Orthonormal wavelet decomposition of turbulent 
flows: intermittency and coherent structures

Camussi, Roberto; Guj, G.

doi:10.1017/s0022112097006551

Cited by 135 publications

(100 citation statements)

References 24 publications

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“…A continuous wavelet transform 25,69,70 yields wavelet coefficients, w( j, k) of a time series x(t) at a scale, j > 0, and a position, k ∈ ℜ, from a convolution of the time series with a wavelet function, ψ, whose integral is zero and whose square integrates to unity,…”

Section: Appendix: Wavelet Transformsmentioning

confidence: 99%

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

2015

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This work explores the properties of the velocity increment distributions for wakes of contrasting local Reynolds number and nature of generation (a cylinder wake and a multiscale-forced case, respectively). It makes use of a technique called gradual wavelet reconstruction (GWR) to generate constrained randomizations of the original data, the nature of which is a function of a parameter, ϑ. This controls the proportion of the energy between the Markov-Einstein length (∼ 0.8 Taylor scales) and integral scale that is fixed in place in the synthetic data. The properties of the increments for these synthetic data are then compared to the original data as a function of ϑ. We write a Fokker-Planck equation for the evolution of the velocity increments as a function of spatial scale, r, and, in line with previous work, expand the drift and diffusion terms in terms up to fourth order in the increments and find no terms are relevant beyond the quadratic terms. Only the linear contribution to the expansion of the drift coefficient is non-zero and it exhibits a consistent scaling with ϑ for different flows above a low threshold. For the diffusion coefficient, we find a local Reynolds number independence in the relation between the constant term and ϑ for the multiscale-forced wakes. This term characterizes small scale structure and can be contrasted with the results for the Kolmogorov capacity of the zero-crossings of the velocity signals, which measures structure over all scales and clearly distinguishes between the types of forcing. Using GWR shows that results for the linear and quadratic terms in the expansion of the diffusion coefficient are significant, providing a new means for identifying intermittency and anomalous scaling in turbulence datasets. All our data showed a similar scaling behavior for these parameters irrespective of forcing type or Reynolds number, indicating a degree of universality to the anomalous scaling of turbulence. Hence, these terms are a useful metric for testing the efficacy of synthetic turbulence generation schemes used in large eddy simulation, and we also discuss the implications of our approach for reduced order modeling of the Navier-Stokes equations.

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Section: Appendix: Wavelet Transformsmentioning

confidence: 99%

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

2015

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“…Partial studies have been made near weak vortices [4], in inhomogeneous wakes [5,6] or near a boundary layer [7,8]. Here we study turbulence The fluid is confined in a cylindrical vessel of height 40 cm and radius 11.7 cm.…”

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confidence: 99%

Inhomogeneous turbulence in the vicinity of a large-scale coherent vortex

2000

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Abstract. -We study the statistics of turbulent velocity fluctuations in the neighbourhood of a strong large scale vortex at very large Reynolds number. At each distance from the vortex core, we observe that the velocity spectrum has a power law "inertial range" of scales and that intermittencydefined as the variation of the probability density function (PDF) of velocity increments as the length of the increment is varied -is also present. We show that the spectrum scaling exponents and intermittency characteristics vary with the distance to the vortex. They are also influenced by the large scale dynamics of the vortex.Introduction. -Much efforts have been devoted to the study of high Reynolds number turbulence, assuming the properties of local homogeneity and isotropy. Under these assumptions it has been shown [1] that, in between the integral scale at which energy is fed into the flow and the dissipative scale at which viscosity smoothes out the velocity gradients, there exists an "inertial range" where: (i) the velocity spatial power spectrum follows a power law E(k) ∼ ǫ 2/3 k −5/3 , (ii) the energy transfer rate ǫ is related to the third order structure function S 3 (r) = δu 3 (r) = −

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“…These signatures can be extracted by using peaks in the LIM as a trigger for a conditional averaging procedure, which gives a time record of the signal produced by coherent structures in the flow [15]. The method works by first computing the wavelet transform of sections of the signal f (i).…”

Section: Data Processingmentioning

confidence: 99%

Noise mechanisms in motorcycle helmet noise

Carley

Holt

Walker

2010

Proceedings of Meetings on Acoustics

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A unique set of results on the acoustics of motorcycle helmets has been gathered during road tests on a rider wearing a representative modern helmet. The data were collected during a study of the noise which can cause hearing damage and, possibly, distraction in riders. They consisted of simultaneous measurements of noise at the rider's ear and unsteady pressure on the helmet surface, combined with GPS measurements of rider position and speed. These signals have been analyzed to educe the coherent structures in the turbulent flow responsible for noise generation. The identified structures appear to be produced by a vortex street shed by the motorcycle windscreen. The internal and external pressures proved to be poorly correlated over most of the frequency range, which has been identified as a result of the insertion loss of the helmet. The implications of these findings are that the majority of variation in helmet noise is a function of such extrinsic factors as motorcycle configuration and rider build and position. Efforts to reduce the harmful effects of noise in motorcycling should, then, move to studying the whole system of rider, helmet, motorcycle and external environment.

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Orthonormal wavelet decomposition of turbulent flows: intermittency and coherent structures

Cited by 135 publications

References 24 publications

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

Inhomogeneous turbulence in the vicinity of a large-scale coherent vortex

Noise mechanisms in motorcycle helmet noise

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