Preprint Article Version 1 NOT YET PEER-REVIEWED

Calculating Energy Spectra from Drifters

  1. Department of Geosciences, University of Oslo, Oslo, Norway
Version 1 : Received: 22 July 2016 / Approved: 28 July 2016 / Online: 28 July 2016 (04:48:33 CEST)

Copyright: 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.

How to cite: LaCasce, J. Calculating Energy Spectra from Drifters. Preprints 2016, 2016070087 (doi: 10.20944/preprints201607.0087.v1). LaCasce, J. Calculating Energy Spectra from Drifters. Preprints 2016, 2016070087 (doi: 10.20944/preprints201607.0087.v1).

A peer-reviewed article of this Preprint also exists.

Journal reference: Fluids 2016, 1, 33
DOI: 10.3390/fluids1040033


The relations between the kinetic energy spectrum and the second order longitudinal structure function in two dimensions are derived, and several examples are considered. The forward conversion (from spectrum to structure function) is illustrated first with idealized power law spectra, representing turbulent inertial ranges. The forward conversion is also applied to the zonal kinetic energy spectrum of Nastrom and Gage (1985) and the result agrees well with the longitudinal structure function of Lindborg (1999). The inverse conversion (from structure function to spectrum) is tested with data from 2D turbulence simulations. When applied to the theoretical structure function (derived from the forward conversion of the spectrum), the result closely resembles the original spectrum, except at the largest wavenumbers. However the inverse conversion is much less successful when applied to the structure function obtained from pairs of particles in the flow. This is because the inverse conversion favors large pair separations, which are typically noisy with particle data. Fitting the structure function to a polynomial improves the result, but not sufficiently to distinguish the correct inertial range dependencies. Furthermore the inversion of non-local spectra is largely unsuccessful. Thus it appears that focusing on structure functions with Lagrangian data is preferable to estimating spectra.

Subject Areas

Turbulence; Spectra; Lagrangian

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