (when the nonlocal interactions are the dominating ones). This mechanism totally suppresses the local interactions (cascades) in isotropic turbulence at the Taylor-scale based Reynolds number $R_λ < 10^2$. This value of $R_λ$ (that can be considered as a bifurcation value at which the local regime emerges from the nonlocal one in isotropic turbulence) is in agreement with recent direct numerical simulations data. Applicability of this approach to channel flows is also briefly discussed. A theory of multimode bifurcations has been developed in order to explain anomalous (in comparison with the Landau-Hopf bifurcations) properties of the nonlocal-local bifurcation in isotropic turbulence.
Coherent properties of the baryon-photon fluid decoupling are considered in the terms of an effective nonlinear Schrödinger equation for a macroscopic wave function that specifies the index of the coherent state. Generation of a transitional acoustic turbulence preceding formation of large-scale condensate in the plasma and its influence on the CMB power spectrum has been studied. A scaling $k^{-1}$ law is derived for the CMB Doppler spectrum $E(k)$ (angle-averaged) in the {\it wavenumber} space, for sufficiently large wavenumber $k$ and for the weak nonlinear and completely disordered initial conditions. Using the recent WMAP data it is shown that the so-called first acoustic peak represents (in a compensated spectral form) a pre-condensate fraction of the spectrum $E(k)$ at a rather advance stage of the condensate formation process.
Transition to condensate state in the degenerate gas of bosons is studied using the Gross-Pitaevskii equation. It is shown that adiabatic invariance of an enstrophy (mean squared vorticity) based on a generalized vorticity $curl (|ψ|^2 {\bf v})/|ψ|^2$, controls dynamics of the transitional turbulence just before formation of the condensate with its tangles of quantized vortices ($|ψ|^2 {\bf v}$ is the weighted velocity field defined on the macroscopic wave function $ψ$). Scaling of the angle-averaged occupation number spectrum, $N_k \sim k^{-1}$, has been obtained for the free developing transitional turbulence for the weak nonlinear (and completely disordered) initial conditions. Results of the three-dimensional numerical simulations have been used to support the theoretical consideration.
It is shown that nonlocal interactions determine energy spectrum in isotropic turbulence at small Reynolds numbers. It is also shown that for moderate Reynolds numbers the bottleneck effect is determined by the same nonlocal interactions. Role of the large and small scales covariance at the nonlocal interactions and in energy balance has been investigated. A possible hydrodynamic mechanism of the nonlocal solution instability at large scales has been briefly discussed. A quantitative relationship between effective strain of the nonlocal interactions and viscosity has been found. All results are supported by comparison with the data of experiments and numerical simulations.
An analytic perturbation theory is suggested in order to find finite-size corrections to the scaling power laws. In the frame of this theory it is shown that the first order finite-size correction to the scaling power laws has following form $S(r) \cong cr^{α_0}[\ln(r/η)]^{α_1}$, where $η$ is a finite-size scale (in particular for turbulence, it can be the Kolmogorov dissipation scale). Using data of laboratory experiments and numerical simulations it is shown shown that a degenerate case with $α_0 =0$ can describe turbulence statistics in the near-dissipation range $r > η$, where the ordinary (power-law) scaling does not apply. For moderate Reynolds numbers the degenerate scaling range covers almost the entire range of scales of velocity structure functions (the log-corrections apply to finite Reynolds number). Interplay between local and non-local regimes has been considered as a possible hydrodynamic mechanism providing the basis for the degenerate scaling of structure functions and extended self-similarity. These results have been also expanded on passive scalar mixing in turbulence. Overlapping phenomenon between local and non-local regimes and a relation between position of maximum of the generalized energy input rate and the actual crossover scale between these regimes are briefly discussed.
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.
Since the strong clustering of luminous matter in the observable universe is a consequence of an initial non-uniformity of the baryon-photon fluid in the last scattering surface, an investigation of clustering of the isotherms in the cosmic microwave background has been performed. The isotherms clustering has been related to the baryon-photon fluid dynamics and the Taylor-microscale Reynolds number of this motion is estimated to be $10^2$. 3-year WMAP cosmic microwave background map has been used in this investigation.
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.