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A Multi-scale Limit of a Randomly Forced Rotating 3-D Compressible Fluid
Copyright policy )A Multi-scale Limit of a Randomly Forced Rotating 3-D Compressible Fluid
We study a singular limit of a scaled compressible Navier--Stokes--Coriolis system driven by both a deterministic and stochastic forcing terms in three dimensions. If the Mach number is comparable to the Froude number with both proportional to say $\varepsilon\ll 1$, whereas the Rossby number scales like $\varepsilon^m$ for $m>1$ large, then we show that any family of weak martingale solution to the $3$-D randomly forced rotating compressible equation (under the influence of a deterministic centrifugal force) converges in probability, as $\varepsilon\rightarrow0$, to the $2$-D incompressible Navier--Stokes system with a corresponding random forcing term.
40 pages
- Heriot-Watt University Malaysia
- Heriot Watt University
- Heriot-Watt University United Kingdom
- Heriot-Watt University United Arab Emirates
arXiv: Mathematics::Analysis of PDEs Physics::Fluid Dynamics
Microsoft Academic Graph classification: Random forcing Compressible flow Rossby number symbols.namesake Froude number Mathematics Mathematical analysis Mach number symbols Compressibility Stochastic forcing Martingale (probability theory)
FOS: Physical sciences, Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematical Physics, Applied Mathematics, Probability (math.PR), Fluid Dynamics (physics.flu-dyn), Physics - Fluid Dynamics, Condensed Matter Physics, Computational Mathematics, Mathematics - Probability, Analysis of PDEs (math.AP)
FOS: Physical sciences, Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematical Physics, Applied Mathematics, Probability (math.PR), Fluid Dynamics (physics.flu-dyn), Physics - Fluid Dynamics, Condensed Matter Physics, Computational Mathematics, Mathematics - Probability, Analysis of PDEs (math.AP)
arXiv: Mathematics::Analysis of PDEs Physics::Fluid Dynamics
Microsoft Academic Graph classification: Random forcing Compressible flow Rossby number symbols.namesake Froude number Mathematics Mathematical analysis Mach number symbols Compressibility Stochastic forcing Martingale (probability theory)
2012
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Citations provided by BIP!Popularity provided by BIP!- Heriot-Watt University Malaysia
- Heriot Watt University
- Heriot-Watt University United Kingdom
- Heriot-Watt University United Arab Emirates
We study a singular limit of a scaled compressible Navier--Stokes--Coriolis system driven by both a deterministic and stochastic forcing terms in three dimensions. If the Mach number is comparable to the Froude number with both proportional to say $\varepsilon\ll 1$, whereas the Rossby number scales like $\varepsilon^m$ for $m>1$ large, then we show that any family of weak martingale solution to the $3$-D randomly forced rotating compressible equation (under the influence of a deterministic centrifugal force) converges in probability, as $\varepsilon\rightarrow0$, to the $2$-D incompressible Navier--Stokes system with a corresponding random forcing term.
40 pages