Space plasma turbulence

The difficulties in understanding turbulence, "the last unsolved problem in classical statistical mechanics" (according to Feynman), arise from the multi-scale nonlinear interaction of large number of degrees of freedom. Here, the word "large" means something like huge or infinite, certainly not fully accessible with the available computer horsepower. This project concentrates on less ambitious, nevertheless significant problems of fundamental importance - non-locality of nonlinear interactions in space plasma turbulence. Non-locality is associated with other "non-properties", being induced through the richness in spatio-temporal conditions of turbulence generation. The profusion of coherent structures, boundaries and waves in magnetohydrodynamic flows and their interactions prevent us to formulate the underlying physical laws in an entirely universal manner. Contrarily to the classical Kolmogorov phenomenology, which provides a universal description for small-scale turbulence, the role of non-local interactions, leading to non-universal scalings and anisotropy, is gradually recognized in many hydrodynamic and MHD systems. The solar wind represents an optimal test bed for statistical studies of the outlined non-properties of turbulent flows. Non-locality is observable through spectral and higher- order statistical characteristics of fluctuations. In order to identify the specific large-scale conditions in the solar wind, single and multi-spacecraft methods will be used. To ensure robustness, stationarity tests and supervised estimation techniques will be employed. The interdependence of statistical moments can reveal peculiarities of multi-scale couplings and acting long-range forces in turbulence. Non-extensive thermostatistics makes the understanding of basic physics of long-range forces and non-locality possible at the fundamental level. The non- extensive approach assures for experimental studies of solar wind intermittency independence from the influence of a-priori model assumptions. In this concept intermittency of the turbulent fluctuations is related physically to the non-extensive character of the interplanetary medium counting for nonlocal interactions via entropy generalization. This approach also facilitates to propose a non-local shell model of turbulence with a defined level of non- extensivity. The final goal is to understand how universal is the non-universal behavior in space and astrophysical plasma turbulence and what are the basic rules governing non-universality.

The difficulties in understanding turbulence, "the last unsolved problem in classical statistical mechanics" (according to Feynman), arise from the multi-scale nonlinear interaction of large number of degrees of freedom. Here, the word "large" means something like huge or infinite, certainly not fully accessible with the available computer horsepower. This project concentrates on less ambitious, nevertheless significant problems of fundamental importance - non-locality of nonlinear interactions in space plasma turbulence. Non-locality is associated with other "non-properties", being induced through the richness in spatio-temporal conditions of turbulence generation. The profusion of coherent structures, boundaries and waves in magnetohydrodynamic flows and their interactions prevent us to formulate the underlying physical laws in an entirely universal manner. Contrarily to the classical Kolmogorov phenomenology, which provides a universal description for small-scale turbulence, the role of non-local interactions, leading to non-universal scalings and anisotropy, is gradually recognized in many hydrodynamic and MHD systems. The solar wind represents an optimal test bed for statistical studies of the outlined non-properties of turbulent flows. Non-locality is observable through spectral and higher- order statistical characteristics of fluctuations. In order to identify the specific large-scale conditions in the solar wind, single and multi-spacecraft methods will be used. To ensure robustness, stationarity tests and supervised estimation techniques will be employed. The interdependence of statistical moments can reveal peculiarities of multi-scale couplings and acting long-range forces in turbulence. Non-extensive thermostatistics makes the understanding of basic physics of long-range forces and non-locality possible at the fundamental level. The non- extensive approach assures for experimental studies of solar wind intermittency independence from the influence of a-priori model assumptions. In this concept intermittency of the turbulent fluctuations is related physically to the non-extensive character of the interplanetary medium counting for nonlocal interactions via entropy generalization. This approach also facilitates to propose a non-local shell model of turbulence with a defined level of non- extensivity. The final goal is to understand how universal is the non-universal behavior in space and astrophysical plasma turbulence and what are the basic rules governing non-universality.