Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulation

Kang, Hyung Suk; Chester, Stuart; Meneveau, Charles

doi:10.1017/s0022112002003579

Cited by 321 publications

(285 citation statements)

References 33 publications

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“…In subsequent work he stresses that for constant ν (and η), only the case α = 1 can be realized. For nonhelical MHD, this is indeed compatible with simulations [23][24][25], but not for HD [26] nor for helical MHD [3,18]. In this Letter, we argue that the scaling exponent q is not primarily determined by the initial value of α, as suggested by Eq.…”

supporting

confidence: 76%

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Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

2017

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We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, while the infrared slope of the initial conditions plays only a limited role. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wavenumber k), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k 4 ). [7], galaxy clusters [8], and the early Universe [9,10]. In the latter case, cosmological magnetic fields generated in the early Universe provide the initial source of turbulence, which leads to a growth of the correlation length by an inverse cascade mechanism [11], in addition to the general cosmological expansion of the Universe. In the last two decades, this topic has gained significant attention [12]. The time span since the initial magnetic field generation is enormous, but it is still uncertain whether it is long enough to produce fields at sufficiently large length scales to explain the possibility of contemporary magnetic fields in the space between clusters of galaxies [13].In this Letter, we use direct numerical simulations (DNS) of both hydrodynamic (HD) and magnetohydrodynamic (MHD) decaying turbulence to classify different types by their decay behavior. The decay is characterized by the temporal change of the kinetic energy spec- * Electronic address: brandenb@nordita.org † Electronic address: tinatin@andrew.cmu.edu trum, E K (k, t), and, in MHD, also by the magnetic energy spectrum, E M (k, t). Here, k is the wavenumber and t is time. In addition to the decay laws of the energies E i (t) = E i (k, t) dk, with i = K or M for kinetic and magnetic energies, there are the kinetic and magnetic integral scales,We quantify the decay by the instantaneous scaling exponents p(t) ≡ d ln E/d ln t and q(t) ≡ d ln ξ/d ln t. Thus, we study the decay behaviors by plotting p(t) vs. q(t) in a parametric representation. The pq diagram turns out to be a powerful diagnostic tool. Earlier work [8,14,15] has suggested that the decay behavior, and thus the positions of solutions in the pq diagram, depend on the exponent α for initial conditions of the form E ∼ k α e −k/k0 , where k 0 is a cutoff wavenumber. Motivated by earlier findings [2,11] of an inverse cascade in decaying MHD turbulence, Olesen considered the time-dependent energy spectra E(k, t) to be of the form [15]where ξ(t) ∝ t q , with q being an as yet undetermined scaling exponent, and ψ is a function that depends on the dissipative and turbulent processes that lead to a departure from a powerlaw at large k. Moreover, the slope ψ ′ ≡ dψ/dκ with κ = kξ must vanish for κ → 0. This turns out to be a critical restriction. Olesen then makes use of the f...

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supporting

confidence: 76%

“…This decay behavior departs from what would be expected if the Loitsiansky integral were conserved, i.e., q = 2/7 and β = 4. A slower decay law with p = 6/5, corresponding to q = 2/5 and β = 2 has been favored by Saffman [29], while experiments and simulations suggest p = 5/4 [26,30].…”

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confidence: 99%

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

2017

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“…They found that both the velocity and temperature fluctuations decayed at similar rates. More recently, Kang et al (2003) performed an update of the Comte-Bellot and Corrsin (1971) dataset at a higher Reynolds number and compared it with LES using different subgrid-scale models.…”

Section: Introductionmentioning

confidence: 99%

A Simple Model for the Afternoon and Early Evening Decay of Convective Turbulence Over Different Land Surfaces

Nadeau

Pardyjak

Higgins

et al. 2011

Boundary-Layer Meteorol

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A simple model to study the decay of turbulent kinetic energy (TKE) in the convective surface layer is presented. In this model, the TKE is dependent upon two terms, the turbulent dissipation rate and the surface buoyancy fluctuations. The time evolution of the surface sensible heat flux is modelled based on fitting functions of actual measurements from the LITFASS-2003 field campaign. These fitting functions carry an amplitude and a time scale. With this approach, the sensible heat flux can be estimated without having to solve the entire surface energy balance. The period of interest covers two characteristic transition subperiods involved in the decay of convective boundary-layer turbulence. The first sub-period is the afternoon transition, when the sensible heat flux starts to decrease in response to the reduction in solar radiation. It is typically associated with a decay rate of TKE of approximately t −2 (t is time following the start of the decay) after several convective eddy turnover times. The early evening transition is the second sub-period, typically just before sunset when the surface sensible heat flux becomes negative. This sub-period is characterized by an abrupt decay in TKE associated with the rapid collapse of turbulence. Overall, the results presented show a significant improvement of the modelled TKE decay when compared to the often applied assumption of a sensible heat flux decreasing instantaneously or with a very short forcing time scale. In addition, for atmospheric modelling studies, it is suggested that the afternoon and early evening decay of sensible heat flux be modelled as a complementary error function.

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“…However, various studies have already documented some limitations of LES results, for example when considering structure functions and space-time correlations (Kang, Chester & Meneveau 2003;Yang, He & Wang 2008). Matching some lower-order statistics is thus no guarantee that all other statistics are also accurately simulated.…”

Section: Futurementioning

confidence: 99%

Challenging the large eddy simulation technique with advanced a posteriori tests

Bou‐Zeid

2014

J. Fluid Mech.

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The large eddy simulation (LES) technique will soon be 50 years old. Since Deardorff's first papers in 1970 introducing this approach, major advances in the theory of LES and its computational implementation have been made and widely adopted. However, in terms of validation, LES studies continue to largely focus on the first-and second-order statistics, which in fact are the same tests that Deardorff conducted 45 years ago. Further advances in LES and wider adoption for new flows require advanced and more challenging tests to be developed and documented to serve as benchmarks. The paper by Stevens, Wilczek & Meneveau (J. Fluid Mech., 2014, vol. 757, pp. 888-907) does precisely that. The authors demonstrate the ability of LES to capture the recently established log-law of streamwise velocity variance and the related log-laws for even-order statistics up to order 10, as well as the departure of these statistics from a Gaussian distribution. The paper also provides key insights into the role of grid resolution on the computed turbulence field.

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Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulation

Cited by 321 publications

References 33 publications

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

A Simple Model for the Afternoon and Early Evening Decay of Convective Turbulence Over Different Land Surfaces

Challenging the large eddy simulation technique with advanced a posteriori tests

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