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A Model for Vortex-Trapped Internal Waves

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  • 1 School of Oceanography, University of Washington, Seattle, Washington
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Abstract

Regions of negative vorticity are observed to trap and amplify near-inertial internal waves, which are sources of turbulent mixing 10–100 times higher than typically found in the stratified ocean interior. Because these regions are of finite lateral extent, trapped waves will not form a continuum but be quantized in modes. A model for the radial structure of near-inertial azimuthal modes in an axisymmetric vortex is described in order to explain intense near-inertial motions observed in the cores of a Gulf Stream warm-core ring and a vortex cap above Fieberling Seamount. Observed signals exhibit little variability of the rectilinear phase ϕ = arctan(υ/u) in the core and evanesce rapidly outside the swirl velocity maximum, where u is the zonal velocity and υ the meridional velocity. The authors focus on azimuthal mode n = −1 (propagating clockwise around the vortex) and the gravest radial mode (no zero crossing) that appears to dominate observations. Model solutions resemble Bessel functions inside the velocity maximum and modified Bessel function decay outside, consistent with observations and solutions previously found by Kunze et al. using a less complete model. The improved model supports their conclusions concerning radial wavelengths, vertical group velocities, and energy fluxes for trapped waves.

* Current affiliation: College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon.

Corresponding author address: Dr. Eric Kunze, School of Oceanography, University of Washington, Box 357940, Seattle, WA 98195-7940.

Email: kunze@ocean.washington.edu

Abstract

Regions of negative vorticity are observed to trap and amplify near-inertial internal waves, which are sources of turbulent mixing 10–100 times higher than typically found in the stratified ocean interior. Because these regions are of finite lateral extent, trapped waves will not form a continuum but be quantized in modes. A model for the radial structure of near-inertial azimuthal modes in an axisymmetric vortex is described in order to explain intense near-inertial motions observed in the cores of a Gulf Stream warm-core ring and a vortex cap above Fieberling Seamount. Observed signals exhibit little variability of the rectilinear phase ϕ = arctan(υ/u) in the core and evanesce rapidly outside the swirl velocity maximum, where u is the zonal velocity and υ the meridional velocity. The authors focus on azimuthal mode n = −1 (propagating clockwise around the vortex) and the gravest radial mode (no zero crossing) that appears to dominate observations. Model solutions resemble Bessel functions inside the velocity maximum and modified Bessel function decay outside, consistent with observations and solutions previously found by Kunze et al. using a less complete model. The improved model supports their conclusions concerning radial wavelengths, vertical group velocities, and energy fluxes for trapped waves.

* Current affiliation: College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon.

Corresponding author address: Dr. Eric Kunze, School of Oceanography, University of Washington, Box 357940, Seattle, WA 98195-7940.

Email: kunze@ocean.washington.edu

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