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8 - Dynamic consistency and Lagrangian data in oceanography: mapping, assimilation, and optimization schemes
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- By Toshio M. Chin, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA, Kayo Ide, University of California at Los Angeles, Los Angeles, California, USA, Christopher K. R. T. Jones, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA, Leonid Kuznetsov, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA, Arthur J. Mariano, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
- Edited by Annalisa Griffa, University of Miami, A. D. Kirwan, Jr., University of Delaware, Arthur J. Mariano, University of Miami, Tamay Özgökmen, University of Miami, H. Thomas Rossby, University of Rhode Island
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- Book:
- Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics
- Published online:
- 07 September 2009
- Print publication:
- 10 May 2007, pp 204-230
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Summary
Introduction
As illustrated throughout this book, Lagrangian data can provide us with a unique perspective on the study of geophysical fluid dynamics, particle dispersion, and general circulation. Drifting buoys, floats, and even a crate-full of rubber ducks or athletic shoes lost in mid-ocean (Christopherson, 2000) may be used to gain insights into ocean circulation. All Lagrangian instruments will be referred to as “drifters” hereafter for simplicity. Because movement of a drifter tends to follow that of a water parcel, the primary attributes of Lagrangian measurements are (i) horizontal coverage due to dispersion in time, (ii) that many of the observed variables obey conservation laws approximately over some lengths of time, and (iii) their ability to trace circulation features such as meanders and vortices at a wide range of spatial scales. Due mainly to inherently irregular spatial distributions, the Lagrangian measurements must first be interpolated for most applications. As we will see, the design of interpolation and mapping schemes that can preserve the Lagrangian attributes is often non-trivial.
To observe finer dynamical details of oceanic and coastal phenomena and to forecast drifter trajectories more accurately (for search-and-rescue operation, spill containment, and so on), Lagrangian data afford a particularly informative and novel perspective if they are combined with a dynamical model, rather than mapped by a standard synoptic-scale interpolation procedure which can smear some details at smaller and faster scales. Data assimilation can be viewed as a methodology for imposing dynamical consistency upon observed data for the purpose of space-time interpolation.
Experimental and numerical studies of an eastward jet over topography
- YUDONG TIAN, ERIC R. WEEKS, KAYO IDE, J. S. URBACH, CHARLES N. BAROUD, MICHAEL GHIL, HARRY L. SWINNEY
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- Journal:
- Journal of Fluid Mechanics / Volume 438 / 10 July 2001
- Published online by Cambridge University Press:
- 05 July 2001, pp. 129-157
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Motivated by the phenomena of blocked and zonal flows in Earth's atmosphere, we conducted laboratory experiments and numerical simulations to study the dynamics of an eastward jet flowing over wavenumber-two topography. The laboratory experiments studied the dynamical behaviour of the flow in a barotropic rotating annulus as a function of the experimental Rossby and Ekman numbers. Two distinct flow patterns, resembling blocked and zonal flows in the atmosphere, were observed to persist for long time intervals.
Earlier model studies had suggested that the atmosphere's normally upstream- propagating Rossby waves can resonantly lock to the underlying topography, and that this topographic resonance separates zonal from blocked flows. In the annulus, the zonal flows did indeed have super-resonant mean zonal velocities, while the blocked flows appear subresonant. Low-frequency variability, periodic or irregular, was present in the measured time series of azimuthal velocity in the blocked regime, with dominant periodicities in the range of 6–25 annulus rotations. Oscillations have also been detected in zonal states, with smaller amplitude and similar frequency. In addition, over a large region of parameter space the two flow states exhibited spontaneous, intermittent transitions from the one to the other.
We numerically simulated the laboratory flow geometry in a quasi-geostrophic barotropic model over a similar range of parameters. Both flow regimes, blocked and zonal, were reproduced in the simulations, with similar spatial and temporal characteristics, including the low-frequency oscillations associated with the blocked flow. The blocked and zonal flow patterns are present over wide ranges of forcing, topographic height, and bottom friction. For a significant portion of parameter space, both model flows are stable. Depending on the initial state, either the blocked or the zonal flow is obtained and persists indefinitely, showing the existence of multiple equilibria.