Venus Atmosphere Puzzle, one man's struggle with atmospheric physics |
Venus Atmosphere Puzzle, one man's struggle with atmospheric physics |
Jun 5 2006, 12:15 PM
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Junior Member Group: Members Posts: 57 Joined: 13-February 06 From: Brisbane, Australia Member No.: 679 |
Hi All
This might seem like a really dumb question, but what's the mass of the Cytherean atmosphere per unit area? At first pass I thought it was easy - same as for an isothermal atmosphere, Po/g, where Po is surface pressure and g is surface gravity. Simple. Except Venus doesn't come close to approximating an isothermal atmosphere. From a graph in Mark Bullock's PhD thesis (Hi Mark if you're visiting) I pulled the figures for Po and To as 92 bar and 735 K, while the left-side of the temperature curve was 250 K at 0.1 bar and 63 km. At about 210 K the temperature drop with altitude stops, then slowly rises into the Cytherean stratosphere. Ok. My atmospheric physics is pretty limited - I 'modelled' that lapse rate pressure curve as a power law: P/Po = (T/To)^n and likewise for density, d/do = (T/To)^n. Temperature, T, as a function of altitude, Z, I computed as T(Z) = To*(1-Z/(n.Zo)). Zo = (k.T/m.g), where k is Boltzmann's constant and m is the molecular mass of the atmosphere. These equations I then integrated between 210 K and 0.033 bar, 70 km, and 735 K and 92 bar, zero altitude. The resulting equation is m = (n/(n+1))*(do.Zo)*(1 - (T/To))^(n+1) - a bit of simple algebra and the Gas equation shows that do.Zo = Po/g. Thus the mass is lower than for a simple isothermal atmosphere by roughly (n/(n+1)). In this case n = 6.33, higher than the dry adiabat for CO2 which gives n = 4.45. Now an adiabatic or polytropic atmosphere is an idealisation, but it seems odd to me that whenever Venus' atmospheric mass is discussed people always use the higher isothermal value. Have I missed something important in the physics, or is Venus's atmospheric mass just 86.4% of the usually quoted value? |
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Jun 25 2006, 12:50 AM
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Junior Member Group: Members Posts: 57 Joined: 13-February 06 From: Brisbane, Australia Member No.: 679 |
Hi Messenger & ngunn
Hey thanks for the nice comments and useful gedankenexperiments. More update as follows... I've 'discovered' that the US NIST has the proper fit equation for Cp of CO2 online - I was close as it's almost a quadratic. I just did a rough fit from a table of values, but I was pretty close. Now I need to work out a simplified equation for 'g' for a future C version of the model. Of course I could just use the good odd inverse square law, but why make it easy on me and hard on the number cruncher? Gravity varies almost linearly with altitude in the range we're discussing. The less maths functions I need to call from the C library the better. Also I've managed to find a discussion of cloud formation with data on Venus's sulphuric acid clouds, so I'll be able to add that little refinement to the higher altitude computations. Also I did an Earth version of the model based on the International Standard Atmosphere's lapse rates and altitudes, all the way to the Stratopause's ceiling at 51 km. The match is pretty good and the mass of the air column is exactly as expected, Po/g. The ISA uses 'geopotential altitude' so I didn't need to compute 'g'. Now all I need is to figure out the heat transfer equations and I can model the atmosphere temporally too. I've got a copy of Mark Bullock's thesis and he covers that in some detail, probably more detail than my poor laptop can number crunch in a meaningful time. Adam |
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