arXiv subjects

Katepalli R. Sreenivasan

Publications and source records attributed to Katepalli R. Sreenivasan.

84 records · Page 5Linked to original sources

arXiv2005

Statistics and geometry of passive scalars in turbulence

We present direct numerical simulations (DNS) of the mixing of the passive scalar at modest Reynolds numbers (10 =< R_λ=< 42) and Schmidt numbers larger than unity (2 =< Sc =< 32). The simulations resolve below the Batchelor scale up to a factor of four. The advecting turbulence is homogeneous and isotropic, and maintained stationary by stochastic forcing at low wavenumbers. The passive scalar is rendered stationary by a mean scalar gradient in one direction. The relation between geometrical and statistical properties of scalar field and its gradients is examined. The Reynolds numbers and Schmidt numbers are not large enough for either the Kolmogorov scaling or the Batchelor scaling to develop and, not surprisingly, we find no fractal scaling of scalar level sets, or isosurfaces, in the intermediate viscous range. The area-to-volume ratio of isosurfaces reflects the nearly Gaussian statistics of the scalar fluctuations. The scalar flux across the isosurfaces, which is determined by the conditional probability density function (PDF) of the scalar gradient magnitude, has a stretched exponential distribution towards the tails. The PDF of the scalar dissipation departs distinctly, for both small and large amplitudes, from the lognormal distribution for all cases considered. The joint statistics of the scalar and its dissipation rate, and the mean conditional moment of the scalar dissipation, are studied as well. We examine the effects of coarse-graining on the probability density to simulate the effects of poor probe-resolution in measurements.

nlin.CD↗

arXiv2005

Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations

The connection between anomalous scaling of structure functions (intermittency) and numerical methods for turbulence simulations is discussed. It is argued that the computational work for direct numerical simulations (DNS) of fully developed turbulence increases as $Re^{4}$, and not as $Re^{3}$ expected from Kolmogorov's theory, where $Re$ is a large-scale Reynolds number. Various relations for the moments of acceleration and velocity derivatives are derived. An infinite set of exact constraints on dynamically consistent subgrid models for Large Eddy Simulations (LES) is derived from the Navier-Stokes equations, and some problems of principle associated with existing LES models are highlighted.

nlin.CD↗

arXiv2005

Very fine structures in scalar mixing

We explore very fine scales of scalar dissipation in turbulent mixing, below Kolmogorov and around Batchelor scales, by performing direct numerical simulations at much finer grid resolution than is usually adopted in the past. We consider the resolution in terms of a local, fluctuating Batchelor scale and study the effects on the tails of the probability density function and multifractal properties of the scalar dissipation. The origin and importance of these very fine-scale fluctuations are discussed. One conclusion is that they are unlikely to be related to the most intense dissipation events.

nlin.CD↗

arXiv2004

Sign-symmetry of temperature structure functions

New scalar structure functions with different sign-symmetry properties are defined. These structure functions possess different scaling exponents even when their order is the same. Their scaling properties are investigated for second and third orders, using data from high-Reynolds-number atmospheric boundary layer. It is only when structure functions with disparate sign-symmetry properties are compared can the extended self-similarity detect two different scaling ranges that may exist, as in the example of convective turbulence.

nlin.CD↗

arXiv2004

On the intermittency exponent of the turbulent energy cascade

We consider the turbulent energy dissipation from one-dimensional records in experiments using air and gaseous helium at cryogenic temperatures, and obtain the intermittency exponent via the two-point correlation function of the energy dissipation. The air data are obtained in a number of flows in a wind tunnel and the atmospheric boundary layer at a height of about 35 m above the ground. The helium data correspond to the centerline of a jet exhausting into a container. The air data on the intermittency exponent are consistent with each other and with a trend that increases with the Taylor microscale Reynolds number, R_λ, of up to about 1000 and saturates thereafter. On the other hand, the helium data cluster around a constant value at nearly all R_λ, this being about half of the asymptotic value for the air data. Some possible explanation is offered for this anomaly.

physics.flu-dyn↗

arXiv2003

Geometric features of the mixing of passive scalars at high Schmidt numbers

The mixing of passive scalars of decreasing diffusivity, advected in each case by the same three-dimensional Navier-Stokes turbulence, is studied. The mixing becomes more isotropic with decreasing diffusivity. The local flow in the vicinity of steepest negative and positive scalar gradients are in general different, and its behavior is studied for various values of the scalar diffusivity. Mixing approaches monofractal properties with diminishing diffusivity. We consider these results in the context of possible singularities of scalar dissipation.

nlin.CD↗

arXiv2001

Dynamical equations for high-order structure functions, and a comparison of a mean field theory with experiments in three-dimensional turbulence

Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) and R.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] 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.

nlin.CD↗

arXiv1999

The effects of large scales on the inertial range in high-Reynolds-number turbulence

The effects of removing large scales external to the inertial range on the properties of scales within the inertial range are studied in a high-Reynolds-number turbulent flow. Structure functions of both even and odd orders are strongly affected across the entire inertial range, but odd-order moments are affected to a greater degree. In particular, the skewness of velocity increments shows a significant reduction whereas the flatness changes comparatively little. The reduction in skewness is counterbalanced essentially by the interaction between the small-scale energy and the large-scale rate of strain. The implications of these results for the conventional cascade picture are examined briefly.

chao-dyn↗

arXiv1997

The persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows

We argue that important elements of the dynamics of wall-bounded flows reside at the wall-normal position $y_p^+$ corresponding to the peak of the Reynolds shear stress. Specializing to pipe and channel flows, we show that the mean momentum balance in the neighborhood of $y_p^+$ is distinct in character from those in the classical inner and outer layers. We revisit empirical data to confirm that $y_p^+ = O(R^{1/2})$ and show that, in a neighborhood of order $R^{1/2}$ around $y_p^+$, only the viscous effects balance pressure-gradient terms. Here, R is the Reynolds number based on friction velocity and pipe radius (or channel half-width). This observation provides a mechanism by which viscous effects play an important role in regions traditionally thought to be inviscid or inertial; in particular, it throws doubt on the validity of the classical matching principle. Even so, it is shown that the classical semi-logarithmic behavior for the mean velocity distribution can be a useful approximation. It is argued that the recently advanced power-law profiles possess a rich underlying structure, and could be good approximations to the data over an extended region (but they too are unlikely to be exact).

physics.flu-dyn↗

arXiv1997

A Refined Similarity Hypothesis for Transverse Structure Functions

We argue on the basis of empirical data that Kolmogorov's refined similarity hypothesis (RSH) needs to be modified for transverse velocity increments, and propose an alternative. In this new form, transverse velocity increments bear the same relation to locally averaged enstrophy (squared vorticity) as longitudinal velocity increments bear in RSH to locally averaged dissipation. We support this hypothesis by analyzing high-resolution numerical simulation data for isotropic turbulence. RSH and its proposed modification for transverse velocity increments (RSHT) appear to represent two independent scaling groups.

chao-dyn↗

arXiv1997

Fusion Rules in Navier-Stokes Turbulence: First Experimental Tests

We present the first experimental tests of the recently derived fusion rules for Navier-Stokes (N-S) turbulence. The fusion rules address the asymptotic properties of many-point correlation functions as some of the coordinates coalesce, and form an important ingredient of the nonperturbative statistical theory of turbulence. Here we test the fusion rules when the spatial separations lie within the inertial range, and find good agreement between experiment and theory. An unexpected result is a simple linear law for the Laplacian of the velocity fluctuation conditioned on velocity increments across large separations.

chao-dyn↗

arXiv1996

Scaling of Low-Order Structure Functions in Homogeneous Turbulence

High-resolution direct numerical simulation data for three-dimensional Navier-Stokes turbulence in a periodic box are used to study the scaling behavior of low-order velocity structure functions with positive and negative powers. Similar to high-order statistics, the low-order relative scaling exponents exhibit unambiguous departures from the Kolmogorov 1941 theory and agree well with existing multiscaling models. No transition from normal scaling to anomalous scaling is observed.

chao-dyn↗