Gradual wavelet reconstruction of the velocity increments for turbulent wakes

Keylock, Christopher J.; Stresing, Robert; Peinke, Joachim

doi:10.1063/1.4907740

Cited by 15 publications

(9 citation statements)

References 74 publications

(112 reference statements)

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“…More recently, Hosokawa [52] showed a dependence between velocity increments and the local velocity sum that was broadly consistent with the conclusion of Praskovsky et al [51]. Further work on velocity dependence can be seen in studies that move away from considering the velocity increment moments (structure functions) to studying a Fokker-Planck equation for the evolution of the probability density function of the increments [53,54]. By further conditioning the distribution for p(∆u r |∆u 2r ) on the velocity, i.e.…”

Section: Velocity-intermittency Analysissupporting

confidence: 64%

Large eddy simulation of the velocity-intermittency structure for flow over a field of symmetric dunes

2016

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Owing to their frequent occurrence in the natural environment, there has been significant interest in refining our understanding of flow over dunes and other bedforms. Recent work in this area has focused, in particular, on their shear layer characteristics and the manner by which flow structures are generated. However, field-based studies, are reliant on single-, or multi-point measurements, rather than delimiting flow structures from the velocity gradient tensor as is possible in numerical work. Here, we extract pointwise time series from a well-resolved large-eddy simulation as a means to connect these two approaches. The at-a-point analysis technique is termed the velocityintermittency quadrant method and relates the fluctuating, longitudinal velocity, u ′ 1 (t), to its fluctuating pointwise Hölder regularity, α ′ 1 (t).Despite the difference in boundary conditions, our results agree very well with previous experiments that show the importance, in the region above the dunes, of a quadrant 3 (uflow configuration. Our higher density of sampling beneath the shear layer and close to the bedforms relative to past experimental work reveals a negative correlation between u ′ 1 (t) and α

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Section: Velocity-intermittency Analysissupporting

confidence: 64%

Large eddy simulation of the velocity-intermittency structure for flow over a field of symmetric dunes

2016

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“…Based on multi-scale statistics, found that fractal grid generated turbulence exhibits different scaling features and multi-scale statistics than commonly generated flows (cylinder wake and free jet), defining a novel class of turbulence. The work of ; Keylock et al (2015) gives first indications that the turbulent cascade and its Kramers-Moyal coefficients depend on the turbulence generation mechanism. This dependence on turbulence generation contrasts with the universal features found on the basis of 2-point statistics involving structure functions and its scaling exponents.…”

Section: Introductionmentioning

confidence: 99%

On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics

et al. 2018

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Features of the turbulent cascade are investigated for various datasets from three different turbulent flows, namely free jets as well as wake flows of a regular grid and a cylinder. The analysis is focused on the question as to whether fully developed turbulent flows show universal small scale features. Two approaches are used to answer this question. Firstly, 2-point statistics, namely structure functions of longitudinal velocity increments and secondly, joint multi-scale statistics of these velocity increments are analysed. The joint multi-scale characterisation encompasses the whole cascade in one joint probability density function. On the basis of the datasets, evidence of the Markov property for the turbulent cascade is shown, which corresponds to a three point closure that reduces the joint multi-scale statistics to simple conditional probability density functions (cPDF). The cPDF are described by the Fokker-Planck equation in scale and its Kramers-Moyal coefficients (KMCs). KMCs are obtained by a self-consistent optimisation procedure from the measured data and result in a Fokker-Planck equation for each dataset. The knowledge of these stochastic cascade equations enables to make use of the concepts of non-equilibrium thermodynamics and thus to determine the entropy production along individual cascade trajectories. In addition to this new concept, it is shown that the local entropy production is nearly perfectly balanced for all datasets by the integral fluctuation theorem (IFT). Thus the validity of the IFT can be taken as a new law of the turbulent cascade and at the same time independently confirms that the physics of the turbulent cascade is a memoryless Markov process in scale. IFT is taken as a new tool to prove the optimal functional form of the Fokker-Planck equations and subsequently to investigate the question of universality of small scale turbulence in the datasets. The results of our analysis show that the turbulent cascade contains universal and non-universal features. We identify small scale intermittency as a universality breaking feature. We conclude that specific turbulent flows have their own particular multi-scale cascade, with other words their own stochastic fingerprint.

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“…Given that the ρ = 0 surrogates in GWR remove multifractal characteristics, this formulation is very useful for studying the properties of multifractal signals as a function of ρ. For example, an analysis of the velocity increments in turbulence highlighted the importance of two (from four) parameters in a Fokker-Planck model for these increments for the nonlinear structure of turbulence [36]. Gradual wavelet reconstruction showed both that these terms, which are an order of magnitude smaller than the other two terms, are signicantly diferent to zero in turbulent lows and that they are crucial for controlling the multifractal behaviour.…”

Section: Introductionmentioning

confidence: 99%

Gradual multifractal reconstruction of time-series: Formulation of the method and an application to the coupling between stock market indices and their Hölder exponents

Keylock

2018

Physica D: Nonlinear Phenomena

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A technique termed gradual multifractal reconstruction (GMR) is formulated. A continuum is deined from a signal that preserves the pointwise H lder exponent (multifractal) structure of a signal but randomises the locations of the original data values with respect to this (φ = 0), to the original signal itself (φ = 1). We demonstrate that this continuum may be populated with synthetic time series by undertaking selective randomisation of wavelet phases using a dual-tree complex wavelet transform. That is, the φ = 0 end of the continuum is realised using the recently proposed iterated, amplitude adjusted wavelet transform algorithm [Keylock, C. J. 2017. Phys. Rev. E 95, 032123] that fully randomises the wavelet phases. This is extended to the GMR formulation by selective phase randomisation depending on whether or not the wavelet coeicient amplitudes exceeds a threshold criterion. An econophysics application of the technique is presented. The relation between the normalised log-returns and their H lder exponents for the daily returns of eight inancial indices are compared. One particularly noticeable result is the change for the two american indices (NASDAQ 100 and S&P 500) from a non-signiicant to a strongly signiicant (as determined using GMR) cross-correlation between the returns and their H lder exponents from before the 2008 crash to afterwards. This is also relected in the skewness of the phase diference distributions, which exhibit a geographical structure, with asian markets not exhibiting signiicant skewness in contrast to those from elsewhere globally.

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Gradual wavelet reconstruction of the velocity increments for turbulent wakes

Cited by 15 publications

References 74 publications

Large eddy simulation of the velocity-intermittency structure for flow over a field of symmetric dunes

Large eddy simulation of the velocity-intermittency structure for flow over a field of symmetric dunes

On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics

Gradual multifractal reconstruction of time-series: Formulation of the method and an application to the coupling between stock market indices and their Hölder exponents

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