Wavelets and turbulence

Farge, Marie; Kevlahan, Nicholas; Perrier, Valérie; Goirand, Eric

doi:10.1109/5.488705

Cited by 197 publications

(111 citation statements)

References 96 publications

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“…Therefore, we are restricted to investigating very high frequency events occurring at time scales up to 2 seconds. This limitation arises from Heisenberg's uncertainty principle, which dictates that one cannot obtain arbitrary good localisation in both time and frequency, and a trade-off must exist whereby spatial resolution is bad at large scales while scale (frequency) resolution is bad in the small scales (Farge et al, 1996;Foufoula-Georgiou and Kumar, 1994;Grinsted et al, 2004;Lau and Weng, 1995).…”

Section: Spectral Analysis Of Turbulence and Suspensionmentioning

confidence: 99%

Wave-induced coherent turbulence structures and sediment resuspension in the nearshore of a prototype-scale sandy barrier beach

Kassem

Thompson

Amos

et al. 2015

Continental Shelf Research

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Abstract:The suspension of sediments by oscillatory flows is a complex case of fluid-particle interaction. The aim of this study is to provide insight into the spatial (time) and scale (frequency) relationships between wave-generated boundary layer turbulence and eventdriven sediment transport beneath irregular shoaling and breaking waves in the nearshore of a prototype sandy barrier beach, using data collected through the Barrier Dynamics Experiment II (BARDEX II). Statistical, quadrant and spectral analyses reveal the anisotropic and intermittent nature of Reynolds' stresses (momentum exchange) in the wave boundary layer, in all three orthogonal planes of motion. The fractional contribution of coherent turbulence structures appears to be dictated by the structural form of eddies beneath plunging and spilling breakers, which in turn define the net sediment mobilisation towards or away from the barrier, and hence ensuing erosion and accretion trends. A standing transverse wave is also observed in the flume, contributing to the substantial skewness of spanwise turbulence. Observed low frequency suspensions are closely linked to the mean flow (wave) properties. Wavelet analysis reveals that the entrainment and maintenance of sediment in suspension through a cluster of bursting sequence is associated with the passage of intermittent slowly-evolving large structures, which can modulate the frequency of smaller motions. Outside the boundary layer, small scale, higher frequency turbulence drives the suspension. The extent to which these spatially varied perturbation clusters persist is associated with suspension events in the high frequency scales, decaying as the turbulent motion ceases to supply momentum, with an observed hysteresis effect. The suspension of sediment in turbulent flows is a complex case of fluid-particle interaction, governed by shear stresses (momentum exchanges) at the bed and within the benthic boundary layer (BBL). Defining the physical processes which dictate the resuspension of sediments in coastal and estuarine settings is fundamental for accurate predictions of bed morphology evolution (Van Rijn et al., 2007), and has profound implications for the biogeochemical processes that shape their local ecology (Thompson et al., 2011). It is also a prerequisite to quantifying erosion and deposition trends, and hence guiding engineering applications such as beach nourishment, defence schemes against erosion and flooding, maintenance of marine infrastructure and waterways, and aggregate dredging. There is a genuine need for better, robust models of suspended sediment transport in the coastal zone (Aagaard and Jensen, 2013). In a vision paper on future research needs in coastal dynamics, Van Rijn et al. (2013) highlighted the pressing need for research to support such models, focusing in particular on sand transport in the shoreface (non-breaking waves), surf and swash zones; employing field and controlled laboratory experiments.The mobilisation of sediments in the nearshore and shoreface is dominated b...

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Section: Spectral Analysis Of Turbulence and Suspensionmentioning

confidence: 99%

Wave-induced coherent turbulence structures and sediment resuspension in the nearshore of a prototype-scale sandy barrier beach

Kassem

Thompson

Amos

et al. 2015

Continental Shelf Research

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“…Note that if plotted as a function of time the total phase term θ = ωt + φ obtained from the wavelet transform (2.1) will exhibit a well-known sawtooth-like oscillation behaviour (Farge et al 1996). This behaviour appears as a consequence of the ωt term.…”

Section: The Wavelet Analysis Of Time-series Datamentioning

confidence: 99%

“…In equation (2.1) the wavelet transformation is written in the L 1 -norm, which conserves the modulus of the function to be transformed (Farge et al 1996). The localization of the wavelet in Fourier-physical space is governed by the dilatation parameter κ and by the time shift τ.…”

Section: The Wavelet Analysis Of Time-series Datamentioning

confidence: 99%

Temporal subharmonic amplitude and phase behaviour in a jet shear layer: wavelet analysis and Hamiltonian formulation

Gordeyev

Thomas

1999

J. Fluid Mech.

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Fourier and wavelet transformation techniques are utilized in a complementary manner in order to characterize temporal aspects of the transition of a planar jet shear layer. The subharmonic is found to exhibit an interesting temporal amplitude and phase variation that has not been previously reported. This takes the form of intermittent π-shifts in subharmonic phase between two fixed phase values. These phase jumps are highly correlated with local minima of the subharmonic amplitude. In contrast, the fundamental amplitude and phase show no such behaviour. The temporal phase behaviour of the subharmonic has the effect of intermittently disrupting the phase lock with the fundamental. A dynamical systems model is developed which is based on a classic vortex representation of the shear layer. The Hamiltonian formulation of the problem is shown to provide remarkable agreement with the experimental results. All the essential aspects of the temporal amplitude and phase behaviour of the subharmonic are reproduced by the model including amplitude-dependent effects. The model is also shown to provide a dynamical systems based explanation for time-averaged amplitude and phase behaviour observed in these as well as earlier experiments. The results of experiments involving both bimodal forcing at fundamental and subharmonic frequencies with prescribed initial effective phase angle as well as experiments involving only fundamental excitation over an amplitude range extending two orders of magnitude are presented. The temporal subharmonic amplitude and phase behaviour is observed in bimodal forcing experiments in those regions of the flow characterized by subharmonic mode suppression and vortex tearing events (even if the forcing amplitudes are quite large). In addition, temporal subharmonic amplitude and phase behaviour is the rule in experiments involving low-amplitude forcing of the fundamental and the natural development of the subharmonic.

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“…The presence of turbulence and dissipation can also be inferred through wavelet based approach.A turbulent power spectrum has characteristic slopes as -5/3 in the turbulent [23] and -7 in the viscous dissipation regime [24,25]. The Heisenberg model exhibits these power laws, where a smooth transition takes place between them.…”

Section: Continuous Wavelet Transform (Cwt)mentioning

confidence: 99%

Multi-scale dynamics of glow discharge plasma through wavelets: Self-similar behavior to neutral turbulence and dissipation

Giri

Mitra

Panigrahi

et al. 2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The multiscale dynamics of glow discharge plasma is analysed through wavelet transform, whose scale dependent variable window size aptly captures both transients and non-stationary periodic behavior. The optimal time-frequency localization ability of the continuous Morlet wavelet is found to identify the scale dependent periodic modulations efficiently, as also the emergence of neutral turbulence and dissipation, whereas the discrete Daubechies basis set has been used for detrending the temporal behavior to reveal the multi-fractality of the underlying dynamics. The scaling exponents and the Hurst exponent have been estimated through wavelet based detrended fluctuation analysis,and also Fourier methods and rescale range analysis.

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Wavelets and turbulence

Cited by 197 publications

References 96 publications

Wave-induced coherent turbulence structures and sediment resuspension in the nearshore of a prototype-scale sandy barrier beach

Wave-induced coherent turbulence structures and sediment resuspension in the nearshore of a prototype-scale sandy barrier beach

Temporal subharmonic amplitude and phase behaviour in a jet shear layer: wavelet analysis and Hamiltonian formulation

Multi-scale dynamics of glow discharge plasma through wavelets: Self-similar behavior to neutral turbulence and dissipation

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