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Spontaneous generation of a swirling plume in a stratified ambient

  • Francisco Marques (a1) and Juan M. Lopez (a2)

Abstract

The transition from laminar to complex spatio-temporal dynamics of plumes due to a localized buoyancy source is studied numerically. Several experiments have reported that this transition is sensitive to external perturbations. Therefore, a well-controlled set-up has been chosen for our numerical study, consisting of a localized heat source at the bottom of an enclosed cylinder whose sidewall is maintained at a fixed temperature which varies linearly up the wall. Restricting the dynamics to the axisymmetric subspace, the first instability is to a puffing state. However, for smaller Grashof numbers, the plume becomes unstable to three-dimensional perturbations and a swirling plume spontaneously appears. The next bifurcation, viewed in the rotating frame where the plume is stationary, also exhibits puffing and suggests a connection between the unstable axisymmetric puffing solution and the swirling plume. Further bifurcations result in quasi-periodic states with a very low-frequency modulation, and these eventually become spatio-temporally complex.

Copyright

Corresponding author

Email address for correspondence: juan.m.lopez@asu.edu

References

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JFM classification

Type Description Title
VIDEO
Movies

Marques and Lopez supplementary movie
Movie 1 (5a): Isotherms of the axisymmetric periodic puffing plume state at $Gr=3.5 \times 10^5$, $Ar=2$, $A_z=2$, $A_T=1$ and $\sigma=7$ over one puffing period $2\pi/\omega_0 \approx 3.9 \times 10^{−4}$.

 Video (860 KB)
860 KB
VIDEO
Movies

Marques and Lopez supplementary movie
Movie 2 (5b): Azimuthal vorticity contours of the axisymmetric periodic puffing plume state at $Gr=3.5 \times 10^5$, $Ar=2$, $A_z=2$, $A_T=1$ and $\sigma=7$ over one puffing period $2\pi/\omega_0 \approx 3.9 \times 10^{−4}$.

 Video (843 KB)
843 KB
VIDEO
Movies

Marques and Lopez supplementary movie
Movie 3(6a): Isotherms of the axisymmetric periodic puffing plume state at $Gr=10^6$, $Ar=2$, $A_z=2$, $A_T=1$ and $\sigma=7$ over one puffing period $2\pi/\omega_0 \approx 4.1 \times 10^{−4}$.

 Video (3.5 MB)
3.5 MB
VIDEO
Movies

Marques and Lopez supplementary movie
Movie 4 (6b): Azimuthal vorticity contours of the axisymmetric periodic puffing plume state at $Gr=10^6$, $Ar=2$, $A_z=2$, $A_T=1$ and $\sigma=7$ over one puffing period $2\pi/\omega_0 \approx 4.1 \times 10^{−4}$.

 Video (3.0 MB)
3.0 MB
VIDEO
Movies

Marques and Lopez supplementary movie
Movie 5 (12a): Three-dimensional isosurfaces of azimuthal vorticity $\eta$ of the rotating wave state RW at $Gr=2 \times 10^5$, $A_r=2$, $A_z=2$, $A_T=1$ and $\sigma=7$, over one precession period $2\pi/\omega_\text{pr} \approx 5 \times 10^{−4}; the isosurface levels are at $\eta = \pm 10^3$.

 Video (505 KB)
505 KB
VIDEO
Movies

Marques and Lopez supplementary movie
Movie 6 (16): Three-dimensional isosurfaces of azimuthal vorticity $\eta$ of the VLF state at $Gr=3.5 \times 10^5$, $A_r=2$, $A_z=2$, $A_T=1$ and $\sigma=7$; the isosurface levels are at $\eta = \pm 10^3$.

 Video (770 KB)
770 KB

Spontaneous generation of a swirling plume in a stratified ambient

  • Francisco Marques (a1) and Juan M. Lopez (a2)

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