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Are Representative Finite Lyapunov Exponents Observable?

Helga Huntley, B.L. Lipphardt, A.D. Kirwan, M.H.M. Sulman
University of Delaware
(Abstract received 04/05/2012 for session A)
ABSTRACT

A popular method for characterizing Lagrangian pathways in a flow is to identify patterns in finite-time or finite-scale Lyapunov exponent (FLE) fields. These are typically computed either analytically in simple flows or from gridded trajectories based on archived model velocities for numerical solutions. This approach is based on the assumption that ridges in the FLE fields coincide with material transport barriers. Both theoretical and numerical studies indicate that this assumption holds under a wide range of conditions (e.g., Shadden et al., 2005; Branicki and Wiggins, 2010). Some work has also been done to compare transport barriers identified in numerical models with observed pathways (e.g., Toner et al., 2003).

Beyond locating transport barriers, however, FLEs characterize flows by summarizing particle separation behavior. Research into the accuracy of such characterizations vis-ŕ-vis nature is in its infancy, partially because available Lagrangian observations are generally too sparse for a meaningful analysis. Here we use ocean general circulation models to investigate whether a large number of drifters deployed in a dense network would suffice to establish a representative view of FLEs in a confined region. We explore the sensitivity of the FLE estimates to deployment location, drifter number, and deployment stencil. The parameter space is divided into “observable” and “non-observable” regions, which also informs our understanding of which features of an FLE field are ephemeral and which are robust.