### Abstract

A new quantitative formalism describing the dynamics of a Keplerian particulate disk, based on a heuristic description of viscous transport, permits study of rings with a wide range of ensemble and individual particle properties. Here the formalism is developed and applied to the case of a ring with a radial gradient in optical thickness. A steady-state solution for the velocity distribution directly gives the radial mass transport, as well as the viscosity. The formula for viscosity is identical to that derived a decade earlier by Goldreich and Tremaine for a uniform disk, thus validating the assumption by various workers that it could be applied to nonuniform disks, for example in consideration of ringlet instabilities. Our analytical method involves solving a novel form of the Krook equation by separating the distribution of collisional products in phase space into a symmetrical component and a remainder that can be approximated by delta functions. Unlike most past approaches, a Gaussian form for the solution is not assumed. In the case described here, the model is simplified in common with past work (e.g., small, uniform particles and Krook-type treatment of collisions), but the general approach is extendable to less artificially restricted cases.

Original language | English (US) |
---|---|

Pages (from-to) | 146-171 |

Number of pages | 26 |

Journal | Icarus |

Volume | 88 |

Issue number | 1 |

DOIs | |

State | Published - 1990 |

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### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Icarus*,

*88*(1), 146-171. https://doi.org/10.1016/0019-1035(90)90183-A

**Viscosity and mass transport in nonuniform Keplerian disks.** / Ojakangas, G. W.; Greenberg, Richard J.

Research output: Contribution to journal › Article

*Icarus*, vol. 88, no. 1, pp. 146-171. https://doi.org/10.1016/0019-1035(90)90183-A

}

TY - JOUR

T1 - Viscosity and mass transport in nonuniform Keplerian disks

AU - Ojakangas, G. W.

AU - Greenberg, Richard J.

PY - 1990

Y1 - 1990

N2 - A new quantitative formalism describing the dynamics of a Keplerian particulate disk, based on a heuristic description of viscous transport, permits study of rings with a wide range of ensemble and individual particle properties. Here the formalism is developed and applied to the case of a ring with a radial gradient in optical thickness. A steady-state solution for the velocity distribution directly gives the radial mass transport, as well as the viscosity. The formula for viscosity is identical to that derived a decade earlier by Goldreich and Tremaine for a uniform disk, thus validating the assumption by various workers that it could be applied to nonuniform disks, for example in consideration of ringlet instabilities. Our analytical method involves solving a novel form of the Krook equation by separating the distribution of collisional products in phase space into a symmetrical component and a remainder that can be approximated by delta functions. Unlike most past approaches, a Gaussian form for the solution is not assumed. In the case described here, the model is simplified in common with past work (e.g., small, uniform particles and Krook-type treatment of collisions), but the general approach is extendable to less artificially restricted cases.

AB - A new quantitative formalism describing the dynamics of a Keplerian particulate disk, based on a heuristic description of viscous transport, permits study of rings with a wide range of ensemble and individual particle properties. Here the formalism is developed and applied to the case of a ring with a radial gradient in optical thickness. A steady-state solution for the velocity distribution directly gives the radial mass transport, as well as the viscosity. The formula for viscosity is identical to that derived a decade earlier by Goldreich and Tremaine for a uniform disk, thus validating the assumption by various workers that it could be applied to nonuniform disks, for example in consideration of ringlet instabilities. Our analytical method involves solving a novel form of the Krook equation by separating the distribution of collisional products in phase space into a symmetrical component and a remainder that can be approximated by delta functions. Unlike most past approaches, a Gaussian form for the solution is not assumed. In the case described here, the model is simplified in common with past work (e.g., small, uniform particles and Krook-type treatment of collisions), but the general approach is extendable to less artificially restricted cases.

UR - http://www.scopus.com/inward/record.url?scp=38249018389&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249018389&partnerID=8YFLogxK

U2 - 10.1016/0019-1035(90)90183-A

DO - 10.1016/0019-1035(90)90183-A

M3 - Article

VL - 88

SP - 146

EP - 171

JO - Icarus

JF - Icarus

SN - 0019-1035

IS - 1

ER -