Second-order structure function in fully developed turbulence

Huang, Yongxiang; Schmitt, François G; Lu, Ze-Qi; Fougairolles, P.; Gagne, Yves; Liu, Y. L.

doi:10.1103/physreve.82.026319

Cited by 64 publications

(107 citation statements)

References 32 publications

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“…Nam et al [33] theoretically showed that when the Ekman friction is present, the forward enstrophy cascade is then intermittent [34]. As already mentioned above this result is difficult to verify experimentally by using the conventional structure function analysis since the convergence condition requires the scaling exponent β of the Fourier spectrum, i.e., E(k) ∼ k −β , to be in the range (1,3) [1,12,32], see also discussion in Sec. III.…”

Section: Introductionmentioning

confidence: 99%

Intermittency measurement in two-dimensional bacterial turbulence

et al. 2016

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In this paper, an experimental velocity database of a bacterial collective motion , e.g., B. subtilis, in turbulent phase with volume filling fraction 84% provided by Professor Goldstein at the Cambridge University UK, was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the β−limitation. A dual-power-law behavior separated by the viscosity scale ℓ ν was observed for the qth-order Hilbert moment L q (k). This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale R, e.g., the bacterial body length.The measured scaling exponents ζ(q) of both the small-scale (resp. k > k ν ) and large-scale (resp. k < k ν ) motions are convex, showing the multifractality. A lognormal formula was put forward to characterize the multifractal intensity. The measured intermittency parameters are µ S = 0.26 and µ L = 0.17 respectively for the small-and large-scale motions. It implies that the former cascade is more intermittent than the latter one, which is also confirmed by the corresponding singularity spectrum f (α) vs α. Comparison with the conventional two-dimensional Ekman-Navier-Stokes equation, a continuum model indicates that the origin of the multifractality could be a result of some additional nonlinear interaction terms, which deservers a more careful investigation. *

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Section: Introductionmentioning

confidence: 99%

Intermittency measurement in two-dimensional bacterial turbulence

et al. 2016

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“…In future work we plan to consider multifractal properties of pH fluctuations, using structure functions or, to avoid perturbation by energetic large scales (Huang et al, 2010), recent methods based on empirical mode decomposition .…”

Section: Discussionmentioning

confidence: 99%

“…The dotted lines correspond to power laws of slope 0.2 and 0.3, corresponding respectively to active or passive scalar turbulence (Monin and Yaglom, 1975) (see below). The scaling range is limited here, possibly due to contamination from periodic forcing, which may destroy the scaling of structure functions but is less problematic in the Fourier space (see Huang et al, , 2010. …”

Section: Ph Pdfsmentioning

confidence: 99%

“…Furthermore, the mean marine pH value is also more and more cited as a key issue in the framework of climate change, where the increased dissolved CO 2 is assumed to be associated with a decrease of the mean oceanic pH Wickett, 2003, 2005;Blackford and Gilbert, 2007;Iglesias-Rodriguez et al, 2008). This predicted acidification of the global ocean, computed by global models, is expected to be a problem for many trophic entities, including some phytoplankton organisms and for the coral reef (Kleypas et al, 1999;Anthony et al, 2008;Wootton et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

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Scaling properties of pH fluctuations in coastal waters of the English Channel: pH as a turbulent active scalar

Zongo

Schmitt

2011

Nonlin. Processes Geophys.

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Abstract. We consider here pH and temperature fluctuations in marine waters, recorded at fixed points using high resolution automatic devices. We analyze time series coming from 4 monitoring stations located along French coast: one station is situated in the coastal area off Boulogne-sur-mer (Eastern English Channel) and 3 stations in the Bay of Seine. All these pH time series reveal large fluctuations at all scales similar to turbulent temperature fluctuations. We compare the pH and temperature time series through Fourier spectral analysis methods: spectra, compensated spectra, cospectra. We find good scaling properties of pH fluctuations, with power spectral slopes close to 1.5 for marine stations and 1.2 for the estuarine station. These analyses show that pH fluctuations in marine waters are strongly influenced by turbulent hydrodynamical transport, and may be considered as a turbulent active scalar.

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“…Since surface waves often occupy the same frequency range as marine turbulence, it is difficult to separate the latter from waveinduced velocity fluctuations using simple filtration. Therefore, development of various techniques and methods capable to remove the bias produced by surface waves from ADCP measurements of turbulent shear stress was an important issue over the past decade (Shaw and Trowbridge, 2001;Trowbridge and Elgar, 2003;Whipple et al, 2006;Feddersen and Williams, 2007;Rosman et al, 2008;Schmitt et al, 2009;Huang et al, 2010;Kirincich et al, 2010). This paper addresses two challenges.…”

Section: K a Korotenko Et Al: Effect Of Variable Winds On Current mentioning

confidence: 99%

Effect of variable winds on current structure and Reynolds stresses in a tidal flow: analysis of experimental data in the eastern English Channel

2012

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Abstract. Wind and wave effects on tidal current structure and turbulence throughout the water column are examined using an upward-looking acoustic Doppler current profiler (ADCP). The instrument has been deployed on the seafloor of 18-m mean depth, off the north-eastern French coast in the eastern English Channel, over 12 tidal cycles, and covered the period of the transition from mean spring to neap tide, and forcing regimes varied from calm to moderate storm conditions. During storms, we observed gusty winds with magnitudes reaching 15 m s −1 and wave heights reaching up to 1.3 m. Analysis of velocity spectra revealed a noticeable contribution of wind-induced waves to spectral structure of velocity fluctuations within the subsurface layer. Near the surface, stormy winds and waves produced a significant intensification of velocity fluctuations, particularly when the sustained wind blew against the ebb tide flow. As during wavy periods, the variance-derived Reynolds stress estimates might include a wave-induced contamination, we applied the Variance Fit method to obtain unbiased stresses and other turbulent quantities. Over calm periods, the turbulent quantities usually decreased with height above the seabed. The stresses were found to vary regularly with the predominantly semidiurnal tidal flow. The along-shore stress being generally greater during the flood flow (∼ 2.7 Pa) than during the ebb flow (∼ −0.6 Pa). The turbulent kinetic energy production rate, P , and eddy viscosity, A z , followed a nearly regular cycle with close to a quarter-diurnal period. As for the stresses, near the seabed, we found the maximum values of estimated quantities of P and A z to be 0.1 Wm −3 and 0.5 m 2 s −1 , respectively, during the flood flow. Over the storm periods, we found the highest unbiased stress values (∼ −2.6 Pa) during ebb when tidal currents were opposite to the southwesterly winds while, during the flood, the surface stresses slightly exceeded those estimated for a calm period. A comparison of obtained results gives a good agreement with those of other researchers working on direct measurements of turbulence in tidal flows.

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Second-order structure function in fully developed turbulence

Cited by 64 publications

References 32 publications

Intermittency measurement in two-dimensional bacterial turbulence

Intermittency measurement in two-dimensional bacterial turbulence

Scaling properties of pH fluctuations in coastal waters of the English Channel: pH as a turbulent active scalar

Effect of variable winds on current structure and Reynolds stresses in a tidal flow: analysis of experimental data in the eastern English Channel

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