Imperial College London
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ProfessorSergeiChernyshenko

Faculty of Engineering, Department of Aeronautics

Chair in Aerodynamics
 
 
 
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Contact

 

+44 (0)20 7594 5548s.chernyshenko Website

 
 
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Location

 

211aCity and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Huang:2015:10.1098/rspa.2015.0622,
author = {Huang, D and Chernyshenko, SI and Goulart, P and Lasagna, D and Tutty, O and Fuentes, F},
doi = {10.1098/rspa.2015.0622},
journal = {Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences},
pages = {1--18},
title = {Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application},
url = {http://dx.doi.org/10.1098/rspa.2015.0622},
volume = {471},
year = {2015}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the  rotating Couette flow is examined. The flow depends on the Reynolds number and a parameter characterising the magnitude of the Coriolis force. By converting the original Navier-Stokes equations to a finite-dimensional uncertain dynamical system using a partial Galerkin expansion, high-degree polynomial Lyapunov functionals were found by sum-of-squares-of-polynomials optimization. It is demonstrated that the proposed method allows obtaining the exact global stability limit for this flow in a range of values of the parameter characterising the Coriolis force. Outside this range a lower bound for the global stability limit was obtained, which is still better than the energy stability limit. In the course of the study several results meaningful in the context of the method used were also obtained. Overall, the  results obtained demonstrate the applicability of the recently proposed approach to global stability of the fluid flows. To the best of our knowledge, it is the first case in which global stability of a fluid flow has been proved by a generic method for the value of a Reynolds number greater than that which could be achieved with the energy stability approach.
AU  - Huang,D
AU  - Chernyshenko,SI
AU  - Goulart,P
AU  - Lasagna,D
AU  - Tutty,O
AU  - Fuentes,F
DO  - 10.1098/rspa.2015.0622
EP  - 18
PY  - 2015///
SN  - 0080-4630
SP  - 1
TI  - Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application
T2  - Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences
UR  - http://dx.doi.org/10.1098/rspa.2015.0622
UR  - https://royalsocietypublishing.org/doi/10.1098/rspa.2015.0622
UR  - http://hdl.handle.net/10044/1/27862
VL  - 471
ER  -
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