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The theory of homogeneous turbulence
01 Jan 1953-
TL;DR: In this article, the kinematics of the field of homogeneous turbulence and the universal equilibrium theory of decay of the energy-containing eddies are discussed. But the authors focus on the dynamics of decay and not on the probability distribution of u(x).
Abstract: Preface 1 Introduction 2 Mathematics representation of the field of turbulence 3 The kinematics of homogeneous turbulence 4 Some linear problems 5 General dynamics of decay 6 The universal equilibrium theory 7 Decay of the energy-containing eddies 8 The probability distribution of u(x) Bibliography of research on homogeneous turbulence Index
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01 Jan 1996TL;DR: In this article, the authors present a review of rigor properties of low-dimensional models and their applications in the field of fluid mechanics. But they do not consider the effects of random perturbation on models.
Abstract: Preface Part I. Turbulence: 1. Introduction 2. Coherent structures 3. Proper orthogonal decomposition 4. Galerkin projection Part II. Dynamical Systems: 5. Qualitative theory 6. Symmetry 7. One-dimensional 'turbulence' 8. Randomly perturbed systems Part III. 9. Low-dimensional Models: 10. Behaviour of the models Part IV. Other Applications and Related Work: 11. Some other fluid problems 12. Review: prospects for rigor Bibliography.
2,920 citations
TL;DR: In this paper, the authors described the behavior of spectra and cospectra of turbulence in the surface layer using wind and temperature fluctuation data obtained in the 1968 AFCRL Kansas experiments.
Abstract: The behaviour of spectra and cospectra of turbulence in the surface layer is described within the framework of similarity theory using wind and temperature fluctuation data obtained in the 1968 AFCRL Kansas experiments. With appropriate normalization, the spectra and cospectra are each reduced to a family of curves which spread out according to z/L at low frequencies but converge to a single universal curve in the inertial subrange. The paper compares these results with data obtained by other investigators over both land and water.
Spectral constants for velocity and temperature are determined and the variability in the recent estimates of the constants is discussed. The high-frequency behaviour is consistent with local isotropy. In the inertial subrange, where the spectra fall as n−5/3, the cospectra fall faster: uω and ωθ as n−7/3, and uθ, on the average, as n−5/2. The 4/3 ratio between the transverse and longitudinal spectral levels is observed at wavelengths of the order of the height above ground under unstable conditions and at wavelengths of the order of L/10 under stable conditions. This lower isotropic limit is shown to be governed by the combined effects of shear and buoyancy on small-scale eddies.
2,408 citations
TL;DR: In this article, the mean velocity profile is inflected, second moments are strongly inhomogeneous with height, skewnesses are large, and second-moment budgets are far from local equilibrium.
Abstract: ▪ Abstract The single-point statistics of turbulence in the ‘roughness sub-layer’ occupied by the plant canopy and the air layer just above it differ significantly from those in the surface layer. The mean velocity profile is inflected, second moments are strongly inhomogeneous with height, skewnesses are large, and second-moment budgets are far from local equilibrium. Velocity moments scale with single length and time scales throughout the layer rather than depending on height. Large coherent structures control turbulence dynamics. Sweeps rather than ejections dominate eddy fluxes and a typical large eddy consists of a pair of counter-rotating streamwise vortices, the downdraft between the vortex pair generating the sweep. Comparison with the statistics and instability modes of the plane mixing layer shows that the latter rather than the boundary layer is the appropriate model for canopy flow and that the dominant large eddies are the result of an inviscid instability of the inflected mean velocity profi...
1,484 citations
TL;DR: In this paper, a numerical method for solving the time-dependent Navier-Stokes equations in two space dimensions at high Reynolds number is presented, where the crux of the method lies in the numerical simulation of the process of vorticity generation and dispersal, using computer-generated pseudo-random numbers.
Abstract: A numerical method for solving the time-dependent Navier–Stokes equations in two space dimensions at high Reynolds number is presented. The crux of the method lies in the numerical simulation of the process of vorticity generation and dispersal, using computer-generated pseudo-random numbers. An application to flow past a circular cylinder is presented.
1,427 citations