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Fluids 2016, 1(4), 33; doi:10.3390/fluids1040033

Estimating Eulerian Energy Spectra from Drifters

Department of Geosciences, University of Oslo, PO Box 1022 Blindern, 0315 Oslo, Norway
Academic Editor: Pavel S. Berloff
Received: 22 July 2016 / Revised: 4 October 2016 / Accepted: 8 October 2016 / Published: 15 October 2016
(This article belongs to the Collection Geophysical Fluid Dynamics)
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Abstract

The relations between the kinetic energy spectrum and the second-order longitudinal structure function for 2D non-divergent flow are derived, and several examples are considered. The transform from spectrum to structure function is illustrated using idealized power-law spectra of turbulent inertial ranges. The results illustrate how the structure function integrates contributions across wavenumber, which can obscure the dependencies when the inertial ranges are of finite extent. The transform is also applied to the kinetic energy spectrum of Nastrom and Gage (1985), derived from aircraft data in the upper troposphere; the resulting structure function agrees well with that of Lindborg (1999), calculated with the same data. The transform from structure function to spectrum is then tested with data from 2D turbulence simulations. When applied to the (Eulerian) structure function obtained from the transform of the spectrum, the result closely resembles the original spectrum, except at the largest wavenumbers. The deviation at large wavenumbers occurs because the transform involves a filter function which magnifies contributions from large separations. The results are noticeably worse when applied to the structure function obtained from pairs of particles in the flow, as this is usually noisy at large separations. Fitting the structure function to a polynomial improves the resulting spectrum, but not sufficiently to distinguish the correct inertial range dependencies. Furthermore, the transform of steep (non-local) spectra is largely unsuccessful. Thus, it appears that with Lagrangian data, it is probably preferable to focus on structure functions, despite their shortcomings. View Full-Text
Keywords: turbulence; spectra; Lagrangian turbulence; spectra; Lagrangian
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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LaCasce, J.H. Estimating Eulerian Energy Spectra from Drifters. Fluids 2016, 1, 33.

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