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  • 1
    Electronic Resource
    Electronic Resource
    Note on forced Burgers turbulence (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 11 (1999), S. 3738-3742 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A putative powerlaw range of the probability density of velocity gradient in high-Reynolds-number forced Burgers turbulence is studied. In the absence of information about shock locations, elementary conservation and stationarity relations imply that the exponent −α in this range satisfies α≥3, if dissipation within the power-law range is due to isolated shocks. A generalized model of shock birth and growth implies α=7/2 if initial data and forcing are spatially homogeneous and obey Gaussian statistics. Arbitrary values α≥3 can be realized by suitably constructed homogeneous, non-Gaussian initial data and forcing. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870235
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  • 2
    Electronic Resource
    Electronic Resource
    Statistics of an advected passive scalar (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 2264-2277 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An elementary argument shows that non-Gaussian fluctuations in the temperature at a point in space are induced by random advection of a passive temperature field that has a nonlinear mean gradient, whether or not there is molecular diffusion. This is corroborated by exact analysis for the nondiffusive case and by direct numerical simulation for diffusive cases. Eulerian mapping closure gives results close to the simulation data. Non-Gaussian fluctuations of temperature at a point also are induced by a more subtle mechanism that requires both advection and molecular diffusion and is effective even when the statistics are strictly homogeneous. It operates through selectively strong dissipation of regions where intense temperature gradients have been induced by advective straining. This phenomenon is demonstrated by simulations and explored by means of an idealized analytical model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858530
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  • 3
    Electronic Resource
    Electronic Resource
    Lagrangian velocity correlations in homogeneous isotropic turbulence (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 2846-2864 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The Lagrangian velocity autocorrelation and the time correlations for individual wave-number bands are computed by direct numerical simulation (DNS) using the passive vector method (PVM), and the accuracy of the method is studied. It is found that the PVM is accurate when Kmax/kd≥2 where Kmax is the maximum wave number carried in the simulation and kd is the Kolmogorov wave number. The Eulerian and Lagrangian time correlations for various wave-number bands are compared. At moderate to high wave number the Eulerian time correlation decays faster than the Lagrangian, and the effect of sweep on the former is observed. The time scale of the Eulerian correlation is found to be (kU0)−1 while that of the Lagrangian is [∫0k p2E(p)dp]−1/2. The Lagrangian velocity autocorrelation in a frozen turbulent field is computed using the DIA, ALHDIA, and LRA theories and is compared with DNS measurements. The Markovianized Lagrangian renormalized approximation (MLRA) is compared with the DNS, and good agreement is found for one-time quantities in decaying turbulence at low Reynolds numbers and for the Lagrangian velocity autocorrelation in stationary turbulence at moderate Reynolds number. The effect of non-Gaussianity on the Lagrangian correlation predicted by the theories is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858748
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  • 4
    Electronic Resource
    Electronic Resource
    Sweeping decorrelation in isotropic turbulence (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 2019-2024 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Tennekes [J. Fluid Mech. 67, 561 (1975)] estimated the time decorrelation of inertial-range excitation in isotropic turbulence by assuming effective statistical independence of the one-time distributions of inertial-range and energy-range excitation. This picture has been challenged by Yakhot, Orszag, and She [Phys. Fluids A 1, 184 (1989)], who studied forced turbulence by renormalization-group (RNG) methods. The analysis given in the present paper leads to the conclusion that (a) precise coherence between energy-range and inertial-range excitation is needed to inhibit sweeping effects; (b) in the case of randomly forced turbulence, this coherence is impossible and Tennekes' picture is unavoidable; and (c) the RNG analysis does not demonstrate inhibition of sweeping; instead, it discards sweeping effects at the outset. To augment the present study, an advected passive scalar is examined by computer simulation. Sweeping effects on small scales survive even in the case of long-time advection by a frozen velocity field. The observed probability distributions resemble those for the alignment of vorticity and velocity observed in flow simulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857475
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  • 5
    Electronic Resource
    Electronic Resource
    An interpretation of the Yakhot–Orszag turbulence theory (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 2400-2405 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Yakhot and Orszag have recently developed a theory of turbulence [J. Sci. Comput. 1, 3 (1986)] based on dynamic renormalization-group (RNG) techniques. They predict parameters of the Kolmogorov inertial range and then successfully use eddy-viscosity formulas from the inertial-range theory in computations of shear flows. In the present paper a critical analysis of the Yakhot–Orszag theory is offered based on comparison with a simple perturbative model. The latter appears to parallel much of the physical and operational content of the lowest order of the Yakhot–Orszag theory, without using RNG methods. The essence is as follows: (1) the dynamics of modes in the inertial and dissipation ranges are assumed to be dominated by interactions more-or-less local in wavenumber that are modeled by a white-noise force acting against an effective viscosity; and (2) the effective viscosity is estimated by extrapolation from the small contributions of interactions very nonlocal in wavenumber (distant interactions). In common with the Yakhot–Orszag theory, the only explicit contacts with the Navier–Stokes equation are overall energy conservation by nonlinear terms and the interaction coefficients of highly nonlocal wave vector triads.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866130
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  • 6
    Electronic Resource
    Electronic Resource
    Statistics of decaying Burgers turbulence (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 445-457 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Freely decaying Burgers turbulence at low and moderate Reynolds number R is studied by mapping closure and by numerical simulations. Good agreement is found for the single-point probability distribution function (pdf) of velocity gradient ξ, for wave number spectra, and for various integral statistical quantities. The pdf of ξ exhibits a nearly exponential tail at large negative ξ, and a cusp with sharp cutoff at a positive value of ξ. The pdf of fluid density has a power-law tail, so that high-order moments of density do not exist. Asymptotic analysis of the mapping closure as R→∞ yields an inertial-range wave number spectrum of kinetic energy with the form E(k)∝k−2. The pdf cusp becomes infinite as R→∞ and gives rise to a flatness 〈ξ4(approximately-greater-than)/〈ξ2(approximately-greater-than)2∝R in the limit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858868
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  • 7
    Electronic Resource
    Electronic Resource
    On statistical correlations between velocity increments and locally averaged dissipation in homogeneous turbulence (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 458-463 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Kolmogorov postulated in 1962 [J. Fluid Mech. 13, 82 (1962)] that the magnitude of velocity increments δur across an inertial range distance r in high Reynolds number flows is typically (rεr)1/3, where εr is the locally averaged dissipation rate. This refined similarity hypothesis has been widely used in discussions of anomalous exponents of velocity structure functions in connection with the scaling exponents of εr. Recently Hosokawa and Yamamoto [Phys. Fluids A 4, 457 (1992)] have presented numerical evidence from turbulence simulations that δur is uncorrelated with εr in moderate Reynolds number flows. In the present paper, results of similar measurements are offered for flow fields with a wide range of Reynolds numbers obtained from high-resolution numerical simulations of both forced and decaying isotropic turbulence. The present results show clear evidence of correlations between δur and εr, irrespective of the Reynolds number. Kolmogorov's hypothesis is verified for r somewhat larger than the viscous dissipation scale, but at much larger distances the correlation seems to be weaker.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858897
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  • 8
    Electronic Resource
    Electronic Resource
    Non-Gaussian statistics in isotropic turbulence (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 1844-1854 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Several measures of non-Gaussian behavior in simulations of decaying isotropic turbulence are compared with predictions of the direct-interaction approximation (DIA) at an initial Rλ(approximate)35. The quantities studied include the variances and wavenumber power spectra of (a) the total nonlinear term in the Navier–Stokes equation, (b) the time derivative of the velocity at a point, (c) pressure fluctuations, and (d) vorticity and dissipation fluctuations. The direct-interaction approximation gives a good quantitative prediction of the variance of the time derivative and the variance of total nonlinear term, and a fair qualitative prediction of the power spectrum associated with the latter. But DIA totally fails to capture the non-Gaussian statistics associated with pressure fluctuation and vorticity spottiness. Some discussion is given of demands that vorticity and dissipation statistics place upon theories of tubulence at moderate and high Reynolds numbers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857556
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  • 9
    Electronic Resource
    Electronic Resource
    Kolmogorov's constant and local interactions (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 1583-1585 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Suppose that all the wave-vector triad interactions that involve no wavenumber ratio that exceeds β are removed from the Navier–Stokes equation. Within a class of closures, the paradoxical effect is to enhance energy cascade through the Kolmogorov inertial range for 1〈β〈βc, where βc may be as large as 8. This may have implications with regard to force-free structures in the true Navier–Stokes dynamics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866224
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  • 10
    Electronic Resource
    Electronic Resource
    Intermittency and attractor size in isotropic turbulence (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 10-11 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Qualitative arguments suggest that the Kolmogorov 1941 (K41) inertial range for space dimensionality D3 corresponds to a maximum attractor size if compared with alternative inertial ranges in which intermittency increases as a power of wavenumber. Therefore upper bounds on attractor size consistent with K41 do not either rule out or imply intermittency corrections to the −5/3 law. In contrast, the K41 inertial range corresponds to minimum attractor size if D〉4.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865189
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