Hilbert Transform from Wavelet Analysis to Extract the Envelope of an Atmospheric Mode: Examples

Ouergli, A.

doi:10.1175/1520-0426(2002)019<1082:htfwat>2.0.co;2

Cited by 11 publications

(6 citation statements)

References 12 publications

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“…Based on this observation, Mathis, Hutchins & Marusic (2009a) developed a mathematical tool to accurately quantify the degree of amplitude modulation exerted by the largescale events onto the near-wall small-scale structures. Instead of using the Fourier transformation commonly used in turbulence signals analysis, they introduced the Hilbert transformation, which is a more appropriate tool for amplitude-modulated signals (Spark & Dutton 1972;Hristov, Friehe & Miller 1998;Huang, Shen & Long 1999;Ouergli 2002). They quantify the degree of amplitude modulation by calculating the correlation coefficient between the large scales (obtained using a lowpass Fourier filter) and the envelope of the small scales (obtained using the Hilbert transform).…”

Section: Background and Motivationmentioning

confidence: 99%

A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows

2011

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A model is proposed with which the statistics of the fluctuating streamwise velocity in the inner region of wall-bounded turbulent flows are predicted from a measured largescale velocity signature from an outer position in the logarithmic region of the flow. Results, including spectra and all moments up to sixth order, are shown and compared to experimental data for zero-pressure-gradient flows over a large range of Reynolds numbers. The model uses universal time-series and constants that were empirically determined from zero-pressure-gradient boundary layer data. In order to test the applicability of these for other flows, the model is also applied to channel, pipe and adverse-pressure-gradient flows. The results support the concept of a universal inner region that is modified through a modulation and superposition of the large-scale outer motions, which are specific to the geometry or imposed streamwise pressure gradient acting on the flow. Key words: boundary layers IntroductionRecently, the authors presented a predictive model for the streamwise velocity statistics in the near-wall region of zero-pressure-gradient turbulent boundary layers, where the only input required is a large-scale velocity signature from a wall-normal position further from the wall (Marusic, Mathis & Hutchins 2010b, hereafter referred to as MMH). Here, we show the full details of the model, including the procedures for evaluating the constants and functions that make up the mathematical model, and provide insights into the underlying turbulent boundary layer mechanisms that make up the mathematical formulation. Moreover, new tests have been provided in order to demonstrate the validity and reliability of the model. We also extend the comparison to additional statistics, such as the spectrum across the entire near-wall region, and present all moments up to the sixth order (u 6 ). Furthermore, we extend the comparison of the model to wall-bounded flows different to the zero-pressuregradient case. This addresses a comment by Adrian (2010), in the related Science perspectives article, for the need of future work to evaluate the model 'for flow geometries different from the flat plate'. This has subsequently been done and here we show the comparison of the model with experimental results in channel flow, pipe flow and an adverse-pressure-gradient turbulent boundary layer.

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Section: Background and Motivationmentioning

confidence: 99%

A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows

2011

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“…In this paper, we expand upon the initial observations of Hutchins & Marusic (2007b), using the Hilbert transformation in an attempt to quantify the relationship between large-scale fluctuations and any amplitude modulation of the small-scale energy in turbulent boundary layers. The Hilbert transform is particularly well suited to the analysis of amplitude modulation interactions and has often been used in the study of geophysical and atmospheric processes (Spark & Dutton 1972;Hristov, Friehe & Miller 1998;Huang, Shen & Long 1999;Ouergli 2002). However, its use in turbulence studies is far less common than say the Fourier transform.…”

Section: Introductionmentioning

confidence: 99%

Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers

2009

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In this paper we investigate the relationship between the large- and small-scale energy-containing motions in wall turbulence. Recent studies in a high-Reynolds-number turbulent boundary layer (Hutchins & Marusic, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007a, pp. 647–664) have revealed a possible influence of the large-scale boundary-layer motions on the small-scale near-wall cycle, akin to a pure amplitude modulation. In the present study we build upon these observations, using the Hilbert transformation applied to the spectrally filtered small-scale component of fluctuating velocity signals, in order to quantify the interaction. In addition to the large-scale log-region structures superimposing a footprint (or mean shift) on the near-wall fluctuations (Townsend, The Structure of Turbulent Shear Flow, 2nd edn., 1976, Cambridge University Press; Metzger & Klewicki, Phys. Fluids, vol. 13, 2001, pp. 692–701.), we find strong supporting evidence that the small-scale structures are subject to a high degree of amplitude modulation seemingly originating from the much larger scales that inhabit the log region. An analysis of the Reynolds number dependence reveals that the amplitude modulation effect becomes progressively stronger as the Reynolds number increases. This is demonstrated through three orders of magnitude in Reynolds number, from laboratory experiments at Reτ ~ 103–104 to atmospheric surface layer measurements at Reτ ~ 106.

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“…Moreover, for analysis of non-stationary and non-linear univariate time series there are alternative methods, such as the empirical mode decomposition of Huang (Huang et al, 1998) and wavelet analysis (Torrence and Compo, 1998), which have been applied successfully in atmospheric and climate studies (e.g. Wu et al, 1999;Wang et al, 2000;Ouergli, 2002;Coughlin, 2003;Duffy, 2004).…”

Section: Methodsmentioning

confidence: 99%

Surface air temperature variability over turkey and its connection to large-scale upper air circulation via multivariate techniques

2005

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The problem of statistical linkages between large-scale and local-scale processes is investigated through noise reduction by singular spectrum analysis (SSA) and spatial principal component analysis in order to construct appropriate statistical models for estimating the local-scale climate variables from large-scale climate processes. This paper presents an approach for downscaling monthly temperature series over Turkey by upper air circulations derived from the National Centers for Environmental Prediction-National Center for Atmospheric Research Reanalysis data sets (500 hPa geopotential heights and 500-1000 hPa thicknesses). The proposed approach consists of three stages. First, the available data sets are separated into deterministic, statistical components and random components by SSA. Second, the deterministic components are saved and the random components are eliminated by spatial principal component analysis. Subsequently, the statistical components are combined with the deterministic components constituting a noise-free data set. Furthermore, so-called Sampson correlation patterns are determined between the noise-free large-scale and the local-scale variables for interpreting the large-scale process impacts on local-scale features. Third, the significant redundancy variates based on canonical correlation analysis are extracted in order to identify the statistical downscaling model for temperature series of 62 stations in Turkey. The results show that the interpretation of the local-scale processes with the noise-free data sets is more significant than with the raw data sets.

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Hilbert Transform from Wavelet Analysis to Extract the Envelope of an Atmospheric Mode: Examples

Cited by 11 publications

References 12 publications

A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows

A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows

Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers

Surface air temperature variability over turkey and its connection to large-scale upper air circulation via multivariate techniques

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