ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
Passive tracers in steady-state three-dimensional (3-D) convective flows with infinite Prandtl number, which is relevant for the Earth's mantle, show a remarkable flow structure. Individual flowlines as shown by Poincare sections of the tracer paths lie on a two-dimensional (2-D) surface with distorted toroidal topology. Furthermore, the space occupied by the convecting fluid is filled by a set of these toroidal surfaces nested one within another. The small radius of the innermost toroidal surface approaches zero, defining a closed streamline whose location we have determined in specific cases using numerical solutions. The outermost of the toroidal surfaces coincides with the upper and lower surfaces of the layer and with vertical symmetry planes which separate the flow between neighboring cells. Both square and hexagonal convection planforms show a triangular cellular structure with triangles defined by (π/2,π/4,π/4) and (π/2,π/6,π/3), respectively. The outer toroidal surface is closed by a horizontal flow line through the middle of the cell. The numerical experiments suggest that streamlines are not generally closed in any small number of orbits. Instead the toroidal surface appears to be progressively filled in by the trace of a single streamline which, in successive orbits, is displaced across the surface without returning to the same path. This flow structure ensures that, while extreme shear strains can occur, particularly in the vicinity of the cell separatrices, mixing of the material only occurs in 2D. Tracers initially on one toroidal surface remain on that surface indefinitely. Like for 2-D convective flow, time dependence of the solution appears to be a necessary prerequisite for thorough spatial mixing to occur. © 1995 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.868614
