Advection, Phase Distortion, and the Frequency Spectrum of Finescale Fields in the Sea

Abstract

Abstract Continuous depth–time measurements of upper-ocean velocity are used to estimate the wavenumber–frequency spectrum of shear. A fundamental characteristic of these spectra is that the frequency bandwidth increases linearly with increasing wavenumber magnitude. This can be interpreted as the signature of Doppler shifting of the observations by time-changing “background” currents as well as by instrument motion. Here, the hypothesis is posed that the apparently continuous wavenumber–frequency spectrum of oceanic shear results from the advective “smearing” of discrete spectral lines. In the Arctic Ocean, lines at the inertial (ω = −f ) and vortical (ω = 0) frequencies (where f is the Coriolis frequency) account for most of the variance in the shear spectrum. In the tropical ocean, two classes of inertial waves are considered, accounting for 70% of the observed shear variance. A simple model is introduced to quantify the effects of lateral advection, random vertical advection (“fine-structure contamination”), and deterministic (tidal) vertical advection on these “otherwise monochromatic” records. Model frequency spectra are developed in terms of the probability density and/or spectrum of the advecting fields for general but idealized situations. The model successfully mimics the increasing frequency bandwidth of the shear spectrum with increasing vertical wavenumber. Excellent fits to the observed frequency spectrum of shear are obtained for the Arctic (weak advection and short-spatial-scale inertial waves) and low-latitude (strong advection and long and short inertial waves) observations. While successfully replicating the wavenumber–frequency spectrum of shear, the model does not even consider motion at scales greater than ∼250 m, the “energy containing” scales of the internal wave field. To a first approximation, the waves with the majority of the kinetic and potential energy constitute a population apart from those with the momentum, shear, and strain.