Gravity oscillations Assume that the lower troposphere is isothermal with a temp

Question

Gravity oscillations Assume that the lower troposphere is isothermal with a temperature T_A. An airparcel at the surface is heated isobarically to a temperature of T_0 and then released and allowed to ascend dry adiabatically. Assume that the buoyancy is the only force acting on the parcel and that mixing between the parcel and ambient dry air can be neglected. The buoyant parcel will accelerate initially, attain a maximum velocity at some altitude, and then decelerate until its upward motion stops. Then, be colder than its surrounding s, it will start to fall and accelerate downwards. Derive formula for the following quantities: a) The maximum altitude of the parcel b) The altitude at which the vertical velocity is maximum c) The value of the maximum upward velocity d) The value of the maximum downward velocity c) Also evaluate these quantities numerically assuming T_A = 10 degree C and T_0 = 12 degree C

Explanation / Answer

s = ut + 1/2at2

(u = initial velocity, v = final velocity, a = acceleration,

s = displacement, t = time)

s = 1/2 (u + v)t

v = u + at

T0=12°C Initial temperature at the surface   

TA = 10°C is the lower troposphere is isothermal temperature

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