scholarly journals Weak branch and multimodal convection in rapidly rotating spheres at low Prandtl number

2021 ◽  
Vol 6 (12) ◽  
Author(s):  
F. Garcia ◽  
F. Stefani ◽  
E. Dormy
Keyword(s):  
Prandtl Number ◽  
Weak Branch

scholarly journals Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model

2016 ◽  
Vol 808 ◽  
pp. 61-89 ◽  
Author(s):  
Céline Guervilly ◽  
Philippe Cardin
Keyword(s):  
Prandtl Number ◽  
Nonlinear Oscillations ◽  
Liquid Metals ◽  
Rotation Axis ◽  
Three Dimensional ◽  
Zonal Flow ◽  
Onset Of Convection ◽  
Nonlinear Convection ◽  
Rotating Sphere ◽  
Weak Branch

We study nonlinear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals ($Pr\in [10^{-2},10^{-1}]$). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than $10^{-6}$, which is continuous at the onset (supercritical bifurcation) and consists of thermal Rossby waves and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of $10^{-8}$. On the strong branch, the Reynolds number of the flow is greater than $10^{3}$, and a strong zonal flow with multiple jets develops, even close to the nonlinear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis ($Ek=10^{-6}$, $Pr=10^{-2}$). Nonlinear oscillations are observed near the onset of convection for $Ek=10^{-7}$ and $Pr=10^{-1}$.

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