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Homework Help: Show that the atmosphere is neutrally stable

  1. Nov 29, 2011 #1
    1. The problem statement, all variables and given/known data
    Assume that the atmosphere is dry, and that its temperature profile may be approximated by a linear function in height using a constant lapse rate:

    T = T_0 - [itex]\gamma[/itex]Z


    where T_0 is the ground temperature. Also assume that the pressure can be approximated the following equations for a constant lapse rate atmosphere:

    p = p_0((T_0 - [itex]\gamma[/itex]Z)/T_0)^(g/[itex]\gamma[/itex]R_d)

    By using the definition of potential temperature, show that the atmosphere is neutrally stable (i.e d θ/d Z = 0 ) when the value of the constant lapse rate is equal to the dry adiabatic lapse rate, [itex]\gamma[/itex] = g/c_p

    2. Relevant equations

    equation of potential temperature:
    θ = T(100/P)^k

    3. The attempt at a solution
    I believe i need to come up with an expression for the potential temperature using the definition given of T ( as a function of z and a constant lapse rate and the definition of p in a constant lapse rate) but I don't see how to do that to commute for dθ/dz = 0
     
  2. jcsd
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