Extracting waves and vortices from Lagrangian trajectories

• Published in: Geophysical research letters Vol. 38; no. 23
• Main Authors: Lilly, J. M., Scott, R. K., Olhede, S. C.
• Format: Journal Article
• Language: English
• Published: Washington, DC Blackwell Publishing Ltd 01-12-2011; American Geophysical Union; John Wiley & Sons, Inc
• Subjects: barotropic instability; beta plane; coherent vortex; Computational fluid dynamics; Displacement; Earth sciences; Earth, ocean, space; Eddies; eddy; Exact sciences and technology; Fluid flow; Lagrangian data; Mathematical models; Physical oceanography; Rossby wave; Scientific apparatus & instruments; Trajectories; Turbulence; Turbulent flow; Vortices; waves; Operator; Beta plane approximation; Lagrangian; Orbit; high frequency; Time series; eccentricity; Wave property; digital simulation; wavelet transformation; trajectory; frequency; drill cores; numerical models; displacements; Jet; Vortex motion; polarization; particles; Vortex; oscillations; flow; meanders
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2011GL049727

A method for extracting time‐varying oscillatory motions from time series records is applied to Lagrangian trajectories from a numerical model of eddies generated by an unstable equivalent barotropic jet on a beta plane. An oscillation in a Lagrangian trajectory is represented mathematically as the signal traced out as a particle orbits atime‐varyingellipse, a model which captures wavelike motions as well as the displacement signal of a particle trapped in an evolving vortex. Such oscillatory features can be separated from the turbulent background flow through an analysis founded upon a complex‐valued wavelet transform of the trajectory. Application of the method to a set of one hundred modeled trajectories shows that the oscillatory motions of Lagrangian particles orbiting vortex cores appear to be extracted very well by the method, which depends upon only a handful of free parameters and which requires no operator intervention. Furthermore, vortex motions are clearly distinguished from wavelike meandering of the jet—the former are high frequency, nearly circular signals, while the latter are linear in polarization and at much lower frequencies. This suggests that the proposed method can be useful for identifying and studying vortex and wave properties in large Lagrangian datasets. In particular, theeccentricity of the oscillatory displacement signals, a quantity which is not normally considered in Lagrangian studies, emerges as an informative diagnostic for characterizing qualitatively different types of motion.
Key Points
Currents associated with vortices can be automatically extracted from data
Waves and vortices can be clearly distinguished, even if they appear similar
A new representation of a vortex signal as a time‐varying ellipse is validated