Preprints
https://doi.org/10.5194/npg-2022-1
https://doi.org/10.5194/npg-2022-1
 
12 Jan 2022
12 Jan 2022
Status: this preprint was under review for the journal NPG. A revision for further review has not been submitted.

Rigid Sets and Coherent Sets in Realistic Ocean Flows

Florian Feppon1,2 and Pierre Lermusiaux2 Florian Feppon and Pierre Lermusiaux
  • 1Department of Mathematics, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
  • 2Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Mass. Ave., Cambridge, MA - 02139

Abstract. This paper focuses on the extractions of Lagrangian Coherent Sets from realistic velocity fields obtained from ocean data and simulations, each of which can be highly resolved and non volume-preserving. We introduce two novel methods for computing two formulations of such sets. First, we propose a new “diffeomorphism-based” criterion to extract “rigid sets”, defined as sets over which the flow map acts approximately as a rigid transformation. Second, we develop a matrix-free methodology that provides a simple and efficient framework to compute “coherent sets” with operator methods. Both new methods and their resulting rigid sets and coherent sets are illustrated and compared using three numerically simulated flow examples, including a high-resolution realistic, submesoscale to large-scale dynamic ocean current field in the Palau Island region of the western Pacific Ocean.

Florian Feppon and Pierre Lermusiaux

Status: closed (peer review stopped)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on npg-2022-1', Anonymous Referee #1, 01 Feb 2022
  • RC2: 'Comment on npg-2022-1', Anonymous Referee #2, 21 Feb 2022

Status: closed (peer review stopped)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on npg-2022-1', Anonymous Referee #1, 01 Feb 2022
  • RC2: 'Comment on npg-2022-1', Anonymous Referee #2, 21 Feb 2022

Florian Feppon and Pierre Lermusiaux

Florian Feppon and Pierre Lermusiaux

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Short summary
We develop and showcase new methods to extract Lagrangian Coherent Sets from ocean flow data and simulations. The first method extracts “rigid sets” defined as ocean regions that evolve almost as a rigid object. The second method is a matrix-free methodology that provides a simple and efficient framework to compute “coherent sets” with operator methods. We showcase results using three numerically simulated flow examples, including complex ocean current fields in the Palau Island region.