Identifying Finite-Time Coherent Sets from Limited Quantities of Lagrangian Data

A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into pairs of coherent sets, which are sets of initial conditions chosen to minimize the number of trajectories that "leak" from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by posing an optimization problem, which once solved, yields a pair of functions whose signs determine set membership. From prior experience with synthetic, "data rich" test problems and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. As a result, given a fixed amount of data our approach, which can use sets of globally supported basis functions, has the potential to more accurately approximate the desired functions than other functions tailored to use compactly supported indicator functions. This difference enables our approach to produce effective approximations of pairs of coherent sets in problems with relatively limited quantities of Lagrangian data, which is usually the case with real geophysical data. We apply this method to three examples of increasing complexity: the first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.Comment: 14 pages, 7 figure

Trajectory encounter volume as a diagnostic of mixing potential in fluid flows

© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Nonlinear Processes in Geophysics 24 (2017): 189-202, doi:10.5194/npg-24-189-2017.Fluid parcels can exchange water properties when coming into contact with each other, leading to mixing. The trajectory encounter mass and a related simplified quantity, the encounter volume, are introduced as a measure of the mixing potential of a flow. The encounter volume quantifies the volume of fluid that passes close to a reference trajectory over a finite time interval. Regions characterized by a low encounter volume, such as the cores of coherent eddies, have a low mixing potential, whereas turbulent or chaotic regions characterized by a large encounter volume have a high mixing potential. The encounter volume diagnostic is used to characterize the mixing potential in three flows of increasing complexity: the Duffing oscillator, the Bickley jet and the altimetry-based velocity in the Gulf Stream extension region. An additional example is presented in which the encounter volume is combined with the u approach of Pratt et al. (2016) to characterize the mixing potential for a specific tracer distribution in the Bickley jet flow. Analytical relationships are derived that connect the encounter volume to the shear and strain rates for linear shear and linear strain flows, respectively. It is shown that in both flows the encounter volume is proportional to time.This work was supported by NSF grants OCE-1154641, OCE-1558806 and EAR-1520825 as well as by ONR grant N00014-11-10087 and NASA grant NNX14AH29G. Publication of this article was supported by the Office of Naval Research, grant no. N00014-16-1-2492

Zonal Jets as Transport Barriers in Planetary Atmospheres

The connection between transport barriers and potential vorticity (PV) barriers in PV-conserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV-staircase model is used to illustrate important concepts. This flow consists of a sequence of narrow eastward and broad westward zonal jets with a staircase PV structure; the PV-steps are at the latitudes of the cores of the eastward jets. Numerically simulated solutions to the quasigeostrophic PV conservation equation in a perturbed PV-staircase flow are presented. These simulations reveal that both eastward and westward zonal jets serve as robust meridional transport barriers. The surprise is that westward jets, across which the background PV gradient vanishes, serve as robust transport barriers. A theoretical explanation of the underlying barrier mechanism is provided. It is argued that transport barriers near the cores of westward zonal jets, across which the background PV gradient is small, are found in Jupiter's midlatitude weather layer and in the Earth's summer hemisphere subtropical stratosphere.Comment: Accepted for publication in JA

Influence of ocean circulation changes on the inter-annual variability of American eel larval dispersal

Author Posting. © Association for the Sciences of Limnology and Oceanography, 2016. This article is posted here by permission of Association for the Sciences of Limnology and Oceanography for personal use, not for redistribution. The definitive version was published in Limnology and Oceanography 61 (2016): 1574–1588, doi:10.1002/lno.10297.American eel (Anguilla rostrata) complete their life cycle by migrating from the east coast of North America to Sargasso Sea, where they spawn planktonic eggs and dye. Larvae that develop from eggs need to return to North American coastal waters within the first year of life and are influenced by the oceanic currents during this journey. A coupled physical–biological model is used to investigate the extent to which inter-annual changes in the ocean circulation affect the success rates of larvae in reaching coastal nursery habitats. Our results suggest that natural oceanic variability can lead to changes in larval success rates by a factor of 2. Interannual variation in success rates are strongly affected by the Gulf Stream inertial overshoot events, with the largest success in years with an inertial overshoot and the smallest in years with a straighter and more southern configuration of the Gulf Stream downstream of Cape Hatteras. The mean Gulf Stream length and latitude between 75W and 70W longitude can be used as proxies for characterizing the overshoot events and can be converted into success rates using linear regression.I.I.R. and L.J.P. were supported by grant 85464100 (OCE-1154641) from the National Science Foundation. M.S.L. gratefully acknowledges support from the National Science Foundation

Mode filters and energy conservation

Author Posting. © Acoustical Society of America, 2010. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 127 (2010): EL185-EL191, doi:10.1121/1.3327240.The discrete form of the mode filtering problem is considered. The relevant equations constitute a linear inverse problem. Solutions to problems of this type are subject to a well-known trade-off between resolution and precision. But unlike the typical linear inverse problem, the correctly formulated mode filtering problem is subject to an energy conservation constraint. This letter focuses on the importance of satisfying, approximately at least, the energy conservation constraint when mode filtering is performed.This work was supported by the Office of Naval Research, Code 321, Grant Nos. N000140610245 and N000140810195

Properties and origins of the anisotropic eddy-induced transport in the North Atlantic

Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 45 (2015): 778–791, doi:10.1175/JPO-D-14-0164.1.This study examines anisotropic transport properties of the eddying North Atlantic flow, using an idealized model of the double-gyre oceanic circulation and altimetry-derived velocities. The material transport by the time-dependent flow (quantified by the eddy diffusivity tensor) varies geographically and is anisotropic, that is, it has a well-defined direction of the maximum transport. One component of the time-dependent flow, zonally elongated large-scale transients, is particularly important for the anisotropy, as it corresponds to primarily zonal material transport and long correlation time scales. The importance of these large-scale zonal transients in the material distribution is further confirmed with simulations of idealized color dye tracers, which has implications for parameterizations of the eddy transport in non-eddy-resolving models.IK would like to acknowledge support through the NSF Grant OCE-1154923. IR was supported by the NSF OCE-1154641 and NASA Grant NNX14AH29G.2015-09-0