Spin-down in a rapidly rotating cylinder container with mixed rigid and stress-free boundary conditions
| Autor: | Ludivine Oruba, Emmanuel Dormy, Andrew M. Soward |
|---|---|
| Přispěvatelé: | Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Newcastle University, School of Mathematics and Statistics, Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2016 |
| Předmět: |
010504 meteorology & atmospheric sciences
Direct numerical simulation Boundary (topology) FOS: Physical sciences [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph] Angular velocity 01 natural sciences Omega 010305 fluids & plasmas Base (group theory) Physics::Fluid Dynamics 0103 physical sciences [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] Boundary value problem ComputingMilieux_MISCELLANEOUS 0105 earth and related environmental sciences Physics Mechanical Engineering Mathematical analysis Fluid Dynamics (physics.flu-dyn) Physics - Fluid Dynamics Condensed Matter Physics Inertial wave 13. Climate action Mechanics of Materials Ekman number |
| Zdroj: | Journal of Fluid Mechanics Journal of Fluid Mechanics, Cambridge University Press (CUP), 2017, 818, pp.205-240. ⟨10.1017/jfm.2017.134⟩ |
| ISSN: | 0022-1120 1469-7645 |
| DOI: | 10.48550/arxiv.1611.06511 |
| Popis: | A comprehensive study of the classical linear spin-down of a constant density viscous fluid (kinematic viscosity \nu) rotating rapidly (angular velocity \Omega) inside an axisymmetric cylindrical container (radius L, height H) with rigid boundaries, that follows the instantaneous small change in the boundary angular velocity at small Ekman number $E=\nu/H^2\Omega \ll 1$, was provided by Greenspan & Howard (1963). $E^{1/2}$-Ekman layers form quickly triggering inertial waves together with the dominant spin-down of the quasi-geostrophic (QG) interior flow on the $O(E^{-1/2}\Omega^{-1})$ time-scale. On the longer lateral viscous diffusion time-scale $O(L^2/\nu)$, the QG-flow responds to the $E^{1/3}$-side-wall shear-layers. In our variant the side-wall and top boundaries are stress-free; a setup motivated by the study of isolated atmospheric structures, such as tropical cyclones, or tornadoes. Relative to the unbounded plane layer case, spin-down is reduced (enhanced) by the presence of a slippery (rigid) side-wall. This is evinced by the QG-angular velocity, \omega*, evolution on the O(L^2/\nu) time-scale: Spatially, \omega* increases (decreases) outwards from the axis for a slippery (rigid) side-wall; temporally, the long-time ($\gg L^2/\nu)$ behaviour is dominated by an eigensolution with a decay rate slightly slower (faster) than that for an unbounded layer. In our slippery side-wall case, the $E^{1/2} \times E^{1/2}$ corner region that forms at the side-wall intersection with the rigid base is responsible for a $\ln E$ singularity within the $E^{1/3}$-layer causing our asymptotics to apply only at values of E far smaller than can be reached by our Direct Numerical Simulation (DNS) of the entire spin-down process. Instead, we solve the $E^{1/3}$-boundary-layer equations for given E numerically. Our hybrid asymptotic-numerical approach yields results in excellent agreement with our DNS. Comment: 33 pages, 10 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|