Breaking of Internal Waves Parametrically Excited by Ageostrophic Anticyclonic Instability

Yohei Onuki aResearch Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka, Japan
bENS de Lyon, CNRS, Laboratoire de Physique, Lyon, France

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Sylvain Joubaud bENS de Lyon, CNRS, Laboratoire de Physique, Lyon, France
cInstitut Universitaire de France, Paris, France

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Thierry Dauxois bENS de Lyon, CNRS, Laboratoire de Physique, Lyon, France

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Abstract

A gradient-wind balanced flow with an elliptic streamline parametrically excites internal inertia-gravity waves through ageostrophic anticyclonic instability (AAI). This study numerically investigates the breaking of internal waves and the following turbulence generation resulting from the AAI. In our simulation, we periodically distort the calculation domain following the streamlines of an elliptic vortex and integrate the equations of motion using a Fourier spectral method. This technique enables us to exclude the overall structure of the large-scale vortex from the computation and concentrate on resolving the small-scale waves and turbulence. From a series of experiments, we identify two different scenarios of wave breaking conditioned on the magnitude of the instability growth rate scaled by the buoyancy frequency λ/N. First, when λ/N0.008, the primary wave amplitude excited by AAI quickly goes far beyond the overturning threshold and directly breaks. The resulting state is thus strongly nonlinear turbulence. Second, if λ/N0.008, weak wave–wave interactions begin to redistribute energy across frequency space before the primary wave reaches a breaking limit. Then, after a sufficiently long time, the system approaches a Garrett–Munk-like stationary spectrum, in which wave breaking occurs at finer vertical scales. Throughout the experimental conditions, the growth and decay time scales of the primary wave energy are well correlated. However, since the primary wave amplitude reaches a prescribed limit in one scenario but not in the other, the energy dissipation rates exhibit two types of scaling properties. This scaling classification has similarities and differences with D’Asaro and Lien’s wave–turbulence transition model.

Significance Statement

Due to the gradients in buoyancy and pressure, density-stratified seawater supports oscillatory vertical motion called internal waves. When waves significantly skew a density isosurface, dense water lifts over lighter water resulting in gravitational instability and high energy dissipation. In this wave-breaking process, seawater is vertically mixed, transporting heat and nutrients essential to maintain Earth’s climate and ecosystems. This study investigates the generation and breaking of ocean internal waves in a novel numerical simulation setup; we temporally distort the model shape to emulate the wave excitation forced by a larger-size horizontal eddy, a ubiquitous situation at O(1–10) km scales in the upper ocean. The simulation results exhibit two unique wave-breaking scenarios with distinct scaling features in turbulence energy dissipation rates.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yohei Onuki, onuki@riam.kyushu-u.ac.jp

Abstract

A gradient-wind balanced flow with an elliptic streamline parametrically excites internal inertia-gravity waves through ageostrophic anticyclonic instability (AAI). This study numerically investigates the breaking of internal waves and the following turbulence generation resulting from the AAI. In our simulation, we periodically distort the calculation domain following the streamlines of an elliptic vortex and integrate the equations of motion using a Fourier spectral method. This technique enables us to exclude the overall structure of the large-scale vortex from the computation and concentrate on resolving the small-scale waves and turbulence. From a series of experiments, we identify two different scenarios of wave breaking conditioned on the magnitude of the instability growth rate scaled by the buoyancy frequency λ/N. First, when λ/N0.008, the primary wave amplitude excited by AAI quickly goes far beyond the overturning threshold and directly breaks. The resulting state is thus strongly nonlinear turbulence. Second, if λ/N0.008, weak wave–wave interactions begin to redistribute energy across frequency space before the primary wave reaches a breaking limit. Then, after a sufficiently long time, the system approaches a Garrett–Munk-like stationary spectrum, in which wave breaking occurs at finer vertical scales. Throughout the experimental conditions, the growth and decay time scales of the primary wave energy are well correlated. However, since the primary wave amplitude reaches a prescribed limit in one scenario but not in the other, the energy dissipation rates exhibit two types of scaling properties. This scaling classification has similarities and differences with D’Asaro and Lien’s wave–turbulence transition model.

Significance Statement

Due to the gradients in buoyancy and pressure, density-stratified seawater supports oscillatory vertical motion called internal waves. When waves significantly skew a density isosurface, dense water lifts over lighter water resulting in gravitational instability and high energy dissipation. In this wave-breaking process, seawater is vertically mixed, transporting heat and nutrients essential to maintain Earth’s climate and ecosystems. This study investigates the generation and breaking of ocean internal waves in a novel numerical simulation setup; we temporally distort the model shape to emulate the wave excitation forced by a larger-size horizontal eddy, a ubiquitous situation at O(1–10) km scales in the upper ocean. The simulation results exhibit two unique wave-breaking scenarios with distinct scaling features in turbulence energy dissipation rates.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yohei Onuki, onuki@riam.kyushu-u.ac.jp

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