dc.contributor.author | Whitehead, JP | |
dc.contributor.author | Haut, T | |
dc.contributor.author | Wingate, B | |
dc.date.accessioned | 2018-07-31T08:54:16Z | |
dc.date.issued | 2018-08-02 | |
dc.description.abstract | Inspired by the use of fast singular limits in time-parallel numerical methods for a single fast frequency, we consider the limiting, nonlinear dynamics for a system of partial differential equations when two fast, distinct time scales are
present. First order slow equations are derived via the method of multiple time scales when the two small parameters are related by a rational power. We find that the resultant system depends only on the relationship of the two fast time-scales, i.e. which fast time is fastest? Using the theory of cancellation of fast oscillations, we show that with the appropriate assumptions on the nonlinear operator of the full system, this reduced slow system is exactly that which the solution will converge to if each asymptotic limit is considered sequentially. The same result is also obtained via the method of renormalization. The specific example of the rotating, stratified Boussinesq equations is explored in detail, indicating that the most common distinguished limit of this system – quasi-geostrophy, is not the only limiting asymptotic system. | en_GB |
dc.description.sponsorship | We wish to thank the 2 anonymous referees whose comments significantly enhanced the presentation and scope of this article. J. P. W. would like to thank A.Larios, K. Julien, G. Chini, and A. Farhat for various discussions that prompted and motivated this work as well as generous support from the Mathematics Department of Brigham Young University. All of the authors wish to acknowledge the DOE LANL/LDRD program for support, as well as the hospitality of the Courant Institute of New York University where some of this work was completed. Wingate also wishes to thank the University of Exeter for support during the completion of this manuscript. | en_GB |
dc.identifier.citation | Published online 02 August 2018. | en_GB |
dc.identifier.doi | 10.1007/s00162-018-0472-2 | |
dc.identifier.uri | http://hdl.handle.net/10871/33602 | |
dc.language.iso | en | en_GB |
dc.publisher | Springer Verlag | en_GB |
dc.rights.embargoreason | Under embargo until 02 August 2019 in compliance with publisher policy. | en_GB |
dc.rights | © Springer-Verlag GmbH Germany, part of Springer Nature 2018. | |
dc.title | The effect of two distinct fast time scales in the rotating, stratified Boussinesq equations: variations from quasi-geostrophy | en_GB |
dc.type | Article | en_GB |
dc.identifier.issn | 0935-4964 | |
dc.description | This is the author accepted manuscript. The final version is available from Springer via the DOI in this record. | en_GB |
dc.identifier.journal | Theoretical and Computational Fluid Dynamics | en_GB |
dcterms.dateAccepted | 2018-07-10 | |
rioxxterms.version | AM | |
refterms.dateFCD | 2018-07-31T08:54:16Z | |
refterms.versionFCD | AM | |