Normal-Mode Decomposition of Small-Scale Oceanic Motions

Abstract

Small-scale oceanic motions consist of vortical motion and internal waves. In a linear or weakly nonlinear system these two types of motions can be unambiguously separated using normal-mode decomposition in which the vortical mode carries the linear perturbation potential vorticity, whereas the gravity mode does not. Normal-mode decomposition can be easily achieved using the fields of horizontal divergence, relative vorticity, and vortex stretching. An attempt to estimate these three fields is made using the Internal Wave Experiment (IWEX) measurements. Estimates of horizontal divergence and relative vorticity using the three-point array are attenuated at horizontal scales smaller than the size of the array and mutually contaminated at the horizontal separation scale of the sensors. Estimates of vortex stretching using vertically separated vertical displacement measurements are also attenuated at small vertical scales. The observed frequency spectra represent oceanic wavenumber frequency spectra subjected to array response functions as spectral windows. In principle, wavenumber frequency spectra can be obtained by applying inverse transformations provided that frequency spectra at different array sizes and vertical separations are measured. The IWEX array does not have a sufficient spatial resolution to reliably perform all of the necessary inverse transformations. Spectral estimates are compared with the GM-76 internal wave spectrum model. Observed frequency spectral estimates of horizontal divergence agree well with the GM model at small Rossby numbers in the entire internal wave frequency band and at moderate Rossby number O(1) in the low-frequency regime (?<1 cph). In contrast, frequency spectra of estimated relative vorticity agree with the GM model only at small Rossby numbers in the low-frequency regime (?≤0.1 cph). Since the calculation of horizontal divergence and relative vorticity spectra for the GM-76 model employs the dispersion relation of linear internal waves, the observed discrepancy could be due to either the failure of the linearity assumption or the existence of small-scale vortical motion. Spectral estimates of vortex stretching are well explained by the GM model, suggesting that fluctuations of vortex stretching are dominated by the gravity mode at vertical scales greater than O(34 m), the smallest resolvable vertical scale in this analysis.