Mathematics – Logic
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010agufm.p42b..04f&link_type=abstract
American Geophysical Union, Fall Meeting 2010, abstract #P42B-04
Mathematics
Logic
[5420] Planetary Sciences: Solid Surface Planets / Impact Phenomena, Cratering
Scientific paper
Layered ejecta deposits of impact craters on Mars take three main morphological classifications: single-layer (SLE), multi-layer (MLE) and double-layer (DLE) ejecta deposits. It has long been thought that these deposits involved fluid-particulate flows, although there has been extensive debate as to the nature (vapor or liquid) and origin (atmospheric or crustal) of the fluid. We have modeled the emplacement of such deposits as overland flows originating from or near the crater rim using a shallow-wave formulation of momentum and volume conservation. Given the prodigious energy of impact, it is conjectured that the initial velocity uo at the crater rim exceeds √gho, where ho is the initial flow depth. When this is the case, the character of the solutions for flow depth h(r,t) and velocity u(r,t) fundamentally features two waves with different forward propagation speeds. The faster wave occupies an advancing outer zone, while both the fast and slow waves interact in an expanding inner zone. The ways in which these waves propagate and interact produce widely varying flow profiles that, in turn, explain the broad features of the three main ejecta deposit types. Measurements of the rampart runouts, heights and leading and trailing slopes were made for 27 ejecta deposits in Lunae Planum. The plane wave solutions suggest that the transit times are only a few minutes or less, with initial velocities in the range 20-100 m s-1. SLE deposits form preferentially when the flow duration is relatively short. MLE deposits, on the other hand, form when the flow is fed for a longer time and instability is promoted. All DLE and most MLE deposits seem to retain the two-component character of the flow. The slope of the advancing front is sensitive to the value of the friction factor C. Measurements of the leading slopes of SLE deposits (1-2°) give C-values two orders of magnitude less than those of terrestrial debris flows, suggesting vapor as a fluidizing agent rather than liquid water. However, if friction becomes too great, the slower wave can overtake the faster one, as has been conjectured to explain the morphologies of some DLE deposits. Similar processes have been reported in the terrestrial debris flow literature. Such a change in friction could be caused by the entrainment of external sediment along the flow path, the loss of the volatile component during transit, or the sorting of larger particles toward the front. The shallow-wave model for ejecta flow provides a unifying interpretation for the formation of SLE, DLE, and MLE deposits. It suggests there is indeed a physical fluid dynamic basis for this ternary morphological classification. Further analysis will incorporate radial effects, entrainment, degassing, and particle sorting during transit, all aimed at determining the nature of the fluidizing agent in these flows.
Baloga Stephen M.
Fagents Sarah A.
Glaze Lori S.
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