Front propagation in a regular vortex lattice: Dependence on the vortex structure

Abstract

We investigate the dependence on the vortex structure of the propagation of fronts in stirred flows. For this, we consider a regular set of vortices whose structure is changed by varying both their boundary conditions and their aspect ratios. These configurations are investigated experimentally in autocatalytic solutions stirred by electroconvective flows and numerically from kinematic simulations based on the determination of the dominant Fourier mode of the vortex stream function in each of them. For free lateral boundary conditions, i.e., in an extended vortex lattice, it is found that both the flow structure and the front propagation negligibly depend on vortex aspect ratios. For rigid lateral boundary conditions, i.e., in a vortex chain, vortices involve a slight dependence on their aspect ratios which surprisingly yields a noticeable decrease of the enhancement of front velocity by flow advection. These different behaviors reveal a sensitivity of the mean front velocity on the flow subscales. It emphasizes the intrinsic multiscale nature of front propagation in stirred flows and the need to take into account not only the intensity of vortex flows but also their inner structure to determine front propagation at a large scale. Differences between experiments and simulations suggest the occurrence of secondary flows in vortex chains at large velocity and large aspect ratios.

Velocity and geometry of propagating fronts in complex convective flow fields

“…In our simulations we have used no-slip boundary conditions where the fluid velocity at all walls is zero. It is interesting to point out that recent experiments studying propagating fronts in cellular electroconvective flows probed the role vortex structure by using rigid and free boundaries and found that the fronts were faster for free boundary conditions [21]. In addition, the nondimensional parameters of our simulations span a range of values that include regions where the approximations of the theoretical predictions become questionable.…”

“…This may be due, in part, to the variation of the vortex structure of the cellular flow for the different boundary conditions as explored in Ref. [21].…”

“…In addition, there has been a broad range of work on propagating fronts for flow fields that are not turbulent. Examples include the study of fronts in a shaken layer of liquid exhibiting Faraday waves [18], convective flows [19][20][21], Hele-Shaw flows [22], Marangoni flows [23], and fields of disordered vortices [24,25] to name a few.…”

Front propagation in cellular flows: scale dependence versus scale invariance

“…An interesting situation to highlight the implication of advection on front propagation relates to steady closed flows (Audoly, Berestycki & Pomeau 2000;Abel et al 2001Abel et al , 2002Cencini et al 2003;Vladimirova et al 2003;Paoletti & Solomon 2005;Pocheau & Harambat 2006, 2008Mahoney et al 2012;Tzella & Vanneste 2014, 2015Beauvier, Bodea & Pocheau 2016, 2017. Then, as streamlines are confined to compact regions, no large-scale advection of the medium and thus no net kinematic effect are expected at long times on fluid particles.…”

Comparing free surface and interface motion in electromagnetically driven thin-layer flows

“…In the inviscid case, 2D flow conserves not only energy but also enstrophy (squared vorticity), giving rise to simultaneous turbulent cascades of energy to large length scales and enstrophy to small length scales [2][3][4]. Furthermore, 2D or quasi-2D flows provide useful models for exploring new physical insights from ideas like Lagrangian coherent structures (LCSs) [5][6][7], exact coherent structures (ECSs) [8,9], transfer of energy and enstrophy among length scales [10][11][12][13], and advection-reaction-diffusion mechanisms [14][15][16][17][18][19], because 2D simulations demand far less computational power than 3D simulations and making high-resolution measurements throughout an experimental domain is far easier in 2D than in 3D. Analysis is also less computationally demanding in 2D than in 3D, whether the data of interest came from simulation or laboratory experiment.…”