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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 decay of Hill's vortex in a rotating flow

   https://doi.org/10.1017/jfm.2021.386  

   Crowe, Matthew N.; Kemp, Cameron J.D.; Johnson, Edward R. (July 2021, Journal of Fluid Mechanics)

   null (Ed.)

   Hill's vortex is a classical solution of the incompressible Euler equations which consists of an axisymmetric spherical region of constant vorticity matched to an irrotational external flow. This solution has been shown to be a member of a one-parameter family of steady vortex rings and as such is commonly used as a simple analytic model for a vortex ring. Here, we model the decay of a Hill's vortex in a weakly rotating flow due to the radiation of inertial waves. We derive analytic results for the modification of the vortex structure by rotational effects and the generated wave field using an asymptotic approach where the rotation rate, or inverse Rossby number, is taken to be small. Using this model, we predict the decay of the vortex speed and radius by combining the flux of vortex energy to the wave field with the conservation of peak vorticity. We test our results against numerical simulations of the full axisymmetric Navier–Stokes equations. 

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3. The evolution of surface quasi-geostrophic modons on sloping topography

   https://doi.org/10.1017/jfm.2023.607  

   Crowe, Matthew N.; Johnson, Edward R. (September 2023, Journal of Fluid Mechanics)

   This work discusses modons, or dipolar vortices, propagating along sloping topography. Two different regimes exist, which are studied separately using the surface quasi-geostrophic equations. First, when the modon propagates in the direction opposite to topographic Rossby waves, steady solutions exist and a semi-analytical method is presented for calculating these solutions. Second, when the modon propagates in the same direction as the Rossby waves, a wave wake is generated. This wake removes energy from the modon, causing it to decay slowly. Asymptotic predictions are presented for this decay and found to agree closely with numerical simulations. Over long times, decaying vortices are found to break down due to an asymmetry resulting from the generation of waves inside the vortex. A monopolar vortex moving along a wall is shown to behave in a similar way to a dipole, though the presence of the wall is found to stabilise the vortex and prevent the long-time breakdown. The problem is equivalent mathematically to a dipolar vortex moving along a density front, hence our results apply directly to this case. 

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4. 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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5. Power Estimation of Flapping Foil Energy Harvesters Using Vortex Impulse Theory

   Siala, F.F.; Liburdy, J.A. (October 2019, Renewable energy)

   This study explores the feasibility of using the vortex impulse approach, based on experimen- tally generated velocity elds to estimate the energy harvesting performance of a sinusoidally apping foil. Phase-resolved, two-component particle image velocimetry measurements are conducted in a low-speed wind tunnel to capture the ow eld surrounding the apping foil at reduced frequencies of k = fc=U1 = 0.06 - 0.16, pitching amplitude of 0 = 70 and heaving amplitude of h0=c = 0:6. The model results show that for the conditions tested, a maximum energy harvesting eciency of 25% is attained near k = 0:14, agreeing very well with published numerical and experimental results in both accuracy and general trend. The vortex impulse method identi es key contributions to the transient power production from both linear and angular momentum eects. The eciency reduction at larger values of reduced frequencies is shown to be a result of the reduced power output from the angular momentum. Further, the impulse formulation is decomposed into contributions from posi- tive and negative vorticity in the ow and is used to better understand the uid dynamic mechanisms responsible for producing a peak in energy harvesting performance at k = 0:14. At the larger k values, there is a reduction of the advective time scales of the leading edge vortex (LEV) formation. Consequently, the LEV that is shed during the previous half cycle interacts with the foil at the current half cycle resulting in a large negative pitching power due to the reversed direction of the kinematic motion. This vortex capture process signif- icantly decreases the total cycle averaged power output and energy harvesting eciency. These results show the link between the kinematic motion and LEV time scales that aect the overall power production. 

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