Mathematics – Logic
Scientific paper
May 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002agusm.p41a..01h&link_type=abstract
American Geophysical Union, Spring Meeting 2002, abstract #P41A-01
Mathematics
Logic
6225 Mars
Scientific paper
A variety of channel types on Mars suggest the importance of fluvial water in shaping the Martian surface. Extensive valley networks, huge ancient circum- Chyrse channels, and extremely recent, smaller flood channels indicate the prevalence of surface water flow throughout Martian history. An accurate method for quantifying flow in these various channels would provide important clues to Mars' geologic, hydrologic, and atmospheric history. Previous estimates of Martian flood flow velocities used a form of the Manning equation, i.e., V = (k/n) R (2/3) So(1/2) where R (hydraulic radius, i.e., cross-sectional area divided by wetted perimeter) and So (channel slope) are derived from MOLA data. Channel roughness (Manning's n) has usually been taken as 0.040, appropriate for a rough lava surface. The constant k is either 0.5 (arbitrary, from Carr 1979) or 0.38 (ratio of Mars to Earth gravity). Manning's equation is an empirical equation valid for clear-water flow. Because of its empirical derivation, and a likely heavy sediment load due to Mars' lower gravity, Manning's equation may not be appropriate for Martian fluvial flow. We derived from a force balance on an element of fluid a velocity equation appropriate for the Martian environment. Velocity is calculated as a function of a gravity force resolved in the downslope direction and a retarding friction force that is a function of the Reynold's number and channel equivalent roughness, i.e., V = \sqrt{(8g/f)} \sqrt{(Dh/4)sin\theta} In the second equation, Dh is 4 x hydraulic radius, and sin theta is the channel slope, both determinable from MOLA data. The friction factor f, a function of the calculated Reynold's number, is estimated iteratively from channel and fluid properties. Thus, our method takes Martian gravity explicitly into account and is valid for a range of flow conditions as parameterized by the Reynold's number. Our velocity calculations are consistently lower, by a factor of 5 to 6, than velocities calculated by the Manning equation; for example, in one section of the Kasei Vallis, we calculated a velocity of 5.8 m s-1, versus values of 25.5 m s-1 (k = 0.38) and 33.7 m s-1 (k = 0.5) with Manning's equation. Discharge magnitudes (velocity x cross-sectional area) would be lower by the equivalent factor. Our method will be useful in refining both the magnitude of discrete catastrophic flooding events, and in constraining the surface movement of water in general throughout Mars' history.
Beckhorn J.
DeKoskie D.
Fonte Sergio
Hassett J. M.
McCague S.
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