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Research > Nonlinear Dynamics

Dynamical systems theory provides a wealth of mathematical tools and geometrical concepts for explaining complex real-world phenomena. We utilize these in the investigation of fundamental fluid flow phenomena in laboratory experiments. In the past, we have demonstrated that low-dimensional models can explain the behavior of highly-complex flows of a liquid crystal. More recently, the latest concepts regarding Lagrangian Coherent Structures have provided insight into the structure of turbulent fluid flow, the nature of unsteady flow separation and helped uncover internal wave attractors.

Funding for our research on Nonlinear Dynamics is provided by the MIT Ferry Fund, the ONR and the NSF.

Spotlight

Unsteady separation

Unsteady separation is the phenomenon in which a sharp spike of fluid is ejected from a rigid boundary. This is currently a limiting factor in the performance of most transport vehicles. Recent research from the ENDLab has helped establish the credibility of a somewhat controversial new criterion based on ideas from nonlinear dynamics. Perhaps most remarkably, the experiments clearly demonstrate that separation at a fixed location can occur even in a random experimental flow field that is kinematically equivalent to the conditions within a turbulent boundary layer. [read the paper]

Read the news story released by MIT [link].

Relevant Publications

  1. Mullin, T. and Peacock, T., "Hydrodynamic instabilities in nematic liquid crystals under oscillatory shear," Proceedings of the Royal Society of London A, 455, 2635-2653 (1999). [link]
  2. Peacock, T., Mullin, T. and Binks, D.J., "Bifurcation phenomena in flows in a nematic liquid crystal," International Journal of Bifurcations and Chaos, 9, 427-441 (1999). [link]
  3. Peacock, T., Binks, D.J. and Mullin, T., "From low- to high-dimensional dynamics in a microscopic fluid flow," Physical Review Letters, 82, 1446-1449 (1999). [link]
  4. Peacock, T. and Mullin, T., "Homoclinic bifurcations in a liquid crystal flow," Journal of Fluid Mechanics, 432, 369-386 (2000). [link]
  5. Peacock, T. and Mullin T., "The transition to turbulence in a microscopic fluid flow," Physics of Fluids, 12, S8 (2000). [link]
  6. Mathur, M., Haller, G., Peacock, T., Ruppert-Felsot, J.E. and Swinney, H.L., "Uncovering the lagrangian skeleton of turbulence," Physical Review Letters, 98 (14), Art. No. 144502 (2007). [link]
  7. Peacock, T. and Bradley, E., "Going with (or against) the flow," Science, 320 (5881), 1302-1303 (2008). [link]
  8. Weldon, M., Peacock, T., Jacobs, G.B., Helu, M. and Haller, G., "Experimental and numerical investigation of the kinematic theory of unsteady separation," Journal of Fluid Mechanics, 611, 1-11 (2008). [link]
  9. Echeverri, P., Balmforth, N.J. and Peacock, T., "Internal tide attractors in double ridge systems," submitted to Journal of Fluid Mechanics (2009). [link]
  10. Tang, W.E. and Peacock, T., "Lagrangian coherent structures and internal tide attractors," submitted to CHAOS. [link]

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