Regolith mechanics: models, experiments and possible theory on the base
of the Navier-Stokes equation.

**Dr. Nick Gorkavyi**

**703/754-7263, <gorkavyi@gist.us>**

**Greenwich Institute for Science and Technology**

**P.O.Box 797, Haymarket, VA, 20168**

[**www.gist.us**](http://www.gist.us/)

Description of analytical a three-stage models for collision of a body
and a solid surface covered by a thin layer of loose regolith, that was
proposed by Gorkavyi (1985) within investigation of mutual collision of
particles of Saturnian rings. The prediction of the theoretical model
was strange: the restitution coefficient increases with increasing
velocity. This fact had not been experimentally noted before. This
prediction and all other qualitative features of the model have been
confirmed during experiment by Gorkavyi (1989) (see details for the
model and experiment in the book by Fridman & Gorkavyi "Physics of
Planetary Rings" \[1\]). An experiment was carried out to measure the
restitution coefficient of a metallic sphere (\~ 1 lb) falling on a
massive limestone slab, covered by a layer of dry fine sea sand (other
test was done for concrete slab covered by dry cement dust). Inelastic
deformation energy of regolith was determined. Existing an air wave
sweeping the regolith away from under the incident body has been
confirmed (according Hartmann (1978) experiments, the impact dispersion
of the regolith in the Earth atmosphere was in three orders of magnitude
larger than the ejection of regolith from the impact zone in vacuum).

These models and experiments provided important information, that was
necessary for developing transport theory for flows of inelastic
collided macroparticles inside planetary rings (\[1\], Chapter 7). In
order to construct the hydrodynamics of macroparticles in planetary
rings one must obtain from the kinetic equation with collision integral
for inelastic collisions a set of moment equations and close it through
using kinetic theory to evaluate the viscosity and thermal conductivity
coefficients. The classical methods of kinetic theory, developed by
Chapman and Enskog (see, Chapman and Cowling \[2\]) made it possible to
obtain from the kinetic equation a closed system of moment equation or
the set of equations of viscous hydrodynamics. Inelasticity somewhat
changes the form of the moment equations and makes the problem of
whether the distribution function is stationary more complicated. On
base of developed transport theory for inelastic particles a set of new
instabilities of particles flow was discovered (\[1\], Chapter 8).

Probably, similar program can be realized for developing regolith
"hydrodynamics". Many factors are similar for hydrodynamics of regolith
and hydrodynamics of particles of Saturnian rings: inelastic
macroparticles as basic elements of media; non-uniform flows and heating
due to landslides (analog of well-known heating of planetary rings due
non-uniform rotation); non-diffusion transfer of particles by air and
origin of dunes (analog of structures created by accretion instability
in planetary rings \[1\]). Discussion of developing regolith
hydrodynamics includes nest points:

-   analytical simple models and non-expensive tests for verification of
    models. This data will be useful for practical goals (planning space
    missions) and for developing advanced mechanical models for accurate
    soil dynamics prediction;

-   analytical modified Navier-Stokes equation for regolith flows;

-   numerical approach on base of modified Navier-Stokes equation for
    simulation of realistic cases that include all physical important
    factors and used parameters from experiments. In this simulation
    regolith will be considered in two phases: in solid stationary state
    and in "liquid" dynamical phase, that will be included effects of
    air pressure and air flows.

Also application of remote sensing for estimation of regolith parameters
will be discussed using author' experience in processing LIDAR/IFSAR
data \[3\]: LIDAR scanning for investigation of 3D-surface of regolith
and relief, IR-albedo and Seeliger effects for porosity; radar
observation for estimation of density and underground water/ice. Remote
sensing together with numerical simulation can provide reasonable
estimation of geological environment before landing and *in-siti* tests.

References:

1.  Fridman, A.M. and Gorkavyi, N.N. Physics of Planetary Rings.
    Celestial Mechanics of Continuous Media. Springer-Verlag. 1999. 436
    p.

2.  Chapman, S. and Cowling, T.G. The Mathematical Theory of Non-Uniform
    Gases. Cambridge Univ. Press. 1953.

3.  Nick Gorkavyi, Tanya Taidakova, "Automatic Processing LIDAR Data and
    3D Terrain Models", NASA Capability Roadmap Public Workshop,
    Washington, DC, November 30, 2004