Transport structures in a 3D periodic flow

Chang, Henry; Huntley, Helga S.; Kirwan, A. D.; Lipphardt, B. L.; Sulman, Mohamed H. M.

doi:10.1016/j.cnsns.2018.01.014

Cited by 4 publications

(2 citation statements)

References 42 publications

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“…Furthermore, we can demonstrate that the x-axis, {y = 0}, is an attracting S-ridge. Note that s − (x 0 , y 0 ) = −1 + 3y 2 0 < 0 for y 0 = 0, satisfying the attraction criterion, (32). Since ∇s − (x 0 , y 0 ) = [0, 6y 0 ] , then along the xaxis we have ∇s − (x 0 , y 0 )| y0=0 • e − = 0, satisfying the ridge criterion, (33).…”

Section: Two-dimensional Nonlinear Saddle Flowmentioning

confidence: 98%

Finite-time Lyapunov exponents in the instantaneous limit and material transport

Nolan,

Serra,

Ross

2019

Preprint

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Lagrangian techniques, such as the Finite-Time Lyapunov Exponent (FTLE) and hyperbolic Lagrangian coherent structures, have become popular tools for analyzing unsteady fluid flows. These techniques identify regions where particles transported by a flow will converge to and diverge from over a finite-time interval, even in a divergence-free flow. Lagrangian analyses, however, are time consuming and computationally expensive, hence unsuitable for quickly assessing short-term material transport. A recently developed method called OECSs [Serra, M. and Haller, G., "Objective Eulerian Coherent Structures", Chaos 26( 5), 2016] rigorously connected Eulerian quantities to short-term Lagrangian transport. This Eulerian method is faster and less expensive to compute than its Lagrangian counterparts, and needs only a single snapshot of a velocity field. Along the same line, here we define the instantaneous Lyapunov Exponent (iLE), the instantaneous counterpart of the FTLE, and connect the Taylor series expansion of the right Cauchy-Green deformation tensor to the infinitesimal integration time limit of the FTLE. We illustrate our results on geophysical fluid flows from numerical models as well as analytical flows, and demonstrate the efficacy of attracting and repelling instantaneous Lyapunov exponent structures in predicting short-term material transport.

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Section: Two-dimensional Nonlinear Saddle Flowmentioning

confidence: 98%

Finite-time Lyapunov exponents in the instantaneous limit and material transport

Nolan,

Serra,

Ross

2019

Preprint

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“…For instance, a 2D flow is divergent in an upwelling region (which drives the particle convergence in garbage patches), while a 3D flow is nondivergent. However, attracting structures (Bettencourt et al, 2012) and transport barriers (Bettencourt et al, 2015;Chang et al, 2018) of 3D particle paths can also emerge inside the ocean. In this way, particles can cluster in specific areas when they are collected at a 2D surface after their sinking journey (Monroy et al, 2017;Eaton and Fessler, 1994), as is also measured at the ocean subsurface (Mitchell et al, 2008;Logan and Wilkinson, 1990).…”

Section: Introductionmentioning

confidence: 99%

Sedimentary microplankton distributions are shaped by oceanographically connected areas

et al. 2022

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Abstract. Having descended through the water column, microplankton in ocean sediments is representative of the ocean surface environment, where it originated. Sedimentary microplankton is therefore used as an archive of past and present surface oceanographic conditions. However, these particles are advected by turbulent ocean currents during their sinking journey. So far, it is unknown to what extent this particle advection shapes the microplankton composition in sediments. Here we use global simulations of sinking particles in a strongly eddying global ocean model, and define ocean bottom provinces based on the particle surface origin locations. We find that these provinces can be detected in global datasets of sedimentary microplankton assemblages, demonstrating the effect provincialism has on the composition of sedimentary remains of surface plankton. These provinces explain the microplankton composition, in addition to, e.g., the ocean surface environment. Connected provinces have implications for the optimal spatial extent of microplankton sediment sample datasets that are used for palaeoceanographic reconstruction, and for the optimal spatial averaging of sediment samples over global datasets.

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Finite-time Lyapunov exponents in the instantaneous limit and material transport

2020

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Transport structures in a 3D periodic flow

Cited by 4 publications

References 42 publications

Finite-time Lyapunov exponents in the instantaneous limit and material transport

Finite-time Lyapunov exponents in the instantaneous limit and material transport

Sedimentary microplankton distributions are shaped by oceanographically connected areas

Finite-time Lyapunov exponents in the instantaneous limit and material transport

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