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  • 1
    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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  • 2
    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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  • 3
    Electronic Resource
    Electronic Resource
    Lagrangian velocity autocorrelation in isotropic turbulence (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1924-1933 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An analysis is made of the Lagrangian and the Eulerian velocity autocorrelations RL(s,t) and RE(s,t) at times s and t for small time lag τ=s−t in isotropic decaying turbulence, and it is shown that under appropriate conditions RE≤RL for small τ in three dimensions, irrespective of the form of the energy spectrum. The behaviors of RE and RL not limited to small τ are studied by direct numerical simulations in two dimensions. The values of RL obtained by the Lagrangian renormalized approximation are found to be in good agreement with the simulations and with the existing data of three-dimensional simulations and experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857922
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  • 4
    Electronic Resource
    Electronic Resource
    Probability density functions in steady-state Burgers turbulence (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 11 (1999), S. 2143-2148 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Probability density functions (PDFs) for steady-state Burgers turbulence supported by white-in-time random forcing at low wave numbers are studied by direct numerical simulation and compared to theoretical predictions. The velocity PDFs decay slightly faster than a Gaussian at large amplitudes. The putative power law exponent α of the PDF Q(ξ)∝|ξ|−α of velocity gradient ξ is examined at large Reynolds number and found to be approximately 3 or slightly greater. The tail of Q(ξ) behaves like |Rξ|−1exp(−c(|ξ|/Rξf)θ1) at large negative ξ, where ξf is a forcing parameter. The exponent θ1 is near unity, which is smaller than predicted by theory. It decreases slowly with the Reynolds number R up to R=14 000. The central parts of the PDFs of higher velocity space derivatives are found to be cusp-like, and the cusp exponents are measured. The PDF tails are stretched exponentials. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870106
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  • 5
    Electronic Resource
    Electronic Resource
    Steady-state Burgers turbulence with large-scale forcing (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 2859-2866 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Steady-state Burgers turbulence supported by white-in-time random forcing at low wave numbers is studied analytically and by computer simulation. The peak of the probability distribution function (pdf) Q(ξ) of velocity gradient ξ is at ξ=O(ξf), where ξf is a forcing parameter. It is concluded that Q(ξ) displays four asymptotic regimes at Reynolds number R(very-much-greater-than)1: (A) Q(ξ)∼ξf−2ξexp(−ξ3/3ξf3) for ξ(very-much-greater-than)ξf (reduction of large positive ξ by stretching); (B) Q(ξ)∼ξf2|ξ|−3 for ξf(very-much-less-than)−ξ(very-much-less-than)R1/2ξf (transient inviscid steepening of negative ξ); (C) Q(ξ)∼|Rξ|−1 for R1/2ξf(very-much-less-than)−ξ(very-much-less-than)Rξf (shoulders of mature shocks); (D) very rapid decay of Q for −ξ≥O(Rξf) (interior of mature shocks). The typical shock width is O(1/Rkf). If R−1/2(very-much-greater-than)rkf(very-much-greater-than)R−1, the pdf of velocity difference across an interval r is found to be P(Δu,r)∝r−1Q(Δu/r) throughout regimes A and B and into the middle of C. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869807
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  • 6
    Electronic Resource
    Electronic Resource
    Lagrangian velocity autocorrelation and eddy viscosity in two-dimensional anisotropic turbulence (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2426-2437 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A numerical study is made of the Lagrangian and Eulerian velocity autocorrelations RL and RE, and the eddy viscosity νeddy in two-dimensional anisotropic turbulence with or without mean flow of simple shearing motion. A short-time analysis is made of RL and RE in anisotropic turbulence, and also of νeddy in initially isotropic turbulence. The Lagrangian renormalized approximation is numerically integrated to compute RL and νeddy, and the results are compared with direct numerical simulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858181
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  • 7
    Electronic Resource
    Electronic Resource
    Experimental study of axial flow in a vortex ring (2002)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 14 (2002), S. 143-149 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: For a vortex ring at Re=1600, it was found that two types of azimuthal flow (axial flow) exist inside the vortex tube. The axial flow appears when the amplitude of a wavy deformation of the vortex ring becomes appreciable. The axial flow starts to grow before the wave-breaking and its speed increases gradually. In order to investigate the relation between the deformation of the vortex core and the axial flow, the flow field was examined experimentally using smoke visualization and the smoke wire technique simultaneously. Axial flow velocities are estimated from flow visualization images. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1420745
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  • 8
    Electronic Resource
    Electronic Resource
    Passive scalar spectrum in the viscous-convective range in two-dimensional steady turbulence (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 12 (2000), S. 155-168 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The spectrum of a passive scalar field in the viscous-convective range convected by two-dimensional steady turbulence was studied using the Lagrangian Renormalized Approximation (LRA) and high resolution DNS with a resolution up to 40962. It was found that the scalar spectrum F(k) using the LRA scales as k−1 in the range, and decays Gaussianly in the far diffusive range, and these wavenumber dependencies in both ranges agree with the DNS data. A new Lagrangian closure approximation that is invariant under random Galilean transformation and random uniform rotation is proposed. The approximation makes better quantitative predictions than the LRA and yields F(k)=CVCχ¯(ν/ε¯)1/2k−1 with CVC=5.25 in the viscous-convective range, which is in good agreement with the DNS value CVC=5.11. The importance of molecular diffusion in the far diffusive range when the viscous-convective range exists is also discussed. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870291
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  • 9
    Electronic Resource
    Electronic Resource
    Dynamics of inviscid truncated model of two-dimensional turbulent shear flow (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 1225-1234 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The method of classical statistical mechanics is applied to an inviscid truncated model system of two-dimensional turbulent shear flow. The idea of canonical equilibrium distribution is extended to treat a time-dependent Liouville equation governing the evolution of probability distribution function in the phase space. Results of numerical simulations supporting the theoretical conjectures based on the canonical distribution are shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857345
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  • 10
    Electronic Resource
    Electronic Resource
    Inertial range statistics of Burgers turbulence (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 3985-3998 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Velocity structure function of Burgers turbulence in the inertial range is studied by mapping closure. It is shown that in the inertial range 〈||u(x+l,t)−u(x,t)||q〉= n(t)〈||Δu(t)||q〉||l|| and the spectrum E(k,t)=(1/2π)n(t)〈||Δu(t)||2〉k−2 for initially support broad spectrum, where n(t) is the average of the number density of shocks and 〈||Δu(t)||q〉 is qth moment of shock strength. Agreement with DNS is found to be good for initially Gaussian fields. Statistics at large time is also studied by the mapping closure using time dependent reference field. It is found that the length scale of the field and the decay law of the total kinetic energy are self-similar in time and various quantities are given as functions of the exponent n of the initial energy spectrum E(k,0) ∝ kn at low wave-number range. Extension to more general initial conditions with non-Gaussian statistics is also discussed. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868388
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