Granular flow on a rotating and gravitating elliptical body

Abstract

Abstract

Regolith flow on top-shaped asteroids

“…as long as |boldn^b⋅bold-italicP⋅false(bold1−boldn^b⊗boldn^bfalse)|⩽|boldn^b⋅bold-italicP⋅boldn^b|tan⁡δ; the above basal yield criterion naturally accompanies the basal interaction law in equation (2.6) invoked during flow. Now, following the procedure of [23, §3.2], we find that regolith is set into motion when |as|>|an|tan⁡δ. Combining equations (2.3) and (3.3), we obtain the maximum and minimum spin rates Ωy± that bound the range of spin rates within which the regolith remains stationary at a downslope location s from Ωy±=g(±cos⁡{η+ζ}−μsin⁡{η+ζ})τ(…”

“…To this end, we develop a continuum description of axisymmetric regolith flow on top-shaped asteroids and couple the shape changes induced by this flow, and the inertia it carries, with the evolution of the asteroid's spin rate. In this, we greatly extend the work of [23] where the system was two-dimensional and the core's spin was decoupled from the regolith's redistribution. We also discuss the effect of mass shedding on the spin rate of the asteroid, and distinguish between mass shedding events resulting from endogenic and exogenic causes such as landslides and meteorite impacts, respectively.…”

“…We ignore terms of O(ε) except for the pressure gradient term ε∂(hp ss τ )/∂s, which is retained because the granular constitutive relation manifests itself in the momentum balances along ês and êϕ only through this term. This treatment is standard and has been followed in previous works on shallow flows over complex topographies [23,24,53]. The final depth-averaged momentum balances in the s and ϕ directions are then found to be, respectively, To obtain the above, we have set…”

“…For the azimuthal flow, we set v=0 at s=0 and normal∂v/normal∂s=0 at s=1. These boundary conditions are implemented computationally through the use of ghost cells, as in [23].…”

“…However, these investigations talk only about the initiation of failure in the regolith and do not discuss the ensuing evolution of the failed regolith, and its impact on surface reshaping. A first step towards developing a continuum model for granular flows on rotating and gravitating irregular small bodies was taken by [23] who investigated flow of regolith on a gravitating and rotating two-dimensional ellipse. For this, they greatly modified the depth-averaged avalanche models developed for terrestrial avalanches in [24].…”