Imperial College London
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DrGeorgiosRigas

Faculty of Engineering, Department of Aeronautics

Senior Lecturer
 
 
 
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Contact

 

+44 (0)20 7594 5065g.rigas CV

 
 
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Location

 

327City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Towne:2019:10.1007/s00162-019-00498-8,
author = {Towne, A and Rigas, G and Colonius, T},
doi = {10.1007/s00162-019-00498-8},
journal = {Theoretical and Computational Fluid Dynamics},
pages = {359--382},
title = {A critical assessment of the parabolized stability equations},
url = {http://dx.doi.org/10.1007/s00162-019-00498-8},
volume = {33},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The parabolized stability equations (PSE) are a ubiquitous tool for studying the stability and evolution of disturbances in weakly nonparallel, convectively unstable flows. The PSE method was introduced as an alternative to asymptotic approaches to these problems. More recently, PSE has been applied with mixed results to a more diverse set of problems, often involving flows with multiple relevant instability modes. This paper investigates the limits of validity of PSE via a spectral analysis of the PSE operator. We show that PSE is capable of accurately capturing only disturbances with a single wavelength at each frequency and that other disturbances are not necessarily damped away or properly evolved, as often assumed. This limitation is the result of regularization techniques that are required to suppress instabilities arising from the ill-posedness of treating a boundary value problem as an initial value problem. These findings are valid for both incompressible and compressible formulations of PSE and are particularly relevant for applications involving multiple modes with different wavelengths and growth rates, such as problems involving multiple instability mechanisms, transient growth, and acoustics. Our theoretical results are illustrated using a generic problem from acoustics and a dual-stream jet, and the PSE solutions are compared to both global solutions of the linearized Navier–Stokes equations and a recently developed alternative parabolization.
AU  - Towne,A
AU  - Rigas,G
AU  - Colonius,T
DO  - 10.1007/s00162-019-00498-8
EP  - 382
PY  - 2019///
SN  - 0935-4964
SP  - 359
TI  - A critical assessment of the parabolized stability equations
T2  - Theoretical and Computational Fluid Dynamics
UR  - http://dx.doi.org/10.1007/s00162-019-00498-8
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000475885300007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://link.springer.com/article/10.1007%2Fs00162-019-00498-8
VL  - 33
ER  -
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