Chaotic Advection in an Archipelago*

Abstract

Techniques from dynamical systems theory have been applied to study horizontal stirring of fluid in the Philippine Archipelago. The authors' analysis is based on velocity fields produced by two high-resolution (3 and 6 km) numerical models. Particular attention is paid to identifying robust surface flow patterns and associating them with dominant Lagrangian coherent structures (LCSs). A recurrent wind-driven dipole in the lee of the coastline is considered in detail. The associated LCSs form a template for stirring, exchange, and biological transport in and around the dipole. Chaotic advection is argued to provide a relevant framework for interpreting mesoscale horizontal stirring processes in an archipelago as a whole. Implications for the formation of filaments, the production of tracer variance, and the scale at which stirring leads to mixing are discussed in connection with an observed temperature record.

Short-term dispersal of Fukushima-derived radionuclides off Japan: modeling efforts and model-data intercomparison

“…Rypina et al (2010) similarly observed an increase in phytoplankton concentration at the perimeter of coupled eddies (dipoles) in the Philippine Archipelago. Fluid exchange processes are different at the perimeter of an eddy compared to its core.…”

“…The southern edge of the distribution is roughly aligned with the Kuroshio Current, suggesting that this strong current acts as a transport barrier, particularly over the western part of the Pacific Ocean where it is most strongly defined. Interestingly, Rypina et al (2010) found that in the North Atlantic, the Gulf Stream also acts as a transport barrier. The similarity in these results suggests that plausibly it is typical for all strong oceanic currents to prevent cross-stream transport.…”

“…Fluid exchange processes are different at the perimeter of an eddy compared to its core. At eddy perimeters the so-called "chaotic advection" mechanism is at play (Mancho et al, 2006;Rypina et al, 2010), which leads to the sequential stretching and folding of fluid elements and facilitates the exchange with the outer waters. Within the Lagrangian core of an eddy, on the other hand, a more "regular" state of motion exists where the behavior of fluid parcels is similar to that found in steady flows.…”

An efficient approach for eigenmode analysis of transient distributive mixing by the mapping method

“…For = 10 −8 this gives n ∈ [82, 196] (T = 0.56) and n ∈ [16, 134] (T = 1.6). However, typical engineering applications are restricted to much lower precision, say = 0.1(10 −2 ), leading to n ∈ [10,24]( [21,49]) and n ∈ [2, 5]( [4,9]) for T = 0.56 and T = 1.6, respectively. This reveals that, in particular for the chaotic flow, the earlier stages of the transient mixing become within the reach of the compact method.…”

“…Further examples include population genetics, distribution of nutrients, oil spills and the prediction of the weather. [1][2][3][4][5][6] Spectral analysis has become popular for the investigation of scalar transport in such flows, as the governing advection-diffusion equation is linear and thus amenable to characterization in terms of the eigenvalues and eigenvectors of the evolution operator. 7 Analysis of its spectral structure has been performed in Cerbelli et al 8 and revealed an exponential decay of the scalar field towards a homogeneous asymptotic state.…”