Effect of finite spatial resolution on the turbulent energy spectrum measured in the coastal ocean bottom boundary layer

Abstract

The effect of finite spatial resolution on the measured energy spectrum is examined via a parametric study using in situ particle image velocimetry (PIV) measurements performed in the bottom boundary layer on the Atlantic continental shelf. Two-dimensional (2D) box spatial filters of various scales are applied to the data, and these filtered distributions are used to compute 1D energy spectra in both frequency and wavenumber domains. It is found that energy levels are attenuated by more than 15% at all length scales that are smaller than 10 times the scale of the filter. Filtering both in the direction of the spectrum as well as perpendicular to it contributes to the extent of attenuation, the latter via implicit integration over all wavenumbers. At scales larger than that of the filter, Gaussian, nonlinear Butterworth, and median filters attenuate less energy than the box filter. When frequency spectra are converted using Taylor's hypothesis, wave energy appears in wavenumber space at a location different than its true physical scale, which is much larger than the filter sizes. Consequently, wave energy is not attenuated and dominates over the turbulence through this spectral range. Because wave energy and turbulence respond differently to the filtering, modified spectral slopes at the transition between wave- and turbulence-dominated regions occur, resulting in inordinately steep spectral slopes. Finally, removal of the pressure-coherent part of the velocity signal is not sufficient to reveal the turbulence within the wave peak spectral range. Remaining energy in this range is still dominated by much larger scales. © 2009 American Meteorological Society.