Computer Science
Scientific paper
Feb 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002p%26ss...50..235w&link_type=abstract
Planetary and Space Science, Volume 50, Issue 2, p. 235-246.
Computer Science
2
Scientific paper
In this paper we derive a special linear non-vortical wave propagation solution in the shearing sheet, a model of a compressible two-dimensional fluid system with constant density, constant shear and constant Coriolis force, but without self-gravity. The linear analysis of the shearing sheet leads to a single differential equation for the azimuthal velocity perturbation. A detailed derivation of a special solution with a prescribed azimuthal wavenumber /k is presented. More general wave solutions, eventually excited by large local `impacts', can be derived by superimposing all /k-modes. The special wave functions so obtained describe the formation of two independent spiral wave arms originating out of a ring-shaped structure. The motivation for this investigation lies in the fact that similar wave propagators can be excited by the transit of a solid or `clumpy' object through a protoplanetary disk. We speculate that a disk-brown dwarf collision can produce in the disk a pair of two spiral density wave fragments triggering the rapid accretion of two giant planets by a gravitational shear instability simultaneously (Hypothesis of a mechanism for the production of giant planets in pairs).
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