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  • 1
    Electronic Resource
    Electronic Resource
    Interacting scales and energy transfer in isotropic turbulence (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 2511-2524 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: 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 range is found to be dominated by relatively nonlocal interactions, supporting the classical notion that the far-dissipation range is slaved to the Kolmogorov scales. The measured energy transfer is compared with the classical models of Heisenberg [Z. Phys. 124, 628 (1948)], Obukhov [Isv. Geogr. Geophys. Ser. 13, 58 (1949)] and the more detailed analysis of Tennekes and Lumley [The First Course of Turbulence (MIT Press, Cambridge, MA, 1972)]. The energy transfer statistics measured in the numerically simulated flows are found to be nearly self-similar for wave numbers in the inertial range. Using the self-similar form measured within the limited scale range of the simulation, an "ideal'' energy transfer function and the corresponding energy flux rate for an inertial range of infinite extent are constructed. From this flux rate the Kolmogorov constant is calculated to be 1.5, in excellent agreement with experiments [A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975), Vol. 2].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858764
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  • 2
    Electronic Resource
    Electronic Resource
    Extended inertial range phenomenology of magnetohydrodynamic turbulence (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 1929-1931 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A phenomenological treatment of the inertial range of isotropic statistically steady magnetohydrodynamic turbulence is presented, extending the theory of Kraichnan [Phys. Fluids 8, 1385 (1965)]. The role of Alfvén wave propagation is treated on equal footing with nonlinear convection, leading to a simple generalization of the relations between the times characteristic of wave propagation, convection, energy transfer, and decay of triple correlations. The theory leads to a closed-form steady inertial range spectral law that reduces to the Kraichnan and Kolmogorov laws in appropriate limits. The Kraichnan constant is found to be related in a simple way to the Kolmogorov constant; for typical values of the latter constant, the former has values in the range 1.22–1.87. Estimates of the time scale associated with spectral transfer of energy also emerge from the new approach, generalizing previously presented "golden rules'' for relating the spectral transfer time scale to the Alfvén and eddy-turnover time scales.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859110
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  • 3
    Electronic Resource
    Electronic Resource
    Analysis and modeling of subgrid scalar mixing using numerical data (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 1224-1236 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: 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: (i) the effect due to the interaction among the subgrid scales, E(very-much-greater-than)φ; and, (ii) the effect due to interaction between the supergrid and the subgrid scales, E(approximately-greater-than)〈φ. Model comparison with DNS data shows good agreement. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868894
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  • 4
    Electronic Resource
    Electronic Resource
    Analytical and phenomenological studies of rotating turbulence (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 2138-2152 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A framework, which combines mathematical analysis, closure theory, and phenomenological treatment, is developed to study the spectral transfer process 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 that is based on the Green's method leads to the Poincaré velocity variables and the Poincaré transformation when applied to rotating turbulence. The effects of the rotation are now conveniently included in the momentum equation as the modifications to the convolution of nonlinear term. The Poincaré transformed equations are used to obtain a time-dependent Taylor–Proudman theorem valid in the asymptotic limit when the nondimensional parameter μ≡Ωt→∞ (Ω is the rotation rate and t is the time). The "split'' of the energy transfer in both direct and inverse directions is established. Second, we apply the Eddy-Damped-Quasinormal-Markovian (EDQNM) closure to the Poincaré transformed Euler/ Navier–Stokes equations. This closure leads to expressions for the spectral energy transfer. In particular, a unique triple velocity decorrelation time is derived with an explicit dependence on the rotation rate. This provides an important input for applying the phenomenological treatment of Zhou [Phys. Fluids 7, 2092 (1995)]. In order to characterize the relative strength of rotation, another nondimensional number, a spectral Rossby number, which is defined as the ratio of rotation, and turbulence time scales, is introduced. Finally, the energy spectrum and the spectral eddy viscosity are deduced. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868988
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  • 5
    Electronic Resource
    Electronic Resource
    Analytical theory of the destruction terms in dissipation rate transport equations (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 3172-3178 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie [Modern Developments in the Theory of Turbulence (Oxford University, Oxford, 1972)] suggested that these models might be derived instead from Kraichnan's [J. Fluid Mech. 47 (1971)] 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 turbulence. Model constants like Ccursive-epsilon2 are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of Ccursive-epsilon2 on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. The time scale in the modeled transport equation depends on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple extension of these methods leads to a preliminary dissipation rate equation for rotating buoyant turbulence. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869090
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  • 6
    Electronic Resource
    Electronic Resource
    Degrees of locality of energy transfer in the inertial range (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 1092-1094 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Recent interpretations of direct numerical simulation (DNS) measurements have led some authors to suggest that energy is largely transferred downscale locally, supporting a basic concept of the Kolmogorov phenomenology that leads to the universal inertial subrange. However, these authors conclude that the local energy transfer results from nonlocal triad interactions. This claim brings into question the validity of the assumption of the statistical independence of the large- and small-scale motions in the Kolmogorov universal theory of turbulence. In this Letter, the measured raw transfer interactions have been summed in a way that directly indicates the scale disparity (s) of contributions to the net energy flux across the spectrum. It is found that the dependence upon s closely follows the s−4/3 form predicted by classical arguments. As a result, it is concluded that DNS measurements, in fact, lend support to the classical Kolmogorov phenomenology of local interactions and local transfer in an inertial range.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858593
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  • 7
    Electronic Resource
    Electronic Resource
    Sweeping and straining effects in sound generation by high Reynolds number isotropic turbulence (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 647-649 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: 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 given originally by Proudman, whereas the sweeping hypothesis leads to a more recent result due to Lilley. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868849
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  • 8
    Electronic Resource
    Electronic Resource
    Analysis of spectral eddy viscosity and backscatter in incompressible, isotropic turbulence using statistical closure theory (2002)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 14 (2002), S. 1244-1258 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The spectral eddy viscosity and backscatter viscosity in three-dimensional, incompressible, unforced, nonhelical, isotropic turbulence are decomposed into a sum of contributions corresponding to the Reynolds and cross-stresses, and studied numerically as a function of different assumed kinetic energy spectra. The eddy viscosities and backscatter viscosities are computed using the kinetic energy transfer obtained from the eddy-damped quasinormal Markovian (EDQNM) closure model as a function of k/kc (where kc is the cutoff wave number) using the sharp Fourier cutoff filter. The behavior of the Reynolds and cross-contributions is studied using a Kolmogorov kinetic energy spectrum, a family of spectra with small wave number scaling proportional to k, and a spectrum from an EDQNM calculation that includes both a k4 energy production subrange and a dissipation subrange. The principal results of this theoretical investigation and sensitivity study are (1) the main contributions from the Reynolds and cross-components of the eddy viscosity arise from modes with k/kc(very-much-less-than)1 and k/kc(approximately-less-than)1, respectively; (2) the contributions from the Reynolds and cross-components of the backscatter viscosity are of the same order, which are nearly zero for k/kc〈1 and rise sharply near the cusp k/kc↑1, and; (3) for both the eddy and backscatter viscosity, the Reynolds components are more sensitive to the details of the production subrange than are the cross-components. The implications of these results for subgrid-scale modeling in spectral large-eddy simulations of incompressible, isotropic turbulence are discussed. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1447913
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  • 9
    Electronic Resource
    Electronic Resource
    A phenomenological treatment of rotating turbulence (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 7 (1995), S. 2092-2094 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this Brief Communication, we first note the strong similarity between the magnetohydrodynamic (MHD) turbulence and initially isotropic turbulence subject to rotation. We then applied the MHD phenomenologies of Kraichnan [Phys. Fluids 8, 1385 (1965)] and Matthaeus and Zhou [Phys. Fluids B 1, 1929 (1989)] to rotating turbulence. We deduced a "rule'' that relates spectral transfer time to the eddy turnover time and the time scale for decay of the triple correlations. Our hypothesis on the triple correlation decay rate leads to the spectral law, which varies between the "−5/3'' (without rotation) and "−2'' laws (with strong rotation). For intermediate rotation rates, the spectrum varies according to the value of a dimensionless parameter that measures the strength of the rotation wave number kΩ=(Ω3/ε)1/2 relative to the wave number k. The eddy viscosity is derived with an explicitly dependence on the rotation rate. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868457
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  • 10
    Electronic Resource
    Electronic Resource
    A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities (2001)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 13 (2001), S. 538-543 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We investigate inertial subrange energy spectra associated with turbulent flows developed by the Rayleigh–Taylor instability and Richtmyer–Meshkov instability (RMI). We argue that the extended Kolmogorov–Kraichnan phenomenology originally developed for turbulent flows with an external agent should also be applicable to these instability driven turbulent flows. A prediction of the mixing zone width for the RMI induced turbulent flow is presented using the RMI modified energy spectrum and a two-equation turbulence model. A possible application to subgrid modeling for large-eddy simulation is discussed briefly. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1336151
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