Vertical wave number spectra of velocity and shear at small internal wave scales

Abstract

We analyze spectra from five sets of hourly vertical profiles of upper‐ocean horizontal velocity collected with the Cartesian Diver velocity recorder. Each set consists of 11 to 27 profiles over depth ranges of 25–220 m to 25–340 m. The vertical wave number (m) power spectra of velocity and shear have no reproducible power law form in the band [0.02–0.1] cpm. Shear spectra tend to rise then fall with increasing wave number, with the transition wave number mc varying within the above band. For shear spectra, steepness at m near 0.1 cpm ranges from m−1/2 to m−2. The data sets fall into two categories. For one group, inverse Richardson functions Ri−1(mc) have values near 2. Despite variability of velocity variance, these sets have Ri−1(0.1 cpm) ≈ 3, suggesting that shear is near saturation. Low variability of Ri−1(0.l), despite high kinetic energy variability for this group, suggests that energy at high wave number (and thus shear) is suppressed. This suggests that instability mechanisms attenuate spectra at high wave number, with attenuation becoming more broadband and influencing progressively lower vertical wave numbers (in addition to consistently influenced high wave numbers) at higher energy. For the other group, Ri−1(0.1) ≈ 1, shear spectra are less steep, and shear is concentrated at high wave number, suggesting less attenuation at the small‐scale end of our measurement band. For both groups, predicted wave numbers of spectral steepening, estimated from the data using two techniques, are related approximately inversely with horizontal kinetic energy in the band [0.005–0.01] cpm, quantifying the shear spectral roll‐off.