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The Dynamic Meteorology of the Stratosphere and Mesosphere by James R Holton

By James R Holton

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0 i< 16 FIG. 1. Annual mean energy cycle for the lower stratosphere (100-30 mb) as computed by Oort (1964) from the Northern Hemisphere IGY data. 27) we obtain an equation for the rate of change of total available energy: d - (K dt - + K' + P + P') = Q + Q' +I (energy fluxes across lower boundary). 28) In the long-term mean the left side approaches zero so that there is an approximate balance between the generation of available potential energy in the stratosphere due to solar differential heating, the flux of energy across the tropopause, and the destruction of available potential energy by infrared radiative damping.

At high latitudes the convergence of the meridians toward the poles produces large geometrical distortions if a beta-plane approximation is used. This distortion can be eliminated, while still preserving much of the analytic attractiveness of the mid-latitude beta-plane 52 CHAPTER2 model, if we follow Charney and Drazin (1961) by retaining the spherical coordinate geometry in the vorticity equation, but replacing both the Coriolis parameter and {3 by constant mid-latitude values. A somewhat similar approach was used by Simmons (1974a) who expanded sin 8 and cos 8 about the pole and employed polar cylindrical coordinates.

L) 2 , (Burger number)}. 18) we obtain the corresponding nondimensional set: Ro-8u ) v sm . () =- F-x Ro -bit - ( 1 + Dt cos () Ro 8 u ) Ro 3 -bv + ( 1 + -Dt Dz oos() Ro - - + Br Dt 1 . 29) Po 8z (p 0 w) = o. 32) In order to proceed further we must now choose specific magnitudes for our scalings. 4 x 106 m, 20. 4 x 10- 4 s-t, andH = 7 x 103m for an isothermal atmosphere with T 0 = 240 K. We then find that the buoyancy frequency and the radius of deformation are N = 2 x 10-2 s- 1 and L = 106 m, respectively.

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