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Unformatted text preview: The mathematics of weather and climate Dr Emily Shuckburgh Equations of fluid flow I Cloud over a hill C(x,y,z,t). In steady state cloud doesnt change in time. Following a particle Lagrangian derivative C t ae fixed point in space = 0 C = dt C t + dx C x + dy C y + dz C z DC Dt = + Advection : ability of fluid to carry properties with it as it moves Equations of fluid flow II 5 key variables ( u,v,w ), p, T 5 eqns: Newtons 2nd (3 eqns), conserve mass (1 eqn), thermodynamics (1 eqn) Hydrostatic balance Ideal gas: ( R gas constant, T temperature) d xd ydz D u Dt = F fric + F gravity + F pressure 1 r p g z p / = g = =  p = / Equations of fluid flow III Conserve mass  mass changes if flux into volume: First law of thermodynamics gives: DQ/Dt comes from latent/radiative heating (note T, p dependency) DQ Dt =  1 D + = 0 Effects of rotation...
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This note was uploaded on 11/11/2011 for the course MATH 220 taught by Professor Kearn during the Fall '11 term at BYU.
 Fall '11
 Kearn
 Equations

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