Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains

Abstract

We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: blackhole vortices [23], objective Eulerian Coherent Structures (OECSs) [37], material barriers to diffusive transport [24,25], and constrained diffusion barriers [25]. The method builds on ideas developed previously in [29], but our implementation alleviates a number of shortcomings and allows for the fully automated detection of such vortices on unprecedentedly challenging real-world flow problems, for which specific human interference is absolutely infeasible. Challenges include very large domains and/or parameter spaces. We demonstrate the efficacy of our method in dealing with such challenges on two test cases: first, a parameter study of a turbulent flow, and second, computing material barriers to diffusive transport in the global ocean.

Vortex boundaries as barriers to diffusive vorticity transport in two-dimensional flows

“…The associated challenges are described in [31] [33]. Recent progress on addressing some of these challenges is reported in [34].…”

GeophysicalFlows.jl: Solvers for geophysical fluid dynamics problems in periodic domains on CPUs GPUs

“…GeophysicalFlows.jl can be used to investigate a variety of scientific research questions thanks to its various modules and high customizability, and its ease-of-use makes it an ideal teaching tool for fluids courses (Constantinou, 2020;Constantinou & Wagner, 2020). Geop hysicalFlows.jl has been used in developing Lagrangian vortices identification algorithms (Karrasch & Schilling, 2020) and to test new theories for diagnosing turbulent energy transfers in geophysical flows (Pearson et al, 2021). Currently, GeophysicalFlows.jl is being used, e.g., (i) to compare different observational sampling techniques in these flows, (ii) to study the bifurcation properties of Kolmogorov flows (Constantinou & Drivas, 2020), (iii) to study the genesis and persistence of the polygons of vortices present at Jovian high latitudes (Siegelman, Young, and Ingersoll; in prep), and (iv) to study how mesoscale macroturbulence affects mixing of tracers (Bisits & Constantinou, 2021).…”

The most robust representations of flow trajectories are Lagrangian coherent structures

“…To generate the data, we solve the two-dimensional, incompressible Navier-Stokes equations on a periodic domain using a pseudospectral method. The flow is made turbulent by stochastic forcing, the exact set-up of which can be found in Karrasch & Schilling (2020). We define a Reynolds number as Re = u rms L/ν, where u rms is the r.m.s.…”