Papers by Katepalli Sreenivasan
Physical Review Letters, Feb 19, 2021
We solve the advection-diffusion equation for a stochastically stationary passive scalar θ, in co... more We solve the advection-diffusion equation for a stochastically stationary passive scalar θ, in conjunction with forced 3D Navier-Stokes equations, using direct numerical simulations in periodic domains of various sizes, the largest being 8192 3. The Taylor-scale Reynolds number varies in the range 140 − 650 and the Schmidt number Sc ≡ ν/D in the range 1 − 512, where ν is the kinematic viscosity of the fluid and D is the molecular diffusivity of θ. Our results show that turbulence becomes an ineffective mixer when Sc is large. First, the mean scalar dissipation rate χ = 2D |∇θ| 2 , when suitably non-dimensionalized, decreases as 1/ log Sc. Second, 1D cuts through the scalar field indicate increasing density of sharp fronts on larger scales, oscillating with large excursions leading to reduced mixing, and additionally suggesting weakening of scalar variance flux across the scales. The scaling exponents of the scalar structure functions in the inertial-convective range appear to saturate with respect to the moment order and the saturation exponent approaches unity as Sc increases, qualitatively consistent with 1D cuts of the scalar.
Physical Review Fluids, 2020
From a database of direct numerical simulations of homogeneous and isotropic turbulence, generate... more From a database of direct numerical simulations of homogeneous and isotropic turbulence, generated in periodic boxes of various sizes, we extract the spherically symmetric part of moments of velocity increments and first verify the following (somewhat contested) results: the 4/5-ths law holds in an intermediate range of scales and that the second order exponent over the same range of scales is anomalous, departing from the self-similar value of 2/3 and approaching a constant of 0.72 at high Reynolds numbers. We compare with some typical theories the dependence of longitudinal exponents as well as their derivatives with respect to the moment order n, and estimate the most probable value of the Hölder exponent. We demonstrate that the transverse scaling exponents saturate for large n, and trace this trend to the presence of large localized jumps in the signal. The saturation value of about 2 at the highest Reynolds number suggests, when interpreted in the spirit of fractals, the presence of vortex sheets rather than more complex singularities. In general, the scaling concept in hydrodynamic turbulence appears to be more complex than even the multifractal description.
Proceedings of the National Academy of Sciences, 2018
Mixing of initially distinct substances plays an important role in our daily lives as well as in ... more Mixing of initially distinct substances plays an important role in our daily lives as well as in ecological and technological worlds. From the continuum point of view, which we adopt here, mixing is complete when the substances come together across smallest flow scales determined in part by molecular mechanisms, but important stages of the process occur via the advection of substances by an underlying flow. We know how smooth flows enable mixing but less well the manner in which a turbulent flow influences it; but the latter is the more common occurrence on Earth and in the universe. We focus here on turbulent mixing, with more attention paid to the postmixing state than to the transient process of initiation. In particular, we examine turbulent mixing when the substance is a scalar (i.e., characterized only by the scalar property of its concentration), and the mixing process does not influence the flow itself (i.e., the scalar is “passive”). This is the simplest paradigm of turbule...
Physical Review E, 2002
We measure temperature fluctuations in the Rayleigh-Bénard apparatus, which is a closed cylindric... more We measure temperature fluctuations in the Rayleigh-Bénard apparatus, which is a closed cylindrical container with the bottom wall heated and the top wall cooled. The aspect ratio, which is the diameter-to-height ratio of the apparatus, is unity. The Rayleigh number is 1.5ϫ10 11. The working fluid is cryogenic helium gas. We compute temperature structure functions up to order 16, and use extended self-similarity to obtain scaling exponents in the Bolgiano regime. In contrast to passive scalars, the scaling exponents tend not to saturate with the order of the structure function, suggesting the absence of ramplike structures in temperature traces of convective motion.
Physics of Fluids A: Fluid Dynamics, 1993
The issue of experimental determination of the intermittency exponent μ, is revisited and it is s... more The issue of experimental determination of the intermittency exponent μ, is revisited and it is shown that the ‘‘best’’ estimate for it is 0.25±0.05. This ‘‘best’’ estimate is obtained from recent atmospheric data, and is based on several different techniques.
Physical Review E, 2000
The statistical objects characterizing turbulence in real turbulent flows differ from those of th... more The statistical objects characterizing turbulence in real turbulent flows differ from those of the ideal homogeneous isotropic model. They contain contributions from various two-and three-dimensional aspects, and from the superposition of inhomogeneous and anisotropic contributions. We employ the recently introduced decomposition of statistical tensor objects into irreducible representations of the SO͑3͒ symmetry group ͑characterized by j and m indices, where jϭ0. .. ϱ,Ϫ jрmр j͒ to disentangle some of these contributions, separating the universal and the asymptotic from the specific aspects of the flow. The different j contributions transform differently under rotations, and so form a complete basis in which to represent the tensor objects under study. The experimental data are recorded with hot-wire probes placed at various heights in the atmospheric surface layer. Time series data from single probes and from pairs of probes are analyzed to compute the amplitudes and exponents of different contributions to the second order statistical objects characterized by j ϭ0, 1, and 2. The analysis shows the need to make a careful distinction between long-lived quasi-twodimensional turbulent motions ͑close to the ground͒ and relatively short-lived three-dimensional motions. We demonstrate that the leading scaling exponents in the three leading sectors ͑jϭ0, 1, and 2͒ appear to be different but universal, independent of the positions of the probe, the tensorial component considered, and the large scale properties. The measured values of the scaling exponent are 2 (jϭ0) ϭ0.68Ϯ0.01, 2 (jϭ1) ϭ1.0 Ϯ0.15, and 2 (jϭ2) ϭ1.38Ϯ0.10. We present theoretical arguments for the values of these exponents using the Clebsch representation of the Euler equations; neglecting anomalous corrections, the values obtained are 2/3, 1, and 4/3, respectively. Some enigmas and questions for the future are sketched.
Physics of Fluids, 2005
A brief report is given of a new 20483 direct numerical simulation of the mixing of passive scala... more A brief report is given of a new 20483 direct numerical simulation of the mixing of passive scalars with uniform mean gradients in forced, stationary isotropic turbulence. The Taylor-scale Reynolds number is close to 700 and Schmidt numbers of 1 and 1∕8 are considered. The data provide the most convincing evidence to date for the inertial-convective scaling. Significant departures from small-scale isotropy are sustained in conventional measures. Subject to some stringent resolution requirements, the data suggest that commonly observed differences between the intermittency of energy and scalar dissipation rates may in part be a finite-Reynolds-number effect.
Proceedings of the National Academy of Sciences of the United States of America, Jan 29, 2014
Turbulent flows in nature and technology possess a range of scales. The largest scales carry the ... more Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries. In the present work, we study three turbulent flows of systematically increasing complexity. These are homogeneous and isotropic turbulence in a periodic box, turbulent shear flow between two parallel walls, and thermal convection in a closed cylindrical container. They are computed by highly resolved direct numerical simulations of the governing dynamical equations. We use these simulation data to establish two fundamental results: (i) at Reynolds numbers Re ∼ 10(2) the fluctuations of the velocity derivatives pass through a transition from nearly Gaussian (or slightly sub-Gaussian) to intermittent behavior that is characteristic of fully devel...
Physical Review E, 2000
We make an attempt at obtaining the scaling exponents for the anisotropic components of structure... more We make an attempt at obtaining the scaling exponents for the anisotropic components of structure functions of order 2 through 6. We avoid mixing these components with their isotropic counterparts for each order by using tensor components that are entirely anisotropic. We do this by considering terms of the isotropic sector corresponding to jϭ0 in the SO͑3͒ decomposition of each tensor, and then constructing components that are explicitly zero in the isotropic sector. We use an interpolation formula to compensate for the large-scale encroachment of inertial-range scales. This allows us to examine the lowest order anisotropic scaling behavior. The resulting anisotropic exponents for a given tensorial order are larger than those known for the corresponding isotropic part. One conclusion that emerges is that the anisotropy effects diminish with decreasing scale, although much more slowly than previously thought.
Physical Review E, 2001
derive, through two different approaches that have the Navier-Stokes equations as the common star... more derive, through two different approaches that have the Navier-Stokes equations as the common starting point, a set of steady-state dynamic equations for structure functions of arbitrary order in hydrodynamic turbulence. These equations are not closed. Yakhot proposed a "mean field theory" to close the equations for locally isotropic turbulence, and obtained scaling exponents of structure functions and an expression for the tails of the probability density function of transverse velocity increments. At high Reynolds numbers, we present some relevant experimental data on pressure and dissipation terms that are needed to provide closure, as well as on aspects predicted by the theory. Comparison between the theory and the data shows varying levels of agreement, and reveals gaps inherent to the implementation of the theory.
Springer Proceedings in Physics
Reviews of Modern Physics, 2006
Lars Onsager, a giant of twentieth-century science and the 1968 Nobel Laureate in Chemistry, made... more Lars Onsager, a giant of twentieth-century science and the 1968 Nobel Laureate in Chemistry, made deep contributions to several areas of physics and chemistry. Perhaps less well known is his groundbreaking work and lifelong interest in the subject of hydrodynamic turbulence. He wrote two papers on the subject in the 1940s, one of them just a short abstract. Unbeknownst to Onsager, one of his major results was derived a few years earlier by A. N. Kolmogorov, but Onsager's work contains many gems and shows characteristic originality and deep understanding. His only full-length article on the subject in 1949 introduced two novel ideas-negative-temperature equilibria for two-dimensional ideal fluids and an energy-dissipation anomaly for singular Euler solutions-that stimulated much later work. However, a study of Onsager's letters to his peers around that time, as well as his private papers of that period and the early 1970s, shows that he had much more to say about the problem than he published. Remarkably, his private notes of the 1940s contain the essential elements of at least four major results that appeared decades later in the literature: ͑1͒ a mean-field Poisson-Boltzmann equation and other thermodynamic relations for point vortices; ͑2͒ a relation similar to Kolmogorov's 4/5 law connecting singularities and dissipation; ͑3͒ the modern physical picture of spatial intermittency of velocity increments, explaining anomalous scaling of the spectrum; and ͑4͒ a spectral turbulence closure quite similar to the modern eddy-damped quasinormal Markovian equations. This paper is a summary of Onsager's published and unpublished contributions to hydrodynamic turbulence and an account of their place in the field as the subject has evolved through the years. A discussion is also given of the historical context of the work, especially of Onsager's interactions with his contemporaries who were acknowledged experts in the subject at the time. Finally, a brief speculation is offered as to why Onsager may have chosen not to publish several of his significant results.
Pramana, 2005
A logarithmic scaling for structure functions, in the form Sp ∼ [ln(r/η)] ζp , where η is the Kol... more A logarithmic scaling for structure functions, in the form Sp ∼ [ln(r/η)] ζp , where η is the Kolmogorov dissipation scale and ζp are the scaling exponents, is suggested for the statistical description of the near-dissipation range for which classical power-law scaling does not apply. From experimental data at moderate Reynolds numbers, it is shown that the logarithmic scaling, deduced from general considerations for the near-dissipation range, covers almost the entire range of scales (about two decades) of structure functions, for both velocity and passive scalar fields. This new scaling requires two empirical constants, just as the classical scaling does, and can be considered the basis for extended self-similarity.
Physics Today, 2006
Turbulent flows, with their irregular behavior, confound any simple attempts to understand them. ... more Turbulent flows, with their irregular behavior, confound any simple attempts to understand them. But physicists have succeeded in identifying some universal properties of turbulence and relating them to broken symmetries.
Physics of Fluids, 2005
We propose a simple empirical model to describe the Rayleigh–Taylor (RT) turbulent mixing of immi... more We propose a simple empirical model to describe the Rayleigh–Taylor (RT) turbulent mixing of immiscible, miscible and stratified fluids. For immiscible fluids, the rate of momentum loss is an invariant of the flow, whereas the energy dissipation rate increases linearly with time. Turbulent diffusion, accounted for through temperature fluctuations, does not terminate mixing but slows it down significantly. A stratified density distribution can stabilize RT mixing.
Physics of Fluids, 2003
We propose a generalized perspective on the behavior of high-order derivative moments in turbulen... more We propose a generalized perspective on the behavior of high-order derivative moments in turbulent shear flows by taking account of the roles of small-scale intermittency and mean shear, in addition to the Reynolds number. Two asymptotic regimes are discussed with respect to shear effects. By these means, some existing disagreements on the Reynolds number dependence of derivative moments can be explained. That odd-order moments of transverse velocity derivatives tend not to vanish as expected from elementary scaling considerations does not necessarily imply that small-scale anisotropy persists at all Reynolds numbers.
Physics of Fluids, 2002
We study temperature structure functions of second, fourth, and sixth orders at heights of up to ... more We study temperature structure functions of second, fourth, and sixth orders at heights of up to 2 m above the ground in moderately heated atmosphere. Most of the data come from measurements over salt flats of the Utah desert, with well-defined wind direction and uniform temperature boundary conditions. As in high-Rayleigh-number convection in a closed container, a thermal boundary layer develops near the ground, its thickness here being of the order of 50 cm. We demonstrate the coexistence of two scaling ranges, one of which corresponds to the classical inertial range and the other to the buoyant range influenced by thermal convection. The determination of scaling exponents in the two ranges is facilitated by the use of a scaling function. We present the variations with height of scaling exponents in both ranges, as well as the crossover scales from one range to another.
Physics of Fluids, 2008
Existing experimental and numerical data suggest that the turbulence energy dissipation and enstr... more Existing experimental and numerical data suggest that the turbulence energy dissipation and enstrophy (i.e., the square of vorticity) possess different scaling properties, while available theory suggests that there should be no differences at sufficiently high Reynolds numbers. We have performed a series of direct numerical simulations with up to 20483 grid points where advanced computational power is used to increase the Reynolds number (up to 650 on the Taylor scale) or to resolve the small scales better (down to 1∕4 of a Kolmogorov scale). Our primary goal is to assess the differences and similarities between dissipation and enstrophy. Special attention is paid to the effects of small-scale resolution on the quality and reliability of the data, in view of recent theoretical work [V. Yakhot and K. R. Sreenivasan, “Anomalous scaling of structure functions and dynamic constraints on turbulence simulations,” J. Stat. Phys. 121, 823 (2005)] which stipulates the resolution needed to ob...
Physics of Fluids, 2007
Using liquid helium, liquid nitrogen, and water as test fluids, we attempt to generate homogeneou... more Using liquid helium, liquid nitrogen, and water as test fluids, we attempt to generate homogeneous turbulence in a steadily rotating system. We create turbulence by pulling a grid in rotating channels with both square and round cross sections, and observe large-scale inertial waves in the flow. These inertial waves quickly sense the boundaries, and resonate at frequencies characteristic of the container. We describe some of their properties and argue that the resultant inhomogeneity is a feature of any real system.
Physics of Fluids, 2010
Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of ... more Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of research in recent years. Many challenges remain in theory, scaling, physical understanding, experimental techniques, and numerical simulations. In this paper we distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters such as the von Kármán “constant,” the parametrization of roughness effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that may provide answers to these questions, notably the improvement of measuring techniques and the construction of new facilities, are identified. We also highlight aspects where differences of opinion persist, with the expectation that this discussion might mark the beginning of their resolution.
Uploads
Papers by Katepalli Sreenivasan