The Wavenumber–Frequency Spectrum of Vortical and Internal-Wave Shear in the Western Arctic Ocean

Robert Pinkel Marine Physical Laboratory, Scripps Institution of Oceanography, La Jolla, California

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Abstract

Upper-ocean velocity and shear data were obtained from Doppler sonars operated at the Surface Heat Budget of the Arctic Ocean (SHEBA) ice camp during the camp’s year-long drift across the western Arctic Ocean. These are used to estimate wavenumber–frequency spectra of shear E(κz, σ) during three selected time intervals. The Arctic shear spectra are similar in form to typical oceanic spectra, except that they have roughly an order-of-magnitude less variance. The slope of the frequency dependence is also steeper (σ−3σ−4 for σ < −f, where f is the Coriolis frequency) in the internal-wave band, and the vertical wavenumber dependence is centered at higher wavenumber. Given the small vertical scales and low velocities of Arctic signals, a careful assessment of sonar precision is performed. Fluctuations at vertical scales > 10 m and time scales > 1 h are deemed significant. At subinertial frequencies, a vortical (quasigeostrophic) contribution to the shear spectrum is seen. The vertical wavenumber dependence of the shear spectrum in this frequency range is distinctly red, in contrast to the band-limited form of the superinertial spectrum; that is, E(κz, σ) ∼ κ−1z for |σ| < f. A fundamental characteristic of both the internal-wave and vortical spectral contributions is that the observed frequency bandwidth increases linearly with increasing vertical wavenumber magnitude. This is interpreted as the signature of the Doppler shifting of the observations by random “background” currents and by ice motion and is responsible for the distinctly “nonseparable” nature of the shear spectrum. As a consequence, the vertical wavenumber spectrum of the subinertial motion field is white: Evort(κz) = ∫Evort(κz, σ) κ0z.

Corresponding author address: Robert Pinkel, Marine Physical Laboratory, Scripps Institution of Oceanography, La Jolla, CA 92093-0213. Email: rpinkel@ucsd.edu

Abstract

Upper-ocean velocity and shear data were obtained from Doppler sonars operated at the Surface Heat Budget of the Arctic Ocean (SHEBA) ice camp during the camp’s year-long drift across the western Arctic Ocean. These are used to estimate wavenumber–frequency spectra of shear E(κz, σ) during three selected time intervals. The Arctic shear spectra are similar in form to typical oceanic spectra, except that they have roughly an order-of-magnitude less variance. The slope of the frequency dependence is also steeper (σ−3σ−4 for σ < −f, where f is the Coriolis frequency) in the internal-wave band, and the vertical wavenumber dependence is centered at higher wavenumber. Given the small vertical scales and low velocities of Arctic signals, a careful assessment of sonar precision is performed. Fluctuations at vertical scales > 10 m and time scales > 1 h are deemed significant. At subinertial frequencies, a vortical (quasigeostrophic) contribution to the shear spectrum is seen. The vertical wavenumber dependence of the shear spectrum in this frequency range is distinctly red, in contrast to the band-limited form of the superinertial spectrum; that is, E(κz, σ) ∼ κ−1z for |σ| < f. A fundamental characteristic of both the internal-wave and vortical spectral contributions is that the observed frequency bandwidth increases linearly with increasing vertical wavenumber magnitude. This is interpreted as the signature of the Doppler shifting of the observations by random “background” currents and by ice motion and is responsible for the distinctly “nonseparable” nature of the shear spectrum. As a consequence, the vertical wavenumber spectrum of the subinertial motion field is white: Evort(κz) = ∫Evort(κz, σ) κ0z.

Corresponding author address: Robert Pinkel, Marine Physical Laboratory, Scripps Institution of Oceanography, La Jolla, CA 92093-0213. Email: rpinkel@ucsd.edu

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