The sound radiated by isotropic turbulence is computed using inertial range scaling expressions for the relevant two time and two point correlations. The result depends on whether the decay of Eulerian time correlations is dominated by large scale sweeping or by local straining: the straining hypothesis leads to an expression for total acoustic power, whereas the sweeping hypothesis leads to a more recent result.

Topics: NASA Technical Reports Server (NTRS), HIGH REYNOLDS NUMBER, ISOTROPIC TURBULENCE, SOUND GENERATORS,...

The dissipation range energy balance of the direct interaction approximation is applied to rotating turbulence when rotation effects persist well into the dissipation range. Assuming that RoRe (exp 1/2) is much less than 1 and that three-wave interactions are dominant, the dissipation range is found to be concentrated in the wavevector plane perpendicular to the rotation axis. This conclusion is consistent with previous analyses of inertial range energy transfer in rotating turbulence, which...

Topics: NASA Technical Reports Server (NTRS), ENERGY TRANSFER, TURBULENCE, WAVE INTERACTION, VORTICES,...

A recent paper on rotating turbulence by Canuto and Dubovikov is examined from both an historical and scientific perspective. It is first shown that their claim of finding a new energy spectrum scaling is inaccurate; such a scaling law has been published in the literature by other authors using the same physical assumptions. Canuto and Dubovikov actually only offered a different estimate for the constant. Finally, it is demonstrated that the alternative model for the dissipation rate transport...

Topics: DTIC Archive, Zhou, Ye, INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA,...

Taylor series expansions of turbulent time correlation functions are applied to show that helicity influences Eulerian time correlations more strongly than Lagrangian time correlations: to second order in time, the helicity effect on Lagrangian time correlations vanishes, but the helicity effect on Eulerian time correlations is nonzero. Fourier analysis shows that the helicity effect on Eulerian time correlations is confined to the largest inertial range scales. Some implications for sound...

Topics: NASA Technical Reports Server (NTRS), LAGRANGIAN FUNCTION, FOURIER ANALYSIS, SOUND WAVES, TIME...

Lam's phenomenological epsilon-renormalization group (RNG) model is quite different from the other members of that group. It does not make use of the correspondence principle and the epsilon-expansion procedure. We demonstrate that Lam's epsilon-RNG model is essentially the physical space version of the classical closure theory in spectral space and consider the corresponding treatment of the eddy viscosity and energy backscatter.

Topics: NASA Technical Reports Server (NTRS), NAVIER-STOKES EQUATION, RENORMALIZATION GROUP METHODS,...

Motivated by a recent survey of experimental data, we examine data on the Kolmogorov spectrum constant in numerical simulations of isotropic turbulence, using results both from previous studies and from new direct numerical simulations over a range of Reynolds numbers (up to 240 on the Taylor scale) at grid resolutions up to 512(exp 3). It is noted that in addition to k(exp -5/3) scaling, identification of a true inertial range requires spectral isotropy in the same wavenumber range. We found...

Topics: NASA Technical Reports Server (NTRS), ISOTROPIC TURBULENCE, DIRECT NUMERICAL SIMULATION, KOLMOGOROV...

The energy transfer statistics measured in numerically simulated flows are found to be nearly self-similar for wavenumbers in the inertial range. Using the measured self-similar form, an 'ideal' energy transfer function and the corresponding energy flux rate were deduced. From this flux rate, the Kolmogorov constant was calculated to be 1.5, in excellent agreement with experiments.

Topics: NASA Technical Reports Server (NTRS), ENERGY TRANSFER, FLUX DENSITY, KOLMOGOROV THEORY, TRANSFER...

Turbulence under strong stratification and rotation is usually characterized as quasi-two dimensional turbulence. We develop a "quasi-two dimensional" energy spectrum which changes smoothly between the Kolmogorov -5/3 law (no stratification), the -2 scalings of Zhou for the case of strong rotation, as well as the -2 scalings for the case of strong rotation and stratification. For strongly stratified turbulence, the model may give the -2 scaling predicted by Herring; and the -5/3...

Topics: NASA Technical Reports Server (NTRS), ENERGY SPECTRA, STRATIFICATION, TURBULENCE MODELS, TWO...

Galilean invariance has been an important issue in lattice-based hydrodynamics models. Previous models concentrated on the nonlinear advection term. In this paper, we take into account the nonlinear response effect in a systematic way. Using the Chapman-Enskog expansion up to second order, complete Galilean invariant lattice BGK models in one dimension (theta = 3) and two dimensions (theta = 1) for the Navier-Stokes equation have been obtained.

Topics: NASA Technical Reports Server (NTRS), BOLTZMANN TRANSPORT EQUATION, HYDRODYNAMICS, MODELS,...

The dependence of the energy transfer process on the disparity of the interacting scales is investigated in the inertial and far-dissipation ranges of isotropic turbulence. The strategy for generating the simulated flow fields and the choice of a disparity parameter to characterize the scaling of the interactions is discussed. The inertial range is found to be dominated by relatively local interactions, in agreement with the Kolmogorov assumption. The far-dissipation is found to be dominated by...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, ENERGY TRANSFER, FLOW...

To study the effect of cancellations within long-range interactions on local isotropy at the small scales, we calculate explicitly the degree of cancellation in distant interactions in the simulations of Yeung & Brasseur and Yeung, Brasseur & Wang using the single scale disparity parameter 's' developed by Zhou. In the simulations, initially isotropic simulated turbulence was subjected to coherent anisotropic forcing at the large scales and the smallest scales were found to become...

Topics: NASA Technical Reports Server (NTRS), ANISOTROPY, ENERGY TRANSFER, LOW REYNOLDS NUMBER, TURBULENCE,...

Analytical studies of compressible turbulence have found that compressible velocity fluctuations create both effective fluid transport properties and an effective equation of state. This paper investigates the effects of rotation on compressible turbulence. It is shown that rotation modifies the transport properties of compressible turbulence by replacing the turbulence time scale by a rotational time scale, much as rotation modifies the transport properties of incompressible turbulence. But...

Topics: NASA Technical Reports Server (NTRS), ACOUSTIC VELOCITY, COMPRESSIBILITY, TRANSPORT PROPERTIES,...

The advection of a passive scalar by incompressible turbulence is considered using recursive renormalization group procedures in the differential sub grid shell thickness limit. It is shown explicitly that the higher order nonlinearities induced by the recursive renormalization group procedure preserve Galilean invariance. Differential equations, valid for the entire resolvable wave number k range, are determined for the eddy viscosity and eddy diffusivity coefficients, and it is shown that...

Topics: NASA Technical Reports Server (NTRS), ADVECTION, DIFFUSIVITY, EDDY VISCOSITY, RENORMALIZATION GROUP...

Reynolds stress closure models based on the recursion renormalization group theory are developed for the prediction of turbulent separated flows. The proposed model uses a finite wavenumber truncation scheme to account for the spectral distribution of energy. In particular, the model incorporates effects of both local and nonlocal interactions. The nonlocal interactions are shown to yield a contribution identical to that from the epsilon-renormalization group (RNG), while the local interactions...

Topics: NASA Technical Reports Server (NTRS), BACKWARD FACING STEPS, RENORMALIZATION GROUP METHODS,...

The spectrum, energy transfer, and spectral interactions in steady Burgers turbulence are studied using numerically generated data. The velocity field is initially random and the turbulence is maintained steady by forcing the amplitude of a band of low wavenumbers to be invariant in time, while permitting the phase to change as dictated by the equation. The spectrum, as expected, is very different from that of Navier-Stokes turbulence. It is demonstrated that the far range of the spectrum...

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, ENERGY TRANSFER, INTERACTIONAL AERODYNAMICS,...

The well-known translation between the power law of energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this...

Topics: NASA Technical Reports Server (NTRS), ENERGY SPECTRA, TURBULENCE, NUMERICAL FLOW VISUALIZATION,...

The dissipation rate of a Newtonian fluid with constant shear viscosity can be shown to include three constituents: dilatation, vorticity, and surface strain. The last one is found to make no contributions to the change of kinetic energy. These dissipation constituents arc used to identify typical compact turbulent flow structures at high Reynolds numbers. The incompressible version of the simplified kinetic-energy equation is then cast to a novel form, which is free from the work rate done by...

Topics: NASA Technical Reports Server (NTRS), ENERGY DISSIPATION, HIGH REYNOLDS NUMBER, KINETIC ENERGY,...

The strong similarity between the magnetohydrodynamic (MHD) turbulence and initially isotropic turbulence subject to rotation is noted. We then apply the MHD phenomenologies of Kraichnan and Matthaeus & Zhou to rotating turbulence. When the turbulence is subject to a strong rotation, the energy spectrum is found to scale as E(k) = C(sub Omega)(Omega(sub epsilon))(sup 1/2)k(sup -2), where Omega is the rotation rate, k is the wavenumber, and epsilon is the dissipation rate. This spectral form...

Topics: NASA Technical Reports Server (NTRS), ENERGY SPECTRA, ENERGY TRANSFER, ISOTROPIC TURBULENCE,...

A framework, which combines mathematical analysis, closure theory, and phenomenological treatment, is developed to study the spectral transfer process and reduction of dimensionality in turbulent flows that are subject to rotation. First, we outline a mathematical procedure that is particularly appropriate for problems with two disparate time scales. The approach which is based on the Green's method leads to the Poincare velocity variables and the Poincare transformation when applied to...

Topics: NASA Technical Reports Server (NTRS), EDDY VISCOSITY, ENERGY TRANSFER, ROTATING FLUIDS, TURBULENCE,...

Direct numerical simulations (DNS) of passive scalar mixing in isotropic turbulence is used to study, analyze and, subsequently, model the role of small (subgrid) scales in the mixing process. In particular, we attempt to model the dissipation of the large scale (supergrid) scalar fluctuations caused by the subgrid scales by decomposing it into two parts: (1) the effect due to the interaction among the subgrid scales; and (2) the effect due to interaction between the supergrid and the subgrid...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, ISOTROPIC TURBULENCE, REACTING...

In 1952, Lighthill developed a theory for determining the sound generated by a turbulent motion of a fluid. With some statistical assumptions, Proudman applied this theory to estimate the acoustic power of isotropic turbulence. Recently, Lighthill established a simple relationship that relates the fourth-order retarded time and space covariance of his stress tensor to the corresponding second-order covariance and the turbulent flatness factor, without making statistical assumptions for a...

Topics: NASA Technical Reports Server (NTRS), AEROACOUSTICS, AERODYNAMIC NOISE, HIGH REYNOLDS NUMBER,...

Theories of turbulent time correlations are applied to compute frequency spectra of sound radiated by isotropic turbulence and by turbulent shear flows. The hypothesis that Eulerian time correlations are dominated by the sweeping action of the most energetic scales implies that the frequency spectrum of the sound radiated by isotropic turbulence scales as omega(exp 4) for low frequencies and as omega(exp -3/4) for high frequencies. The sweeping hypothesis is applied to an approximate theory of...

Topics: NASA Technical Reports Server (NTRS), TURBULENT FLOW, AEROACOUSTICS, SOUND PROPAGATION, SHEAR FLOW,...

Evaluation of the sound sources in a high Reynolds number turbulent flow requires time-accurate resolution of an extremely large number of scales of motion. Direct numerical simulations will therefore remain infeasible for the forseeable future: although current large eddy simulation methods can resolve the largest scales of motion accurately the, they must leave some scales of motion unresolved. A priori studies show that acoustic power can be underestimated significantly if the contribution...

Topics: NASA Technical Reports Server (NTRS), SOUND WAVES, TURBULENT FLOW, VELOCITY DISTRIBUTION,...

The dependence of the energy transfer process on the disparity of the interacting scales is investigated in the inertial and far-dissipation ranges of isotropic turbulence. The strategy for generating the simulated flow fields and the choice of a disparity parameter to characterize the scaling of the interactions is discussed. The inertial range is found to be dominated by relatively local interactions, in agreement with the Kolmogorov assumption. The far-dissipation is found to be dominated by...

Topics: DTIC Archive, Zhou, Ye, INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA,...

This letter investigates the compressible energy transfer process. We extend a methodology developed originally for incompressible turbulence and use databases from numerical simulations of a weak compressible turbulence based on Eddy-Damped-Quasi-Normal-Markovian (EDQNM) closure. In order to analyze the compressible mode directly, the well known Helmholtz decomposition is used. While the compressible component has very little influence on the solenoidal part, we found that almost all of the...

Topics: NASA Technical Reports Server (NTRS), COMPRESSIBILITY EFFECTS, COMPRESSIBLE FLOW, ENERGY TRANSFER,...

The terms renormalization and renormalization group are explained by reference to various physical systems. The extension of renormalization group to turbulence is then discussed; first as a comprehensive review and second concentrating on the technical details of a few selected approaches. We conclude with a discussion of the relevance and application of renormalization at group to turbulence modelling.

Topics: DTIC Archive, Zhou, Ye, INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA,...

The term renormalization and renormalization group are explained by reference to various physical systems. The extension of renormalization group to turbulence is then discussed; first as a comprehensive review and second concentrating on the technical details of a few selected approaches. We conclude with a discussion of the relevance and application of renormalization group to turbulence modelling.

Topics: NASA Technical Reports Server (NTRS), RENORMALIZATION GROUP METHODS, BOUNDARY LAYER TRANSITION,...

The advection of a passive scalar by incompressible turbulence is considered using recursive renormalization group procedures in the differential subgrid shell thickness limit. It is shown explicitly that the higher order nonlinearities induced by the recursive renormalization group procedure preserve Galilean invariance. Differential equations, valid for the entire resolvable wavenumber k range, are determined for the eddy viscosity and eddy diffusivity coefficients and it is shown that higher...

Topics: DTIC Archive, Zhou, Ye, INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA,...

Reynolds stress closure models based on the recursion renormalization group theory are developed for the prediction of turbulent separated flows. The proposed model uses a finite wavenumber truncation scheme to account for the spectral distribution of energy. In particular, the model incorporates effects of both local and nonlocal interactions. The nonlocal interactions are shown to yield a contribution identical to that from the Epsilon-RNG, while the local interactions introduce higher order...

Topics: DTIC Archive, Zhou, Ye, INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA,...

Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant...

Topics: NASA Technical Reports Server (NTRS), TURBULENCE MODELS, ENERGY DISSIPATION, BUOYANCY, ROTATION,...

Direct numerical simulation at 256(exp 3) resolution have been carried out to study the response of isotropic turbulence to the concurrent effects of solid-body rotation and numerical forcing at the large scales. Because energy transfer to the smaller scales is weakened by rotation, energy input from forcing gradually builds up at the large scales, causing the overall kinetic energy to increase. At intermediate wavenumbers the energy spectrum undergoes a transition from a limited k(exp -5/3)...

Topics: NASA Technical Reports Server (NTRS), DIRECT NUMERICAL SIMULATION, ROTATING BODIES, REYNOLDS...

We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and...

Topics: NASA Technical Reports Server (NTRS), STRESS TENSORS, TURBULENCE MODELS, TURBULENT FLOW,...

Using a two-point closure theory, the Eddy-Damped-Quasi-Normal-Markovian (EDQNM) approximation, we have investigated the energy transfer process and triadic interactions of compressible turbulence. In order to analyze the compressible mode directly, the Helmholtz decomposition is used. The following issues were addressed: (1) What is the mechanism of energy exchange between the solenoidal and compressible modes, and (2) Is there an energy cascade in the compressible energy transfer process? It...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, ENERGY TRANSFER, COMPRESSIBLE...