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Technique for measuring and correcting the Taylor microscale
Author(s) -
Chuychai P.,
Weygand J. M.,
Matthaeus W. H.,
Dasso S.,
Smith C. W.,
Kivelson M. G.
Publication year - 2014
Publication title -
journal of geophysical research: space physics
Language(s) - English
Resource type - Journals
eISSN - 2169-9402
pISSN - 2169-9380
DOI - 10.1002/2013ja019641
Subject(s) - microscale chemistry , extrapolation , taylor series , series (stratigraphy) , range (aeronautics) , dissipation , spectral density , function (biology) , taylor microscale , correlation function (quantum field theory) , mathematics , statistical physics , limit (mathematics) , resolution (logic) , scale (ratio) , sampling (signal processing) , mathematical analysis , algorithm , physics , computer science , statistics , optics , mechanics , reynolds number , materials science , artificial intelligence , detector , composite material , biology , paleontology , quantum mechanics , evolutionary biology , thermodynamics , mathematics education , turbulence
Abstract We discuss and develop methods to estimate and refine measurements of the Taylor microscale from discrete data sets. To study how well a method works, we construct a time series of discrete data with a known power spectrum and Taylor scale, but with various truncations of the resolution that eliminate higher frequencies in a controlled fashion. We compute the second‐order structure function and correlation function, assuming that the unresolved dissipation range spectrum has various values of spectral index. A series of Taylor scale estimates are obtained from parabolic fits to subsets of the correlation function data, and these are extrapolated to the limit of zero separation. The error in this procedure, for finite time resolution sampling, depends on the spectral index in the dissipation range. When the spectral form is known, we can compute a correction factor that improves the estimate of the Taylor microscale value determined from the extrapolation method and band‐limited data. Application of this technique to spacecraft observations of solar wind fluctuations is illustrated.