Frequency–wavenumber velocity spectra, Taylor's hypothesis, and length scales in a natural gravel bed river

Abstract

[1] 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.Citation: MacMahan, J., A. Reniers, W. Ashley, and E. Thornton (2012), Frequency-wavenumber velocity spectra, Taylor's hypothesis, and length scales in a natural gravel bed river, Water Resour. Res., 48, W09548,

Hydrodynamics of intertidal oyster reefs: The influence of boundary layer flow processes on sediment and oxygen exchange

“…For f > 3 Hz there is an expected drop‐off in the spectrum, down to the noise level. Using Taylor's frozen turbulence hypothesis where advection of turbulence past a fixed point can be assumed to be entirely due to the mean flow, frequency was converted to wavenumber as k = f / U (MacMahan et al 2012) and is shown on the upper x ‐axis in Fig. 5.…”

A note on Taylor's hypothesis under large-scale flow variation

“…The validity of this approximation has widely been studied in various geophysical field and laboratory experiments; some examples include oceanic and surface-water turbulence (MacMahan et al, 2012), atmospheric turbulence (Lappe and Davidson, 1963;Mizuno and Panofsky, 1975;Castro et al, 2011), precipitation field distributions in meteorology (Li et al, 2009), wall turbulence (Uddin et al, 1997), and wind tunnel experiments (LeBoeuf and Mehta, 1995).…”

Airborne space-time EO/IR imaging for measuring riverine/estuarine/coastal currents

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