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Frequency–wavenumber velocity spectra, Taylor's hypothesis, and length scales in a natural gravel bed river
Author(s) -
MacMahan Jamie,
Reniers Ad,
Ashley Will,
Thornton Ed
Publication year - 2012
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2011wr011709
Subject(s) - froude number , spectral line , wavenumber , reynolds number , wavelength , length scale , turbulence , spectral slope , physics , geology , geometry , flow (mathematics) , mechanics , optics , mathematics , astronomy
Macroscale 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 streamwise horizontal length scales and persistence of coherent flow structures by measuring the frequency ( f )‐streamwise‐wavenumber ( k s ) energy density velocity spectrum, E ( f , k s ), 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 (∼10 6 ) based on depth and velocity conditions within a gravel bed reach of the Kootenai River, Idaho. 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 s ) spectra fell along a ridge described by V = f / k s , where V is the mean velocity over depth, consistent with Taylor’s hypothesis. New, consistent length scale measures are defined based on averaged wavelengths of the low‐frequency E ( f , k s ) and coherence spectra. Energetic (∼50% of the total spectral energy), low‐frequency (f < 0.05 Hz) streamwise motions were found. Mean length scales, L m , compared with the depth, h , are significantly larger than previously suggested for macroturbulence with L m / h ∼ 28–118. Although the energy appears as low‐pass white noise, it is streamwise coherent along the length of the array. In fast flows with velocities > 1 m/s, L m 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 preexisting macroturbulent motions by the ubiquitous bathymetry‐induced spatial flow accelerations present in a natural gravel bed river.