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Numerical solutions of the isotropic 3wave kinetic equation
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Connaughton, Colm. (2009) Numerical solutions of the isotropic 3wave kinetic equation. Physica D: Nonlinear Phenomena, Vol.238 (No.2324). pp. 22822297. ISSN 01672789

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Official URL: http://dx.doi.org/10.1016/j.physd.2009.09.012
Abstract
We show that the isotropic 3wave kinetic equation is equivalent to the meanfield rate equations for an aggregationfragmentation problem with an unusual fragmentation mechanism. This analogy is used to write the theory of 3wave turbulence almost entirely in terms of a single scaling parameter. A new numerical method for solving the kinetic equation over a large range of frequencies is developed by extending Lee's method for solving aggregation equations. The new algorithm is validated against some analytical calculations of the KolmogorovZakharov (KZ) constant for some families of model interaction coefficients. The algorithm is then applied to study some wave turbulence problems in which the finiteness of the dissipation scale is an essential feature. Firstly, it is shown that for finite capacity cascades, the dissipation of energy becomes independent of the cutoff frequency as this cutoff is taken to infinity. This is an explicit indication of the presence of a dissipative anomaly. Secondly, a preliminary numerical study is presented of the socalled bottleneck effect in a wave turbulence context. It is found that the structure of the bottleneck, depends nontrivially on the interaction coefficient. Finally, some results are presented on the complementary phenomenon of thermalisation in closed wave systems which demonstrates explicitly for the first time the existence of socalled mixed solutions of the kinetic equation which exhibit aspects of both KZ and equilibrium equipartition spectra.
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, Waves  Mathematical models 
Journal or Publication Title:  Physica D: Nonlinear Phenomena 
Publisher:  Elsevier BV 
ISSN:  01672789 
Official Date:  December 2009 
Volume:  Vol.238 
Number:  No.2324 
Number of Pages:  16 
Page Range:  pp. 22822297 
Identification Number:  10.1016/j.physd.2009.09.012 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
Related URLs:  
References:  [1] A. Newell, S. Nazarenko, and L. Biven, Physica D 152 
URI:  http://wrap.warwick.ac.uk/id/eprint/16792 
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