problem 8.1

Thermal wind and jet stream

Horizontal pressure gradient arises in the atmosphere owing to temperature variation which is related to the horizontal density gradient. This is responsible to the thermal wind in a rotating system. Global distribution of average atmospheric temperature T ( x, y, z) generates a thermal wind, called the jet stream (i.e. westerly).

Assuming 2 ? = f k ( f = 2 ? sin ) in (8.15) with k the unit vertical vector in the local ?-plane approximation (of Sec. 8.5), we have the horizontal component v _h (projection to the ( x, y)-plane) of the geostrophic velocity given by (8.21): v _h = (1 /f ) k grad P. Answer the following questions.

1. Suppose that z = z _p( x, y) represents a surface of the altitude of constant pressure ( p = const .). Using the hydrostatic relation (8.13), show the following equation,

   
   

   [ Hint: On the surface z = z _p( x, y), d p _{y =con st} = ? _x pd x + ? _z pd z _p = 0.]

Thus, the pressure gradient in the horizontal surface ? _* = const . is related to the inclination of the surface z = z _p( x, y). The global mean pressure in the...