Analogies and differences between the stability of an isolated pancake vortex and a columnar vortex in stratified fluid
| Autor: | Paul Billant, Eunok Yim |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Physics
Buoyancy 010504 meteorology & atmospheric sciences Mechanical Engineering Baroclinity Stratified flows Reynolds number Mechanics engineering.material Condensed Matter Physics 01 natural sciences Instability 010305 fluids & plasmas Vortex symbols.namesake Classical mechanics Mechanics of Materials 0103 physical sciences Froude number symbols engineering Wavenumber 0105 earth and related environmental sciences |
| Zdroj: | Journal of Fluid Mechanics. 796:732-766 |
| ISSN: | 1469-7645 0022-1120 |
| DOI: | 10.1017/jfm.2016.248 |
| Popis: | In order to understand the dynamics of pancake shaped vortices in stably stratified fluids, we perform a linear stability analysis of an axisymmetric vortex with Gaussian angular velocity in both the radial and axial directions with an aspect ratio of ${\it\alpha}$. The results are compared to those for a columnar vortex (${\it\alpha}=\infty$) in order to identify the instabilities. Centrifugal instability occurs when $\mathscr{R}>c(m)$ where $\mathscr{R}=ReF_{h}^{2}$ is the buoyancy Reynolds number, $F_{h}$ the Froude number, $Re$ the Reynolds number and $c(m)$ a constant which differs for the three unstable azimuthal wavenumbers $m=0,1,2$. The maximum growth rate depends mostly on $\mathscr{R}$ and is almost independent of the aspect ratio ${\it\alpha}$. For sufficiently large buoyancy Reynolds number, the axisymmetric mode is the most unstable centrifugal mode whereas for moderate $\mathscr{R}$, the mode $m=1$ is the most unstable. Shear instability for $m=2$ develops only when $F_{h}\leqslant 0.5{\it\alpha}$. By considering the characteristics of shear instability for a columnar vortex with the same parameters, this condition is shown to be such that the vortex is taller than the minimum wavelength of shear instability in the columnar case. For larger Froude number $F_{h}\geqslant 1.5{\it\alpha}$, the isopycnals overturn and gravitational instability can operate. Just below this threshold, the azimuthal wavenumbers $m=1,2,3$ are unstable to baroclinic instability. A simple model shows that baroclinic instability develops only above a critical vertical Froude number $F_{h}/{\it\alpha}$ because of confinement effects. |
| Databáze: | OpenAIRE |
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