Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations

A study of the Lagrangian statistical properties of velocity and passive scalar fields using direct numerical simulations is presented, for the case of stationary isotropic turbulence with uniform mean scalar gradients. Data at higher grid resolutions (up to 5123 and Taylor-scale Reynolds number 234) allow an update of previous velocity results at lower Reynolds number, including intermittency and dimensionality effects on vorticity time scales. The emphasis is on Lagrangian scalar time series which are new to the literature and important for stochastic mixing models. The variance of the ‘total’ Lagrangian scalar value (ϕ˜+, combining contributions from both mean and fluctuations) grows with time, with the velocity–scalar cross-correlation function and fluid particle displacements playing major roles. The Lagrangian increment of ϕ˜+ conditioned upon velocity and scalar fluctuations is well represented by a linear regression model whose parameters depend on both Reynolds number and Schmidt number. The Lagrangian scalar fluctuation is non-Markovian and has a longer time scale than the velocity, which is due to the strong role of advective transport, and is in contrast to results in an Eulerian frame where the scalars have shorter time scales. The scalar dissipation is highly intermittent and becomes de-correlated in time more rapidly than the energy dissipation. Differential diffusion for scalars with Schmidt numbers between 1/8 and 1 is characterized by asymmetry in the two-scalar cross-correlation function, a shorter time scale for the difference between two scalars, as well as a systematic decrease in the Lagrangian coherency spectrum up to at least the Kolmogorov frequency. These observations are consistent with recent work suggesting that differential diffusion remains important in the small scales at high Reynolds number.

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Differential Diffusion in Breaking Kelvin–Helmholtz Billows

Journal of Physical Oceanography ◽

10.1175/jpo2739.1 ◽

2005 ◽

Vol 35 (6) ◽

pp. 1004-1022 ◽

Cited By ~ 46

Author(s):

W. D. Smyth ◽

J. D. Nash ◽

J. N. Moum

Keyword(s):

Reynolds Number ◽

Numerical Simulations ◽

Density Ratio ◽

Scalar Fields ◽

Direct Numerical Simulations ◽

Density Stratification ◽

Differential Diffusion ◽

Diffusivity Ratio

Abstract Direct numerical simulations are used to compare turbulent diffusivities of heat and salt during the growth and collapse of Kelvin–Helmholtz billows. The ratio of diffusivities is obtained as a function of buoyancy Reynolds number Reb and of the density ratio Rρ (the ratio of the contributions of heat and salt to the density stratification). The diffusivity ratio is generally less than unity (heat is mixed more effectively than salt), but it approaches unity with increasing Reb and also with increasing Rρ. Instantaneous diffusivity ratios near unity are achieved during the most turbulent phase of the event even when Reb is small; much of the Reb dependence results from the fact that, at higher Reb, the diffusivity ratio remains close to unity for a longer time after the turbulence decays. An explanation for this is proposed in terms of the Batchelor scaling for scalar fields. Results are interpreted in terms of the dynamics of turbulent Kelvin–Helmholtz billows, and are compared in detail with previous studies of differential diffusion in numerical, laboratory, and observational contexts. The overall picture suggests that the diffusivities become approximately equal when Reb exceeds O(102). The effect of Rρ is significant only when Reb is less than this value.

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Research on compound fault diagnosis of rolling bearing based on intrinsic time scale decomposition and information fusion

Noise & Vibration Worldwide ◽

10.1177/09574565211055793 ◽

2021 ◽

pp. 095745652110557

Author(s):

Mingyue Yu ◽

Guihong Guo

Keyword(s):

Correlation Function ◽

Information Fusion ◽

Time Scale ◽

Cross Correlation ◽

Rolling Bearing ◽

Cross Correlation Function ◽

Intrinsic Time ◽

Cross Correlation Analysis ◽

Reconstructed Signal ◽

Time Scale Decomposition

In view of the difficulty to effectively extract compound faults of rolling bearing from aero-engine and precisely identify their types, the paper has proposed a method integrating signal separation algorithm and information fusion. Firstly, the method decomposes the vibration acceleration signals collected by sensors from different positions at the same moment based on intrinsic time scale decomposition algorithm. Secondly, cross correlation analysis is given to the proper rotation component (PRC) of the same layer, which are obtained after decomposition and correspond to the sensors from different positions and cross-correlation function is introduced to embody information fusion. Thirdly, signals are reconstructed according to cross-correlation function of each PRC. Finally, based on the frequency spectrum of reconstructed signal, extract the characteristics of rolling bearing and identify the type of faults under different sensor combinations and multiple compound fault types. The result shows, the proposed method can effectively extract the characteristics of compound faults of bearing and precisely identify the type of faults under different sensor combinations and multiple compound fault types of rolling bearing.

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An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number

Journal of Fluid Mechanics ◽

10.1017/s0022112006004204 ◽

2007 ◽

Vol 574 ◽

pp. 405-427 ◽

Cited By ~ 24

Author(s):

MICHELE GUALA ◽

ALEXANDER LIBERZON ◽

ARKADY TSINOBER ◽

WOLFGANG KINZELBACH

Keyword(s):

Reynolds Number ◽

Time Scales ◽

Correlation Functions ◽

Time Scale ◽

Cross Correlation ◽

Strain Tensor ◽

Three Dimensional ◽

Small Scale ◽

Production Term ◽

Long Time

Lagrangian auto- and cross-correlation functions of the rate of strain s2, enstrophy ω2, their respective production terms −sijsjkski and ωiωjsij, and material derivatives, Ds2/Dt and Dω2/Dt are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Reλ=50. The autocorrelation functions are used to estimate the Lagrangian time scales of different quantities, while the cross-correlation functions are used to clarify some aspects of the interaction mechanisms between vorticity ω and the rate of strain tensor sij, that are responsible for the statistically stationary, in the Eulerian sense, levels of enstrophy and rate of strain in homogeneous turbulent flow. Results show that at the Reynolds number of the experiment these quantities exhibit different time scales, varying from the relatively long time scale of ω2 to the relatively shorter time scales of s2, ωiωjsij and −sijsjkski. Cross-correlation functions suggest that the dynamics of enstrophy and strain, in this flow, is driven by a set of different-time-scale processes that depend on the local magnitudes of s2 and ω2. In particular, there are indications that, in a statistical sense, (i) strain production anticipates enstrophy production in low-strain–low-enstrophy regions (ii) strain production and enstrophy production display high correlation in high-strain–high-enstrophy regions, (iii) vorticity dampening in high-enstrophy regions is associated with weak correlations between −sijsjkski and s2 and between −sijsjkski and Ds2/Dt, in addition to a marked anti-correlation between ωiωjsij and Ds2/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay of s2 and its production term, −sijsjkski.

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