Large-scale-vortex dynamos in planar rotating convection

• Published in: Journal of fluid mechanics Vol. 815; pp. 333 - 360
• Main Authors: Guervilly, Céline, Hughes, David W., Jones, Chris A.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.03.2017
• Subjects: Amplitude; Boussinesq approximation; Boussinesq equations; Cell size; Computational fluid dynamics; Convection; Convection modes; Earth; Energy spectra; Fluid flow; Magnetic field; Magnetic fields; Magnetic induction; Oscillations; Reynolds number; Rotating generators; Vortices; United Kingdom > UK; dynamo theory; rotating turbulence; turbulent convection
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2017.56

Several recent studies have demonstrated how large-scale vortices may arise spontaneously in rotating planar convection. Here, we examine the dynamo properties of such flows in rotating Boussinesq convection. For moderate values of the magnetic Reynolds number ( $100\lesssim Rm\lesssim 550$ , with $Rm$ based on the box depth and the convective velocity), a large-scale (i.e. system-size) magnetic field is generated. The amplitude of the magnetic energy oscillates in time, nearly out of phase with the oscillating amplitude of the large-scale vortex. The large-scale vortex is disrupted once the magnetic field reaches a critical strength, showing that these oscillations are of magnetic origin. The dynamo mechanism relies on those components of the flow that have length scales lying between that of the large-scale vortex and the typical convective cell size; smaller-scale flows are not required. The large-scale vortex plays a crucial role in the magnetic induction despite being essentially two-dimensional; we thus refer to this dynamo as a large-scale-vortex dynamo. For larger magnetic Reynolds numbers, the dynamo is small scale, with a magnetic energy spectrum that peaks at the scale of the convective cells. In this case, the small-scale magnetic field continuously suppresses the large-scale vortex by disrupting the correlations between the convective velocities that allow it to form. The suppression of the large-scale vortex at high $Rm$ therefore probably limits the relevance of the large-scale-vortex dynamo to astrophysical objects with moderate values of $Rm$ , such as planets. In this context, the ability of the large-scale-vortex dynamo to operate at low magnetic Prandtl numbers is of great interest.