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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  
Dates: 


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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