We identify Lagrangian coherent vortices in a global mesoscale eddy-permitting ocean model using the rotation-based method of Haller et al. (2016). We present an analysis of the acute sensitivity of the identification results to varying the method’s free parameters, and develop physically justified parameter choices that allow for systematic vortex identification. In contrast to prior vortex studies, we probe the broad spectrum of coherency in the ocean by determining free parameter choices that partition the spectrum into distinct coherency classes, allowing for the identification of strictly coherent, moderately coherent, and leaky vortices. Our tuning methodology is grounded in a combination of sensitivity analysis, convergence tests, and consideration of the ocean model’s physics. To aid in this process, we introduce the Coherency Index, a novel Lagrangian diagnostic for mathematically quantifying the degree of material coherency of a Lagrangian vortex. We aim for this manuscript and the accompanying open-access code to serve as a manual and toolset for the oceanographer interested in harnessing a rigorous Lagrangian method to uncover coherent structures in ocean models and observations.
By introducing an equivalence between magnetostatics and the equations governing buoyant motion, we derive analytical expressions for the acceleration of isolated density anomalies (thermals). In particular, we investigate buoyant acceleration, defined as the sum of the Archimedean buoyancy B and an associated perturbation pressure gradient. For the case of a uniform spherical thermal, the anomaly fluid accelerates at 2B/3, extending the textbook result for the induced mass of a solid sphere to the case of a fluid sphere. For a more general ellipsoidal thermal, we show that the buoyant acceleration is a simple analytical function of the ellipsoid’s aspect ratio. The relevance of these idealized uniform-density results to turbulent thermals is explored by analyzing direct numerical simulations of thermals at a Reynolds number (Re) of 6300. We find that our results fully characterize a thermal’s initial motion over a distance comparable to its length. Beyond this buoyancy-dominated regime, a thermal develops an ellipsoidal vortex circulation and begins to entrain environmental fluid. Our analytical expressions do not describe the total acceleration of this mature thermal, but they still accurately relate the buoyant acceleration to the thermal’s mean Archimedean buoyancy and aspect ratio. Thus, our analytical formulas provide a simple and direct means of estimating the buoyant acceleration of turbulent thermals.
