Estimates of the Vertical Wavenumber–Frequency Spectra of Vertical Shear and Strain

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  • 1 Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
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Abstract

Measurements of vertical shear and strain were acquired from the research platform FLIP during the PATCHEX experiment in October, 1986 (34°N, 127°W). Vertical sheer was shear from two separate Doppler sonar systems. A long-range sonar, with independent estimates every 18 m, sampled from 150–1200 m in depth. A short-range sonar measured fine-scale shear over 150–180 m depth, with 1.5 m vertical resolution. Vertical strain, ∂η/∂z, was estimated from two repeatedly profiling CTDs. These sampled to 560 m once every three minutes. The time variation of the strain field is monitored in both Eulerian (fixed-depth) and semi-Lagrangian (isopycnal-following) reference frames, from 150–406 m depth.

Eulerian vertical wavenumber-frequency (m, ω) spectra of vertical shear and strain exhibit a frequency dependency which is a strong function of wavenumber (ω−2–ω0 for m = 0.01–0.3 cpm). In contrast the semi-Lagrangian strain spectrum is more nearly separable in frequency and wavenumber, in closer agreement with the Garrett–Munk (GM) internal wave spectral model.

When a simulated GM shear field is vertically advected by a GM isopycnal displacement field, the resultant Eulerian vertical wavenumber–frequency spectrum exhibits the same qualitative, nonseparable, form as the PATCHEX shear spectrum: The dominant near-inertial waves are Doppler-shifted across all frequency bands, resulting in a “while” frequency spectrum at high wavenumbers. Measured ratios of Eulerian shear/strain variance support this interpretation. Higher shear-low strain variances (characteristic of near-inertial waves) are seen at high wavenumber, high encounter frequencies. The conclusion is that internal wave vertical self-advection strongly alters the observed frequency at high vertical wavenumbers in an Eulerian reference frame.

Abstract

Measurements of vertical shear and strain were acquired from the research platform FLIP during the PATCHEX experiment in October, 1986 (34°N, 127°W). Vertical sheer was shear from two separate Doppler sonar systems. A long-range sonar, with independent estimates every 18 m, sampled from 150–1200 m in depth. A short-range sonar measured fine-scale shear over 150–180 m depth, with 1.5 m vertical resolution. Vertical strain, ∂η/∂z, was estimated from two repeatedly profiling CTDs. These sampled to 560 m once every three minutes. The time variation of the strain field is monitored in both Eulerian (fixed-depth) and semi-Lagrangian (isopycnal-following) reference frames, from 150–406 m depth.

Eulerian vertical wavenumber-frequency (m, ω) spectra of vertical shear and strain exhibit a frequency dependency which is a strong function of wavenumber (ω−2–ω0 for m = 0.01–0.3 cpm). In contrast the semi-Lagrangian strain spectrum is more nearly separable in frequency and wavenumber, in closer agreement with the Garrett–Munk (GM) internal wave spectral model.

When a simulated GM shear field is vertically advected by a GM isopycnal displacement field, the resultant Eulerian vertical wavenumber–frequency spectrum exhibits the same qualitative, nonseparable, form as the PATCHEX shear spectrum: The dominant near-inertial waves are Doppler-shifted across all frequency bands, resulting in a “while” frequency spectrum at high wavenumbers. Measured ratios of Eulerian shear/strain variance support this interpretation. Higher shear-low strain variances (characteristic of near-inertial waves) are seen at high wavenumber, high encounter frequencies. The conclusion is that internal wave vertical self-advection strongly alters the observed frequency at high vertical wavenumbers in an Eulerian reference frame.

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