The Growth of Point Source Plumes at High Rayleigh Numbers for Prandtl Numbers up to 1000

Details The Growth of Point Source Plumes at High Rayleigh Numbers for Prandtl Numbers up to 1000 The Growth of Point Source Plumes at High Rayleigh Numbers for Prandtl Numbers up to 1000

Dec 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001agufmng42b0425m&link_type=abstract

American Geophysical Union, Fall Meeting 2001, abstract #NG42B-0425

Physics

3210 Modeling, 3220 Nonlinear Dynamics, 3230 Numerical Solutions, 5700 Planetology: Fluid Planets, 5799 General Or Miscellaneous

Scientific paper

Convection at high Rayleigh numbers in finite Prandtl fluids with large Prandtl numbers is important in many geophysical situations. For example, convection can occur in magma chambers and magma oceans. It can also occur in ice/water systems, such as on the Jovian moon Europa. Currently, however, simulations of finite Prandtl number convection have been conducted only up to Prandtl numbers of 100. This study addresses the behavior of convective systems with larger Prandtl numbers. We have conducted numerical simulations of the growth of plumes from a single point source at Rayleigh numbers ranging from Ra = 106 to Ra = 108 for Prandtl numbers ranging from Pr = 7 to 1000. Scaling the time by the free fall velocity (Moses \textit{et al}., 1993) has allowed us to increase the Prandtl number up to 1000. Simulations at Ra = 108 and Pr = 1000 used grid sizes of 256 x 1536. The plumes tend to develop Whitehead instabilities (Skilbeck and Whitehead, 1978) as the local thermal gradient becomes supercritical, and new plumes are produced locally. We have used wavelets to visualize and study the formation of these instabilities. We have also studied the scaling of Nusselt number with Rayleigh number and Prandtl number to better understand how heat flux changes as Prandtl numbers increase. References: Moses, E.; Zocchi G. and Libchaber, A. (1993) An experimental study of laminar plumes. \textit{Journal of Fluid Mechanics} 251: 581-601. Skilbeck, J.N. and Whitehead J.A. (1978) Formation of discrete islands in linear chains. \textit{Nature} 272:499-501.

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