Frequency-Wavenumber Velocity Spectra, Taylor's Hypothesis and Length-Scales in a Natural Gravel-Bed River
Abstract
Macro-scale turbulent coherent flow structures in a natural fast-flowing river were examined with a combination of a novel 2 MHz Acoustic Doppler Beam (ADB) and a Maximum Likelihood Estimator (MLE) to characterize the stream-wise horizontal length scales and persistence of coherent flow structures by measuring the frequency (f)- streamwise-wavenumber (k) energy density velocity spectrum, E(f,k ), for the first time in natural rivers. The ADB was deployed under a range of Froude numbers (0.1-0.6) at high Reynolds Numbers based on depth and velocity conditions within a gravel-bed reach of the Kootenai River, ID. The MLE employed on the ADB data increased our ability to describe river motions with relatively long (>10 m) length scales in ~1 m water depths. The E(f,k) fall along a ridge described by V=f/k, where V is the mean velocity over depth, verifying Taylor's hypothesis. New, consistent length scale measures are defined based on averaged wave lengths of the low frequency E(f,k) and coherence spectra. Energetic (~50% of the total spectral energy), low-frequency (f<0.05Hz) stream-wise motions were found. Mean length scales, L, compared with the depth, h, are significantly larger than previously suggested for macro-turbulence with L/h ~ 28 - 118. Although the energy appears as low-pass white noise, it is stream-wise coherent along the length of the array. In fast flows with velocities >1 m/s, L were found to be significantly longer than their corresponding coherence lengths suggesting that the turbulent structures evolve rapidly under these conditions. This is attributed to the stretching and concomitant deformation of pre-existing macro-turbulent motions by the ubiquitous bathymetry-induced spatial flow accelerations present in a natural gravel-bed river.Mean motion lengths, Lm, (circles) and coherence lengths, Lc, (squares) as a function of the mean streamwise velocity at locations in Zones 1-4.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2012
- Bibcode:
- 2012AGUFMEP52A..06T
- Keywords:
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- 1872 HYDROLOGY / Time series analysis;
- 1895 HYDROLOGY / Instruments and techniques: monitoring