Out of Flatland: 3D transport barriers in oceanography

• Author: A. D. Kirwan, Jr., University of Delaware.


• Names of other authors: Mohamed H. Mahmoud Sulman, Helga S. Huntley, B. L. Lipphardt, Jr.


• Oral or poster: oral.


• Downloadable presentation/poster: click here.


• Abstract:
  Mezic and Wiggins first illustrated how 3D flows can be attacked using dynamical systems theory (J. Nonlinear Sci., 1994). Later Haller (Chaos, 2000) and Haller and Yuan (Physica D, 2000) developed the theory for identifying transport barriers using finite time Lyapunov exponents (FTLE). See also Mendoza and Mancho (Phys. Rev. Lett., 2010) for an alternative approach. Until very recently applications of this methodology in oceanography have been restricted to analyses along a few selected surfaces. In rotating stratified geophysical scale fluids these barriers are 2D surfaces embedded within a finite fluid volume so the intersections of these surfaces with a few level surfaces clearly are inadequate descriptors of the true barriers. The only study that reports on the 2D structure of transport barriers in oceanography that we are aware of is Branicki and Kirwan (Int. J. Engr. Sci., 2010). In their investigation of a large anticyclonic ring in the Gulf of Mexico they reported that the 2D barriers were nearly vertical and that there was entrainment into the ring near its base and detrainment near the surface. However, for technical reasons peculiar to most data assimilating ocean and atmosphere general circulation models they elected not to use the vertical velocity in that analysis. Thus the question addressed in this talk: how representative of true 2D transport barriers are reduced FTLE representations? Specifically we discuss two strategies for identifying these barriers from reduced representations of the Cauchy Green tensor. Our analysis indicates that under typical oceanographic conditions it is important to account for the vertical shear of the horizontal currents in constructing a reduced representation of this tensor. We apply this approach to a high-resolution data assimilating general circulation model to report on the vertical structure of 2D barriers in the Gulf of Mexico.