Imperial College London
Alternate

ProfessorDemetriosPapageorgiou

Faculty of Natural Sciences, Department of Mathematics

Chair in Applied Maths and Mathematical Physics
 
 
 
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Contact

 

+44 (0)20 7594 8369d.papageorgiou Website

 
 
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Location

 

750Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Tomlin:2018:10.1098/rspa.2017.0687,
author = {Tomlin, R and Kalogirou, A and Papageorgiou, D},
doi = {10.1098/rspa.2017.0687},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
title = {Nonlinear dynamics of a dispersive anisotropic Kuramoto–Sivashinsky equation in two space dimensions},
url = {http://dx.doi.org/10.1098/rspa.2017.0687},
volume = {474},
year = {2018}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - A   Kuramoto–Sivashinsky   equation   in   two   spacedimensions arising in thin film flow is considered ondoubly periodic domains. In the absence of dispersiveeffects,   this   anisotropic   equation   admits   chaoticsolutions   for   sufficiently   large   length   scales   withfully  two-dimensional  profiles;  the  one-dimensionaldynamics observed for thin domains are structurallyunstable   as   the   transverse   length   increases.   Wefind   that,   independent   of   the   domain   size,   thecharacteristic   length   scale   of   the   profiles   in   thestreamwise direction is about 10 space units, with thatin the transverse direction being approximately threetimes  larger.  Numerical  computations  in  the  chaoticregime  provide  an  estimate  for  the  radius  of  theabsorbing ball inL2in terms of the length scales, fromwhich we conclude that the system possesses a finiteenergy density. We show the property of equipartitionof energy among the low Fourier modes, and reportthe disappearance of the inertial range when solutionprofiles  are  two-dimensional.  Consideration  of  thehigh   frequency   modes   allows   us   to   compute   anestimate  for  the  analytic  extensibility  of  solutionsinC2.   We   examine   the   addition   of   a   physicallyderived  third-order  dispersion  to  the  problem;  thishas  a  destabilising  effect,  in  the  sense  of  reducinganalyticity  and  increasing  amplitude  of  solutions.However, sufficiently large dispersion may regularisethe  spatiotemporal  chaos  to  travelling  waves.  Wefocus  on  dispersion  where  chaotic  dynamics  persist,and   study   its   effect   on   the   interfacial   structures,absorbing ball, and properties of the power spectrum.
AU  - Tomlin,R
AU  - Kalogirou,A
AU  - Papageorgiou,D
DO  - 10.1098/rspa.2017.0687
PY  - 2018///
SN  - 1364-5021
TI  - Nonlinear dynamics of a dispersive anisotropic Kuramoto–Sivashinsky equation in two space dimensions
T2  - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
UR  - http://dx.doi.org/10.1098/rspa.2017.0687
UR  - http://hdl.handle.net/10044/1/57544
VL  - 474
ER  -
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