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A Fluid Dynamical Treatment of Common Action of Self-Gravitation, Collisions, and Rotation in Saturn'sB-Ring

Schmit, u. and Tscharnuter, W.(1) (1995) A Fluid Dynamical Treatment of Common Action of Self-Gravitation, Collisions, and Rotation in Saturn'sB-Ring. Icarus, pp. 304-319. Academic Press, New York, USA.

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We study the generation of structures in Saturn's B-ring under the common action of self-gravitation, inelastic collisions, and rotation. Folowing a hydrodynamical approach the ring corresponds to a viscous fluid. Then the state of the rings is governed by the surface density dependence of the dynamic viscosity, d(vo)/do, with v being the kinematic viscosity and o the surface density. Several authors have calculated v and e: &#61 d ln(vo)/d ln o. In all of their models e takes a positive quantity. Then two different instabilities may arise. For all e below a small positive number the ring is securlarlyunstable. The wavelengths of the fastest growing modes are of the order of one Jeans length, i.e. 80-120 m in our case. For a sufficient large positive e another unstable branch appears: The ring is overstable. Here individual particle oscillate and the hydrodynamic picture is a standing wave with rapidly growing amplitudes. Again, the wavelength of the fastest growing mode is in the range of about 80 m. Since the ring deviates considerably from a classical gas, it is rather difficult to determine the quamtity e. Although this problem has already been an outstanding matter of investigation for a long time, a generally accepted solution is stillmissing. For that reason we restrict our stability analysis to the parameterized representation of v with v x o_ and &#61 e -1 &#61 const and discuss both the secular instability, which sets already in for small positive e if self-gravitation is included, and the overstable modes that are produced by sufficiently large e>0, even without self-gravitation. In this paper we derive the quasi-linear perturbation equations and solve toe corresponding initial-boundary value problem. The ring's gravitational potential is also treated in a self-consistent way. The aim of the paper is to show that the disk is probably unstable or overstable and small-scale perturbations exhibit a remarkable intensification within a few orbital periods.

Item URL in elib:https://elib.dlr.de/35179/
Document Type:Article
Additional Information: LIDO-Berichtsjahr=1995,
Title:A Fluid Dynamical Treatment of Common Action of Self-Gravitation, Collisions, and Rotation in Saturn'sB-Ring
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Journal or Publication Title:Icarus
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
Page Range:pp. 304-319
Publisher:Academic Press, New York, USA
Series Name:115
HGF - Research field:UNSPECIFIED
HGF - Program:Space (old)
HGF - Program Themes:W EW - Erforschung des Weltraums
DLR - Research area:UNSPECIFIED
DLR - Program:W EW - Erforschung des Weltraums
DLR - Research theme (Project):UNSPECIFIED
Location: Berlin-Adlershof
Institutes and Institutions:Institute of Planetary Research > Institut für Planetenerkundung
Deposited By: DLR-Beauftragter, elib
Deposited On:02 Apr 2006
Last Modified:27 Apr 2009 09:48

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