little_L_
Nov29-11, 04:05 PM
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 - \gammaZ
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 - \gammaZ)/T_0)^(g/\gammaR_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, \gamma = 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
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 - \gammaZ
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 - \gammaZ)/T_0)^(g/\gammaR_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, \gamma = 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