Reaction enhancement of initially distant scalars by Lagrangian coherent structures

Abstract

Turbulent fluid flows have long been recognized as a superior means of diluting initial concentrations of scalars due to rapid stirring. Conversely, experiments have shown that the structures responsible for this rapid dilution can also aggregate initially distant reactive scalars and thereby greatly enhance reaction rates. Indeed, chaotic flows not only enhance dilution by shearing and stretching but also organize initially distant scalars along transiently attracting regions in the flow. To show the robustness of this phenomenon, a hierarchical set of three numerical flows is used: the periodic wake downstream of a stationary cylinder, a chaotic double gyre flow, and a chaotic, aperiodic flow consisting of interacting Taylor vortices. We demonstrate that Lagrangian coherent structures (LCS), as identified by ridges in finite time Lyapunov exponents, are directly responsible for this coalescence of reactive scalar filaments. When highly concentrated filaments coalesce, reaction rates can be orders of magnitude greater than would be predicted in a well-mixed system. This is further supported by an idealized, analytical model that was developed to quantify the competing e↵ects of scalar dilution and coalescence. Chaotic flows, known for their ability to e ciently dilute scalars, therefore have the competing e↵ect of organizing initially distant scalars along the LCS at timescales shorter than that required for dilution, resulting in reaction enhancement. C 2015 AIP Publishing LLC. [http://dx.

Lagrangian structures and mixing in the wake of a streamwise oscillating cylinder

“…A similar correspondence between regions of intense mixing and attracting Lagrangian structures has been observed in previous studies. 5,41 It is clear that mixing is significantly enhanced in the second response branch (where the SA and A-IV modes occur) compared to the case of the near-stationary cylinder, but is not significantly affected by the S-I mode. Symmetric shedding generally occurs when the excitation or , at U r St/ f * = 0.58 while the SA mode was dominant.…”

“…This case was chosen as it exhibited the strongest cross-wake mixing Regions of high |∇C| correspond to points at which you would expect to find the strongest mixing if the streams were "active," e.g., streams of reactive chemical agents 5 or in various biological processes such as the fertilisation of marine species. 41 The fields contains regions where |∇C|D > 8.5, which correspond to points at which the two fluid streams came very close together, i.e., the separation between the two streams is less than the resolution of the PIV fields.…”

“…An alternative approach that overcomes these issues is to identify the wake mode and the Lagrangian structures from the FTLE fields computed in forward-and backward-time, which correspond to the repelling and attracting structures in the flow, respectively. This approach is often used to approximate the LCSs and is capable of revealing the complex processes governing flows, 12,39,40 identifying regions of strong or weak mixing, 38,41 as well as producing strikingly beautiful visualisations. 42 This paper aims to provide new insight into the dynamics and Lagrangian structures associated with the various wake modes observed in streamwise VIV and to investigate their effect on fluid mixing.…”

Effect of instantaneous stirring process on mixing between initially distant scalars in turbulent obstacle wakes

“…If the initial separation distance between the two scalars is smaller than the largest coherent length scales of the local flow, the two scalar fields develop similar instantaneous spatial distributions. While it is easier to envision these processes in simple flows, recent numerical simulations (Pratt et al 2015) have shown that in more complex 2D flows involving multiple interacting vortices, initially distant scalars coalesce in regions of intense mixing and attracting Lagrangian coherent structures.In aquatic ecosystems, structured flows can facilitate stirring and diffusion to enhance reactions or population growth by bringing together species and nutrients (e.g., Richards and Brentnall 2006). Structured flows stir any introduced scalars into thin filament shells (Garrett 1983), enhancing local scalar gradients, increasing the interfacial area of the scalar through chaotic stretching and folding (Hinch 1999), leading finally to increased mixing by molecular diffusion.…”

Generalized Lagrangian coherent structures

“…We specify an unsteady velocity field v that has seen extensive use as a testbed for LCS analysis [142,143,109,144,1,145,38,146,102,77,147,78,79,148,76,88]: the double gyre flow as introduced by Shadden et al [75]. The velocity v = (v 1 , v 2 ) takes the form where the function h is defined by…”