This volume was the product of a workshop held at the Newton Institute in Cambridge, and examines turbulence, intermittency, nonlinear dynamics and fluid mechanics.
This book is a printed edition of the Special Issue Intermittency and Self-Organisation in Turbulence and Statistical Mechanics that was published in Entropy
This book contains original peer-reviewed articles written by some of the most prominent international physicists active in the field of hydrodynamics. The topic is entirely devoted to the study of the transitional regimes of incompressible viscous flow found at the onset of turbulent flows. Nine articles written for this 2020 Special Issue of the journal Entropy (MDPI) have been gathered at the crossroads of fluid mechanics, statistical physics, complexity theory, and applied mathematics. They include experimental, analytic, and computational material of an academic level that has not been published anywhere else.
"The analysis of turbulence by way of higher-order spectral moments is uncommon, despite the relatively frequent use of such statistical analyses in other fields of physics and engineering. In this work, higher-order spectral moments are used to investigate the internal intermittency of the turbulent velocity and passive scalar (temperature) fields. This research first introduces the theory behind higher-order spectral moments as they pertain to the field of turbulence. Then, a short-time-Fourier-transform-based method is developed to estimate the higher-order spectral moments and provide a relative, scale-by-scale measure of intermittency. Experimental data are subsequently analysed and consist of measurements of homogeneous, isotropic, high-Reynolds-number, passive and active grid turbulence and wall-bounded turbulence (fully developed turbulent channel flow) over Taylor microscale Reynolds numbers between 35 and 731. Emphasis is placed on third- and fourth-order spectral moments using the definitions formalised by Antoni (2006), as such statistics are sensitive to transients and provide insight into deviations from Gaussian behaviour in grid turbulence. The higher-order spectral moments are also used to investigate the Reynolds and Péclet number dependence of the internal intermittency of velocity and passive scalar fields, respectively. The results demonstrate that the evolution of higher-order spectral moments with Reynolds number is strongly dependent on wavenumber. Additionally, the relative levels of internal intermittency of velocity and passive scalar fields are compared and a higher level of internal intermittency in the inertial subrange of the scalar field is consistently observed whereas a similar level of internal intermittency is observed for the velocity and passive scalar fields for the high-Reynolds-numbers-cases as the Kolmogorov length scale is approached. Finally, higher-order spectral moments are shown to display increased levels in the near-wall region of a wall-bounded (channel) flow. The increased intermittent activity is believed to be caused by the presence of coherent structures in wall-bounded flows"--
obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each· chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C~apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied (§1-3). A first detailed study of homogeneous turbulent flows follows (§4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in §5 with the l"Csulting ~alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms (§ 1), their general dynamics (§2) with the particular case of homogeneous, isotropie turbulence (§3) whel"C the so-called Kolmogorov's assumptions are discussed at length.