When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and ...computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941). The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959) and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.
Turbulent flows are characterized by the non-linear cascades of energy and other inviscid invariants across a huge range of scales, from where they are injected to where they are dissipated. ...Recently, new experimental, numerical and theoretical works have revealed that many turbulent configurations deviate from the ideal three and two dimensional homogeneous and isotropic cases characterized by the presence of a strictly direct and inverse energy cascade, respectively. New phenomena appear that alter the global and local transfer properties. In this review, we provide a critical summary of historical and recent works from a unified point of view and we present a classification of all known transfer mechanisms. Beside the classical cases of direct and inverse energy cascades, the different scenarios include: split cascades for which an invariant flows both to small and large scales simultaneously, multiple/dual cascades of different quantities, bi-directional cascades where direct and inverse transfers of the same invariant coexist in the same scale-range and finally equilibrium states where no cascades are present, including the case when a large scale condensate is formed. We classify all possible transitions from one scenario to another as the control parameters are changed and we analyse when and why different configurations are observed. Our discussion is based on a set of paradigmatic applications: helical turbulence, rotating and/or stratified flows, magnetohydrodynamics (MHD) turbulence, and passive/active scalars where the transfer properties are altered as one changes the embedding dimensions, the thickness of the domain or other relevant control parameters, as, e.g., the Reynolds, Rossby, Froude, Péclet, or Alfvén numbers. We briefly discuss the presence of anomalous scaling laws in 3D hydrodynamics and in other configurations, in connection with the intermittent nature of the energy dissipation in configuration space. A quick overview is also provided concerning the importance of cascades in other applications such as bounded flows, quantum fluids, relativistic and compressible turbulence, and active matter, together with a discussion of the implications for turbulent modelling. Finally, we present a series of open problems and challenges that future work needs to address.
Turbulence data from the CASES‐99 field experiment, over comparatively horizontally homogeneous and flat terrain, are separated based on the anisotropy of the Reynolds stress tensor (into isotropic, ...two‐component axisymmetric and one‐component turbulence) and flux‐variance similarity scaling relations are tested. Results illustrate that different states of anisotropy correspond to different similarity relations, especially under unstable stratification. Experimental data with close to isotropic turbulence match similarity relationships well. On the other hand, very anisotropic turbulence deviates significantly from the traditional scaling relations. We examine in detail the characteristics of these states of anisotropy, identify conditions in which they occur and connect them with different governing parameters. The governing parameters of turbulence anisotropy are shown to be different for stable and unstable stratification, but are able to delineate clearly the conditions in which each of the anisotropy states occurs.
Near‐surface similarity relations are examined in the light of turbulence anisotropy. Isotropic turbulence is found to fit traditional scaling well, while highly anisotropic data deviate significantly from the scaling. Anisotropy also explains the large scatter in scaled horizontal velocity variances. Parameters governing anisotropy in unstable stratification are found to be wind shear and stability and, for stable stratification, wind speed and turbulent kinetic energy.
It has recently been proposed that the inertial interval in magnetohydrodynamic (MHD) turbulence is terminated at small scales not by a Kolmogorov-like dissipation region, but rather by a new ...sub-inertial interval mediated by tearing instability. However, many astrophysical plasmas are nearly collisionless so the MHD approximation is not applicable to turbulence at small scales. In this paper, we propose an extension of the theory of reconnection-mediated turbulence to plasmas which are so weakly collisional that the reconnection occurring in the turbulent eddies is caused by electron inertia rather than by resistivity. We find that the transition scale to reconnection-mediated turbulence depends on the plasma beta and on the assumptions of the plasma turbulence model. However, in all of the cases analyzed, the energy spectra in the reconnection-mediated interval range from to .
•Effect of blade profiles on the Savonius rotor performance is studied numerically.•Performance studies are made on the basis of torque and power coefficients.•Flow field studies are made based on ...velocity, total pressure and turbulence intensity contours.•Wind tunnel experiments are conducted to validate the numerical results.
In this work, some notable blade profiles of drag-based vertical axis Savonius wind turbine rotor have been investigated both numerically and experimentally to judge their performances on a common platform. At the outset, 2D unsteady simulation is performed for semicircular, Benesh, modified Bach and elliptical profiles keeping the overall rotor diameter in each case to be constant. The simulation has been carried out using the Shear Stress Transport k-ω turbulence model with the help of the finite volume solver ANSYS Fluent. The torque and power coefficients, in each case, are estimated as a function of tip speed ratio. The total pressure, velocity magnitude, and turbulence intensity contours are obtained and analyzed. Finally, wind tunnel tests are conducted to validate the numerical results. From the numerical simulation, the maximum power coefficients for the semicircular, Benesh, modified Bach and elliptical profiles are found to be 0.272, 0.294, 0.304 and 0.34, respectively. However, the wind tunnel tests with the semicircular, Benesh, modified Bach and elliptical-bladed rotors demonstrated the maximum CP to be 0.158, 0.159, 0.162, and 0.19, respectively.
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