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1. The propagation and decay of a coastal vortex on a shelf

   https://doi.org/10.1017/jfm.2021.790  

   Crowe, Matthew N.; Johnson, Edward R. (November 2021, Journal of Fluid Mechanics)

   A coastal eddy is modelled as a barotropic vortex propagating along a coastal shelf. If the vortex speed matches the phase speed of any coastal trapped shelf wave modes, a shelf wave wake is generated leading to a flux of energy from the vortex into the wave field. Using a simple shelf geometry, we determine analytic expressions for the wave wake and the leading-order flux of wave energy. By considering the balance of energy between the vortex and wave field, this energy flux is then used to make analytic predictions for the evolution of the vortex speed and radius under the assumption that the vortex structure remains self-similar. These predictions are examined in the asymptotic limit of small rotation rate and shelf slope and tested against numerical simulations. If the vortex speed does not match the phase speed of any shelf wave, steady vortex solutions are expected to exist. We present a numerical approach for finding these nonlinear solutions and examine the parameter dependence of their structure. 

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2. The Propagation and Decay of a Coastal Vortex on a Shelf

   Crowe, M; Johnson, E (January 2021, Journal of fluid mechanics)

   null (Ed.)

   A coastal eddy is modelled as a barotropic vortex propagating along a coastal shelf. If the vortex speed matches the phase speed of any coastal trapped shelf wave modes, a shelf wave wake is generated leading to a ux of energy from the vortex into the wave eld. Using a simply shelf geometry, we determine analytic expressions for the wave wake and the leading order ux of wave energy. By considering the balance of energy between the vortex and wave eld, this energy ux is then used to make analytic predictions for the evolution of the vortex speed and radius under the assumption that the vortex structure remains self similar. These predictions are examined in the asymptotic limit of small rotation rate and shelf slope and tested against numerical simulations. If the vortex speed does not match the phase speed of any shelf wave, steady vortex solutions are expected to exist. We present a numerical approach for nding these nonlinear solutions and examine the parameter dependence of their structure. 

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3. Interaction of near-inertial waves with an anticyclonic vortex

   https://doi.org/10.1175/JPO-D-20-0257.1  

   Kafiabad, Hossein A.; Vanneste, Jacques; Young, William R. (April 2021, Journal of Physical Oceanography)

   null (Ed.)

   Abstract Anticyclonic vortices focus and trap near-inertial waves so that near-inertial energy levels are elevated within the vortex core. Some aspects of this process, including the nonlinear modification of the vortex by the wave, are explained by the existence of trapped near-inertial eigenmodes. These vortex eigenmodes are easily excited by an initialwave with horizontal scale much larger than that of the vortex radius. We study this process using a wave-averaged model of near-inertial dynamics and compare its theoretical predictions with numerical solutions of the three-dimensional Boussinesq equations. In the linear approximation, the model predicts the eigenmode frequencies and spatial structures, and a near-inertial wave energy signature that is characterized by an approximately time-periodic, azimuthally invariant pattern. The wave-averaged model represents the nonlinear feedback of the waves on the vortex via a wave-induced contribution to the potential vorticity that is proportional to the Laplacian of the kinetic energy density of the waves. When this is taken into account, the modal frequency is predicted to increase linearly with the energy of the initial excitation. Both linear and nonlinear predictions agree convincingly with the Boussinesq results. 

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4. Stimulated generation: extraction of energy from balanced flow by near-inertial waves

   https://doi.org/10.1017/jfm.2018.308  

   Rocha, Cesar B.; Wagner, Gregory L.; Young, William R. (July 2018, Journal of Fluid Mechanics)

   We study stimulated generation – the transfer of energy from balanced flows to existing internal waves – using an asymptotic model that couples barotropic quasi-geostrophic flow and near-inertial waves with $$\text{e}^{\text{i}mz}$$ vertical structure, where $$m$$ is the vertical wavenumber and $$z$$ is the vertical coordinate. A detailed description of the conservation laws of this vertical-plane-wave model illuminates the mechanism of stimulated generation associated with vertical vorticity and lateral strain. There are two sources of wave potential energy, and corresponding sinks of balanced kinetic energy: the refractive convergence of wave action density into anti-cyclones (and divergence from cyclones); and the enhancement of wave-field gradients by geostrophic straining. We quantify these energy transfers and describe the phenomenology of stimulated generation using numerical solutions of an initially uniform inertial oscillation interacting with mature freely evolving two-dimensional turbulence. In all solutions, stimulated generation co-exists with a transfer of balanced kinetic energy to large scales via vortex merging. Also, geostrophic straining accounts for most of the generation of wave potential energy, representing a sink of 10 %–20 % of the initial balanced kinetic energy. However, refraction is fundamental because it creates the initial eddy-scale lateral gradients in the near-inertial field that are then enhanced by advection. In these quasi-inviscid solutions, wave dispersion is the only mechanism that upsets stimulated generation: with a barotropic balanced flow, lateral straining enhances the wave group velocity, so that waves accelerate and rapidly escape from straining regions. This wave escape prevents wave energy from cascading to dissipative scales. 

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5. The transition of tidal Kelvin waves to hybrid Kelvin edge and internal waves in the global ocean

   https://doi.org/10.1016/j.csr.2022.104734  

   Kaur, Harpreet; Buijsman, Maarten C; Yankovsky, Alexander E; Jeon, Chan-Hoo; Wallcraft, Alan J (May 2022, Continental Shelf Research)

   In this study, we investigate the transition of semidiurnal Kelvin waves into Hybrid Kelvin-Edge (HKE) waves and associated generation of internal tides at widening shelves using theory, a realistic global baroclinic ocean model simulation, and quasi-realistic regional barotropic model simulations. Using the global model simulation, we identify several areas where a tidal HKE wave transition co-exists with internal wave generation. Of all areas considered, the Celtic Sea/Bay of Biscay shelf has the widest shelf and the strongest internal tide generation. We find that the global simulation agrees better with the theoretical Kelvin modes on the narrow than with the hybrid edge modes on the wide shelves. To help us understand the effect of complex, realistic bathymetry on the HKE wave transition, we perform quasi-realistic 1/25◦ barotropic simulations of the Celtic Sea/Bay of Biscay shelf areas. In these simulations, we gradually change the realistic bathymetry to a more idealized bathymetry. The idealized simulations show that the complex bathymetry steers the barotropic energy flux and causes standing wave patterns, which mask the HKE wave transition. Based on this analysis, we conclude that the HKE wave transition in the Celtic Sea/Bay of Biscay and other shelf areas in the global ocean is most likely masked by the effects of complex bathymetry and that offshelf baroclinic fluxes cannot be exclusively attributed to the HKE wave transition. 

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