Horizontal implies constant
height above mean sea level (z), so a horizontal pressure gradient is as illustrated. Using
pressure as the vertical coordinate requires horizontal gradients evaluated on a constant
pressure surface. Considering the x-z plane as shown :
[((po +
dp) - po) / dx]z = [((po + dp) - po) / dz]x [dz / dx]p[---]a implies the quantity --- in brackets is valid for constant values of the variable a. Using numbers shown on the diagram is helpful for seeing this equality :
((1010 - 1000) / 5) = ((1010 - 1000) / 2) (2/5) , thus
(2) = (5) (2/5)
though please be aware that the
d symbols represent infinitesimally small changes. Considering limits of the differentials as d's approach 0 :[
¶P/¶x]z = - [¶P/¶z]x [¶z/¶x]pThe minus sign in front of the 2nd term because z decreases as p increases.
Text and embedded images are copyright of Joseph Bartlo, though may be used with proper crediting.