The effect of two distinct fast time scales in the rotating, stratified Boussinesq equations: variations from quasi-geostrophy
Autor: | Jared P. Whitehead, Terry S. Haut, Beth A. Wingate |
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Rok vydání: | 2018 |
Předmět: |
Fluid Flow and Transfer Processes
Partial differential equation 010504 meteorology & atmospheric sciences Numerical analysis Mathematical analysis General Engineering Computational Mechanics Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Power (physics) Renormalization Nonlinear system Slow manifold 0103 physical sciences Multiple time Limit (mathematics) 0105 earth and related environmental sciences Mathematics |
Zdroj: | Theoretical and Computational Fluid Dynamics. 32:713-732 |
ISSN: | 1432-2250 0935-4964 |
DOI: | 10.1007/s00162-018-0472-2 |
Popis: | 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. |
Databáze: | OpenAIRE |
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