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Craig's XY distribution and the statistics of Lagrangian power in twodimensional turbulence
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Bandi, Mahesh M. and Connaughton, Colm. (2008) Craig's XY distribution and the statistics of Lagrangian power in twodimensional turbulence. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol.77 (No.3(2)). 036318 . ISSN 15393755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.77.036318
Abstract
We examine the probability distribution function (PDF) of the energy injection rate (power) in numerical simulations of stationary twodimensional (2D) turbulence in the Lagrangian frame. The simulation is designed to mimic an electromagnetically driven fluid layer, a welldocumented system for generating 2D turbulence in the laboratory. In our simulations, the forcing and velocity fields are close to Gaussian. On the other hand, the measured PDF of injected power is very sharply peaked at zero, suggestive of a singularity there, with tails which are exponential but asymmetric. Large positive fluctuations are more probable than large negative fluctuations. It is this asymmetry of the tails which leads to a net positive mean value for the energy input despite the most probable value being zero. The main features of the power distribution are well described by Craig's XY distribution for the PDF of the product of two correlated normal variables. We show that the power distribution should exhibit a logarithmic singularity at zero and decay exponentially for large absolute values of the power. We calculate the asymptotic behavior and express the asymmetry of the tails in terms of the correlation coefficient of the force and velocity. We compare the measured PDFs with the theoretical calculations and briefly discuss how the power PDF might change with other forcing mechanisms.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics Q Science > QC Physics 
Divisions:  Faculty of Science > Centre for Complexity Science Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  Turbulence, Power (Mechanics)  Mathematical models, Lagrangian functions 
Journal or Publication Title:  Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 
Publisher:  American Physical Society 
ISSN:  15393755 
Official Date:  March 2008 
Volume:  Vol.77 
Number:  No.3(2) 
Number of Pages:  9 
Page Range:  036318 
Identification Number:  10.1103/PhysRevE.77.036318 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
Funder:  United States. Dept. of Energy 
Grant number:  DEAC5206NA25396 (DoE) 
Related URLs:  
References:  [1] H. Schlichting, Boundarylayer theory (New York; 
URI:  http://wrap.warwick.ac.uk/id/eprint/30316 
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