Defining coherent vortices objectively from the vorticity

Abstract

Rotationally coherent Lagrangian vortices are formed by tubes of deforming fluid elements that complete equal bulk material rotation relative to the mean rotation of the deforming fluid volume. We show that the initial positions of such tubes coincide with tubular level surfaces of the Lagrangian-averaged vorticity deviation (LAVD), the trajectory integral of the normed difference of the vorticity from its spatial mean. The LAVD-based vortices are objective, i.e. remain unchanged under time-dependent rotations and translations of the coordinate frame. In the limit of vanishing Rossby numbers in geostrophic flows, cyclonic LAVD vortex centres are precisely the observed attractors for light particles. A similar result holds for heavy particles in anticyclonic LAVD vortices. We also establish a relationship between rotationally coherent Lagrangian vortices and their instantaneous Eulerian counterparts. The latter are formed by tubular surfaces of equal material rotation rate, objectively measured by the instantaneous vorticity deviation (IVD). We illustrate the use of the LAVD and the IVD to detect rotationally coherent Lagrangian and Eulerian vortices objectively in several two-and three-dimensional flows.

Trajectory encounter volume as a diagnostic of mixing potential in fluid flows

“…As with FTLEs, complexity measures (Rypina et al, 2011), Lagrangian descriptors (Mendoza et al, 2014) and other techniques from the dynamical systems theory (BeronVera et al, 2013;Budisic and Mezic, 2012;Froyland et al, 2007;Haller et al, 2016), V can be computed for forwardand backward-time trajectories, with the backward computation revealing the unstable manifolds. Our encounter number could plausibly be related, in a limiting case, to the mixing geometry of Karrash and Keller (2017).…”

“…By analogy with molecular diffusion, the eddy diffusivity, K, is often used to characterize the eddy-induced downgradient tracer transfer in realistic geophysical fluid flows (LaCasce, 2008;Vallis, 2006;Rypina et al, 2012;Kamenkovich et al, 2015). Because of the simplicity of this approach, the majority of existing non-eddy-resolving oceanic numerical models are diffusion based, despite the somewhat questionable assumptions underlying this approach.…”

Large to submesoscale surface circulation and its implications on biogeochemical/biological horizontal distributions during the OUTPACE cruise (SouthWest Pacific)

“…To set up the mesoscale context during the OUTPACE cruise, we used the Lagrangian Averaged Vorticity Deviation method Haller et al, 2016) that allows identification of coherent structures from altimetry-derived 10 surface velocity fields (code available at https://github.com/Hadjighasem/Lagrangian-Averaged-Vorticity-Deviation-LAVD).…”

Meridional and Zonal Wavenumber Dependence in Potential Vorticity Flux in Rossby Waves

“…This is an approximation for the local unstable manifold at this instance in time, since the unstable manifold is known to point northwards to leading-order in ε. These particles are then advected forward by one-time step (i.e., to time t − T + ∆t) according to (18) with the streamfunction (27), using a third-order Runge-Kutta scheme. At this next time-step, another line of particles, emanating northward from a(t − T + ∆t) to a distance δ, is seeded.…”

“…It is this difficulty which has led to the development of many proxies for the stable/unstable manifolds, such as ridges of FTLE fields [32,71], hyperbolic Lagrangian coherent structures [11], sharp transitions in various types of scalar fields generated from the flow using transfer operators [35], clustering [85] or averaging [25][26][27], etc.…”