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Granular flow on a rotating and gravitating elliptical body

Published online by Cambridge University Press:  14 April 2021

Kumar Gaurav Open the ORCID record for Kumar Gaurav [Opens in a new window] ,
Deepayan Banik Open the ORCID record for Deepayan Banik [Opens in a new window] ,
Ishan Sharma Open the ORCID record for Ishan Sharma [Opens in a new window]  and
Pravir Dutt
Kumar Gaurav*
Affiliation:
Mechanics & Applied Mathematics Group, Kanpur, Uttar Pradesh208016, India Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, Uttar Pradesh208016, India
Deepayan Banik
Affiliation:
Mechanics & Applied Mathematics Group, Kanpur, Uttar Pradesh208016, India Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, Uttar Pradesh208016, India
Ishan Sharma
Affiliation:
Mechanics & Applied Mathematics Group, Kanpur, Uttar Pradesh208016, India Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, Uttar Pradesh208016, India
Pravir Dutt
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur, Uttar Pradesh208016, India
*
†Email address for correspondence: kugaurav@iitk.ac.in
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Abstract

We investigate two-dimensional shallow granular flows on a rotating and gravitating elliptical body. This is motivated by regolith flow on small planetary bodies – also called minor planets – which is influenced by the rotation of the body, as well as its irregular topography and complex gravity field. Governing equations are obtained in an elliptic coordinate system attached to the body by extending the framework employed for terrestrial avalanches to incorporate effects of rotation, varying gravity and a curvilinear surface. Additionally, we introduce criteria to monitor grain shedding and to track flow initiation and cessation. We delineate different types of regolith motion that are governed by the rotation rate and surface roughness of the body. We find that grains migrate towards the minor and major axis of the body at low and high rotation rates, respectively. Grains are shed when the basal pressure vanishes, and shedding is encouraged by Coriolis effects during prograde flow. We observe the coexistence of regions of static and mobile regolith and their reorganization owing to the merging or division of flows. We also probe the formation and destruction of dunes – bulges arising from local grain accumulation – and find several aspects of their motion to be different from terrestrial situations. We then perform discrete element simulations that display a good match with theoretical predictions. Finally, we consider the evolution of a bi-disperse regolith. We find that big and small grains occupy, respectively, the top and bottom of the dunes formed on the surface, which is reminiscent of observations on asteroids like Itokawa.

JFM classification

Granular media: Granular media Geophysical and Geological Flows: Shallow water flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A40
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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