Research
Coherent Structures in Fluid Flows
Turbulent fluid flow is an extremely complicated dynamical state, but it is not random. As anyone who has watched, say, a river flow knows, the flow appears to be composed of coherent motions that persist in time: swirls and jets that last for a long time and move about in the fluid. This empirical observation leads one to wonder if we could possibly capture all the complicated behavior of a fluid flow (or at least the "important" parts) by a set of a finite number of coherent structures with known interaction rules that ride on a sea of random background motion.
But how should we define a coherent structure? Formally, it should be some spatiotemporally compact region of the flow over which some macroscopic quantity (such as vorticity or kinetic energy) is strongly correlated. But there are many ways one could define such a structure in practice. How do we know when we have made a good choice?
We have worked over the past several years to make progress on these difficult questions. We are involved both in trying to define and characterize new, useful kinds of coherent structures (both Eulerian and Lagrangian), and, more importantly, in determining the exact contribution of such structures to the flow dynamics. We use a wide range of advanced analysis tools in this work, including curvature fields, finite-time Lyapunov exponent analysis, and spectral filtering. In our most recent work, we are focusing on using the scale-to-scale fluxes of energy and momentum as a criterion to assess different definitions of coherent structures.
Representative Publications
H. Xu, N. T. Ouellette, and E. Bodenschatz, "Multi-particle statistics - Lines, shapes, and volumes in high Reynolds number turbulence," Proceedings of the 5th International Conference on Nonlinear Mechanics, ed. W.-Z. Chien, pp. 1155-1161 (2007).
N. T. Ouellette and J. P. Gollub, "Curvature fields, topology, and the dynamics of spatiotemporal chaos," Phys. Rev. Lett. 99, 194502 (2007).
H. Xu, N. T. Ouellette, and E. Bodenschatz, "Evolution of geometric structures in intense turbulence," New J. Phys. 10, 013012 (2008).
N. T. Ouellette and J. P. Gollub, "Dynamic topology in spatiotemporal chaos," Phys. Fluids 20, 064104 (2008).
N. T. Ouellette and J. P. Gollub, "Detecting topological features of chaotic fluid flow," Chaos 18, 041102 (2008).
S. T. Merrifield, D. H. Kelley, and N. T. Ouellette, "Scale-dependent statistical geometry in two-dimensional flow," Phys. Rev. Lett. 104, 254501 (2010).
D. H. Kelley and N. T. Ouellette, "Separating stretching from folding in fluid mixing," Nature Phys. 7, 477-480 (2011).
A. de Chaumont Quitry, D. H. Kelley, and N. T. Ouellette, "Mechanisms driving shape distortion in two-dimensional flow," EPL 94, 64006 (2011).
D. H. Kelley and N. T. Ouellette, "Spatiotemporal persistence of spectral fluxes in two-dimensional weak turbulence," Phys. Fluids 23, 115101 (2011).
N. T. Ouellette, "On the dynamical role of coherent structures in turbulence," C. R. Physique 13, 866-877 (2012).
Y. Liao and N. T. Ouellette, "Spatial structure of spectral transport in two-dimensional flow," J. Fluid Mech. 725, 281-298 (2013).
D. H. Kelley, M. R. Allshouse, and N. T. Ouellette, "Lagrangian coherent structures separate dynamically distinct regions in fluid flow," Phys. Rev. E 88, 013017 (2013).
Y. Liao and N. T. Ouellette, "Geometry of scale-to-scale energy and enstrophy transport in two-dimensional flow," Phys. Fluids 26, 045103 (2014).
Y. Liao and N. T. Ouellette, "Long-range ordering of turbulent stresses in two-dimensional flow," Phys. Rev. E 91, 063004 (2015).
N. T. Ouellette, C. A. R. Hogg, and Y. Liao, "Correlating Lagrangian structures with forcing in two-dimensional flow," Phys. Fluids 28, 015105 (2016).
T. Ma, N. T. Ouellette, and E. M. Bollt, "Stretching and folding in finite time," Chaos 26, 023112 (2016).