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| Titel |
Cross-correlation between time scales in open-channel river flows |
| VerfasserIn |
Mário J. Franca, Rui M. L. Ferreira, Ulrich Lemmin |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250052980
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| Zusammenfassung |
| In natural river flows different length scales coexist simultaneously including grain scale (e.g.
grain roughness), meso-scale (e.g. bed forms, bank forms and vegetation patches or
elements) and morphological scale (e.g. channel configuration, bends, braiding,
etc.). These length scales have an impression on time scales and, consequently, a
wide range of time-scales co-exists as well which may be analyzed in an Euleurian
frame. Several authors argue that these scales are not independent thus interaction is
expected across energy spectra of instantaneous velocities signals between different
but specific scales. A formal theoretical framework to account for the interaction
between scales of these flows acquires additional complexity when compared to
time-averaged approaches applied to turbulent river flows. In the present research
we study the importance of the cross-correlation between time coherent motions
at different scales and how can this be included in conservation equations. This
analysis is based on 15 instantaneous 3D velocities profiles measured in an armoured
gravel-bed river by means of an Acoustic Doppler Velocity Profiler. 3D instantaneous
velocity profiles were measured with a vertical resolution of 5Â mm in a 0.30x0.40Â m2
horizontal grid for 3.5Â min each with an acquisition frequency of 26Â Hz. With
a water depth of 0.20Â m and the bed material composed of coarse round gravel
with a D50 of 68 mm, the riverbed is hydraulically rough and the flow has relative
submergence of 2.9 (ratio of the water depth by D50). Previous work using the
present data concerned the identification of coherent structures existing within narrow
reaches of the flow energy spectra by means of wavelet decomposition. We identified
and reconstructed a low-frequency oscillation in the streamwise velocity as well,
corresponding to large-scale regions of velocity alternating higher or lower than the
mean using Empirical Mode Decomposition to isolate the oscillation and phase
averaging techniques based on a Hilbert transform of the velocity signal to reconstruct
them. Here a multiple-scale analysis is carried out where the interaction between
different scale bands becomes evident and can be characterized and quantified.
Conditional sampling techniques and wavelet multilevel decomposition of single point
instantaneous velocity measurements are used to isolate the signal corresponding
to a particular scale (the most energetic scale, in the present case). Subsequently,
cross-correlation between the sampled data and the residual signal is analyzed and
discussed. The global contribution of a particular scale to total normal stresses and
also to local stresses within one coherent structure phase cycle is examined. The
present results constitute an attempt to quantify the interaction between different
scales within the flow turbulent structure. A decomposition of the instantaneous
velocity signal accounting for several scales is proposed and the implication of this in
conservation equations (namely momentum equations) is assessed. For time-averaged
quantities, cross-moments between energetic scales and residual signal are insignificant
and negligible. However, for individual coherent events, these crossed interactions
acquire importance for the local flow energy. Cross-moments are never higher than
0.2 of the total signal energy. The results show the importance of the averaging
window for each flow analysis and indicate that further sampling and correlation
techniques have to be applied to determine the interaction between scales. In the future,
the formal introduction of multiple-scale decomposition into transport equations,
with the development of new terms accounting for interaction between scales, is
envisaged.
Research supported by Portuguese Foundation for Science and Technology
(PTDC/ECM/099752/2008) and by the Swiss National Science Foundation (2000-063818). |
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