Eulerian indicators under continuously varying conditions

McIlhany, K.; Wiggins, Stephen

doi:10.1063/1.4732152

Cited by 11 publications

(21 citation statements)

References 16 publications

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“…OSI only explains amplification or reduction in effective near-wall transport. This observation is similar to concepts of mobility discussed by [39] in a broader context of Eulerian vector field characterization. Regions of low OSI contribute to a more effective near-wall convective tangential transport, whereas high OSI reduces effective transport due to the rapid temporal change in WSS vector.…”

Section: P 10supporting

confidence: 59%

Wall shear stress exposure time: a Lagrangian measure of near-wall stagnation and concentration in cardiovascular flows

Arzani

Gambaruto

Chen

et al. 2016

Biomech Model Mechanobiol

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms suitable in regions of complex hemodynamics that are traditionally difficult to quantify, yet encountered in many disease scenarios. Keywords: advection-diffusion; blood flow; hemodynamics; near-wall transport; residence time; shear stress; p. 2 IntroductionBiomechanical interactions between blood flow and the vessel wall are central to the initiation and progression of most cardiovascular diseases. Indeed, the majority of computational and experimental investigations into blood flow seek to understand how local flow mechanics relates to disease progression in or on the vessel wall. Blood flow conditions in diseased vessels are usually spatially and temporally complex and are challenging to characterize [51,50], even without reference to the coupled biochemical or biophysical processes driving disease progression. Nonetheless, the role of blood flow mechanics in the "near-wall" region is of utmost importance since this is where such couplings are most profound. In the near-wall region, blood flow serves to impart mechanical stresses on the vessel wall, as well as regulate the local transport of reactive material between the tissue and fluid domains. It is this latter mechanism that motivates the work presented herein.A compelling scenario involving the interaction between blood flow and the vessel wall is atherosclerosis, which is a leading cause of death worldwide. Atherosclerosis occurs mainly in locations of disturbed blood flow patterns [9,47]. The local transport of several substances near and at the vessel wall are known to influence atherosclerosis progression [56]. For example, previous studies have looked into transport of low density lipoproteins (LDL) [17,20,30,14], high density lipoproteins (HDL) [40,24], oxygen [16,27], nitric oxide (NO) [45,35], monocytes [12,14], and adenine triphosphate ATP and adenine diphosphate ADP [13,15,8] as important mass transport processes involved in atherosclerosis.Intravascular thrombosis is another compelling pathology associated with most cardiovascular diseases where near-wall transport becomes important [7,25]. The trajectories of individual platelets and the accumulation and residence time of chemical solutes including ADP, thrombin, and various blood factors control clot formation. These solutes, and especially in activated form, are generated at the vessel wall or from bound platelets. Complex hemodynamics and flow stagnation are often associated with prothrombotic conditions. For example, intraluminal thrombus in abdominal aortic aneurysm (AAA) [57,54] complicates disease progression, and is thought to be strongly coupled to flow stagnation and recirculation. The chaotic flow field in AAAs [3] Near-wall transport can either be (i) explicitly modeled for a specific transport problem, or (ii) inferred from appropriate hemodynamics meas...

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Section: P 10supporting

confidence: 59%

Wall shear stress exposure time: a Lagrangian measure of near-wall stagnation and concentration in cardiovascular flows

Arzani

Gambaruto

Chen

et al. 2016

Biomech Model Mechanobiol

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“…This has led to the preponderance of different methods, often called 'Lagrangian coherent structure' (LCS) methods, which continue to be devel-oped to identify these (for reviews, see [1,3,41,42]). These methods include ridges of finite-time Lyapunov exponents (FTLEs) [1,[43][44][45][46][47][48][49][50], curves/surfaces towards which there is extremal repulsion/attraction [1,[51][52][53][54][55][56], sets which are 'almost coherent' with respect to the operation of a transfer operator [57][58][59][60][61], identification of vorticity cores or oscillations [62,63], etc. Thus, the very definition of 'transport barrier' at some finite time is ambiguous.…”

Section: Introductionmentioning

confidence: 99%

Estimating stable and unstable sets and their role as transport barriers in stochastic flows

Balasuriya

Gottwald

2018

Phys. Rev. E

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We consider the situation of a large-scale stationary flow subjected to small-scale fluctuations. Assuming that the stable and unstable manifolds of the large-scale flow are known, we quantify the mean behavior and stochastic fluctuations of particles close to the unperturbed stable and unstable manifolds and their evolution in time. The mean defines a smooth curve in physical space, while the variance provides a time- and space-dependent quantitative estimate where particles are likely to be found. This allows us to quantify transport properties such as the expected volume of mixing as the result of the stochastic fluctuations of the transport barriers. We corroborate our analytical findings with numerical simulations in both compressible and incompressible flow situations. We moreover demonstrate the intimate connection of our results with finite-time Lyapunov exponent fields, and with spatial mixing regions.

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“…In the recent years there has been some effort to derive Eulerian quantities which can be used to draw conclusions about Lagrangian transport phenomena (Sturman and Wiggins, 2009;McIlhany and Wiggins, 2012;McIlhany et al, 2011McIlhany et al, , 2015.…”

Section: Introductionmentioning

confidence: 99%

Detecting and tracking eddies in oceanic flow fields: a Lagrangian descriptor based on the modulus of vorticity

Vortmeyer-Kley

Gräwe

Feudel

2016

Nonlin. Processes Geophys.

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Since eddies play a major role in the dynamics of oceanic flows, it is of great interest to detect them and gain information about their tracks, their lifetimes and their shapes. We present a Lagrangian descriptor based on the modulus of vorticity to construct an eddy tracking tool. In our approach we denote an eddy as a rotating region in the flow possessing an eddy core corresponding to a local maximum of the Lagrangian descriptor and enclosed by pieces of manifolds of distinguished hyperbolic trajectories (eddy boundary). We test the performance of the eddy tracking tool based on this Lagrangian descriptor using an convection flow of four eddies, a synthetic vortex street and a velocity field of the western Baltic Sea. The results for eddy lifetime and eddy shape are compared to the results obtained with the Okubo-Weiss parameter, the modulus of vorticity and an eddy tracking tool used in oceanography. We show that the vorticity-based Lagrangian descriptor estimates lifetimes closer to the analytical results than any other method. Furthermore we demonstrate that eddy tracking based on this descriptor is robust with respect to certain types of noise, which makes it a suitable method for eddy detection in velocity fields obtained from observation.

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Eulerian indicators under continuously varying conditions

Cited by 11 publications

References 16 publications

Wall shear stress exposure time: a Lagrangian measure of near-wall stagnation and concentration in cardiovascular flows

Wall shear stress exposure time: a Lagrangian measure of near-wall stagnation and concentration in cardiovascular flows

Estimating stable and unstable sets and their role as transport barriers in stochastic flows

Detecting and tracking eddies in oceanic flow fields: a Lagrangian descriptor based on the modulus of vorticity

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