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Spontaneous generation of a swirling plume in a stratified ambient

Published online by Cambridge University Press:  26 November 2014

Francisco Marques  and
Juan M. Lopez
Francisco Marques
Affiliation:
Departament de Física Aplicada, Universitat Politècnica de Catalunya, Barcelona 08034, Spain
Juan M. Lopez*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
*
†Email address for correspondence: juan.m.lopez@asu.edu
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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.

JFM classification

Instability: Nonlinear instability Convection: Plumes/thermals Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 761 , 25 December 2014 , pp. 443 - 463
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Copyright
© 2014 Cambridge University Press 

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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 $2\pi/\omega_0 \approx 3.9 \times 10^{−4}$.

Download Marques and Lopez supplementary movie(Video)
Video 860 KB

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 $2\pi/\omega_0 \approx 3.9 \times 10^{−4}$.

Download Marques and Lopez supplementary movie(Video)
Video 843.3 KB

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 $2\pi/\omega_0 \approx 4.1 \times 10^{−4}$.

Download Marques and Lopez supplementary movie(Video)
Video 3.5 MB

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 $2\pi/\omega_0 \approx 4.1 \times 10^{−4}$.

Download Marques and Lopez supplementary movie(Video)
Video 3 MB

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 $\eta = \pm 10^3$.

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Video 504.7 KB

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 $\eta = \pm 10^3$.

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Video 770 KB