No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
Dependence of advection-diffusion-reaction on flow coherent structures
9. J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, 1989), p. 364.
12. S. C. Shadden, F. Lekien, and J. E. Marsden, “Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows,” Physica D 212, 271–304 (2005).
16. M. Sandulescu, C. López, E. Hernández-García, and U. Feudel, “Plankton blooms in vortices: The role of biological and hydrodynamic time scales,” Nonlinear Processes Geophys. 14, 443–454 (2007).
17. V. Artale, G. Boffetta, M. Celani, M. Cencini, and A. Vulpiani, “Dispersion of passive tracers in closed basins: Beyond the diffusion coefficient,” Phys. Fluids 9, 3162–3171 (1997).
22. K. A. Mitchell and J. R. Mahoney, “Invariant manifolds and the geometry of front propagation in fluid flows,” Chaos 22, 037104 (2012).
24. J. P. Crimaldi, J. R. Cadwell, and J. B. Weiss, “Reaction enhancement of isolated scalars by vortex stirring,” Phys. Fluids 20, 073605 (2008).
26. Z. Neufeld and E. Hernández-García, Chemical and Biological Activity in Open Flows: A Dynamical System Approach (Imperial College Press, London, 2009), p. 304.
27. C. L. Winter, D. M. Tartakovsky, and A. Guadagnini, “Numerical solutions of moment equations for flow in heterogeneous composite aquifers,” Water Resour. Res. 38(5), 13–113–8, doi:10.1029/2001WR000222 (2002).
28. C. L. Winter, D. M. Tartakovsky, and A. Guadagnini, “Moment differential equations for flow in highly heterogeneous porous media,” Surv. Geophys. 24(1), 81–106 (2003).
29. C. L. Winter, A. Guadagnini, D. Nychka, and D. M. Tartakovsky, “Multivariate sensitivity analysis of saturated flow through simulated highly heterogeneous groundwater aquifers,” J. Comput. Phys. 217(1), 166–175 (2006).
30. D. M. Tartakovsky, M. Dentz, and P. C. Lichtner, “Probability density functions for advective-reactive transport with uncertain reaction rates,” Water Resour. Res. 45, W07414, doi:10.1029/2008WR007383 (2009).
31. M. Dentz and D. M. Tartakovsky, “Probability density functions for passive scalars dispersed in random velocity fields,” Geophys. Res. Lett. 37, L24406, doi:10.1029/2010GL045748 (2010).
36. F. Lekien, C. Coulliette, A. J. Mariano, E. H. Ryan, L. K. Shay, G. Haller, and J. Marsden, “Pollution release tied to invariant manifolds: A case study for the coast of Florida,” Physica D 210, 1–20 (2005).
37. S. C. Shadden, J. O. Dabiri, and J. E. Marsden, “Lagrangian analysis of fluid transport in empirical vortex ring flows,” Phys. Fluids 18(4), 047105 (2006).
38. W. Tang, M. Mathur, G. Haller, D. C. Hahn, and F. H. Ruggiero, “Lagrangian coherent structures near a subtropical jet stream,” J. Atmos. Sci. 67(7), 2307–2319 (2010).
44. F. Lekien and S. D. Ross, “The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds,” Chaos 20, 017505 (2010).
46. A. Kolmogorov, I. Petrovskii, and N. Piscounov, “A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem,” in Selected Works of A. N. Kolmogorov I (Kluwer, 1991), pp. 248–270, edited by V. M. Tikhomirov
48. J. R. Taylor, “Numerical simulations of the stratified oceanic bottom boundary layer,” Ph.D. thesis (University of California, San Diego, 2008).
50. E. Ott and T. M. Antonsen, Jr., “Fractal measures of passively convected vector fields and scalar gradients in chaotic fluid flows,” Phys. Rev. A 39(7), 3660–3671 (1989).
51. A. Mahadevan and J. W. Campbell, “Biogeochemical patchiness at the sea surface,” Geophys. Res. Lett. 29(19), 1926, doi:10.1029/2001GL014116 (2002).
Article metrics loading...
A study on an advection-diffusion-reaction system is presented. Variability of the reaction process in such a system triggered by a highly localized source is quantified. It is found, for geophysically motivated parameter regimes, that the difference in bulk concentration subject to realizations of different source locations is highly correlated with the local flow topology of the source. Such flow topologies can be highlighted by Lagrangian coherent structures. Reaction is relatively enhanced in regions of strong stretching, and relatively suppressed in regions where vortices are present. In any case, the presence of a divergence-free background flow helps speed up the reaction process, especially when the flow is time-dependent. Probability density of various quantities characterizing the reaction processes is also obtained. This reveals the inherent complexity of the reaction-diffusion process subject to nonlinear background stirring.
Full text loading...
Most read this month