(1) Hydrostatic balance states Әр Equation -1 where p is pressure, z is altitude, p is density and g is the acceleration due to gravity. It can be shown that the reciprocal of hydrostatic balance also applies. That is Equation -2 дz Əz Әр =-pg, 1 pg Use the ideal gas law (p= pRT, where Ra is the gas constant for dry air and T is temperature) to eliminate p from (2). (2) Under geostrophic balance, the following balance is approximately satisfied Equation -3 fu=-g ¹(³), ду where f is the Coriolis parameter, u is the zonal wind, y is meridional distance and z is altitude. (Note that the derivative on the right hand side is taken at constant pressure.) Differentiate (3) with respect to p, and use your expression from part 1 to obtain an expression relating du/ap and T/ay. This expression is called "thermal wind balance".
(1) Hydrostatic balance states Әр Equation -1 where p is pressure, z is altitude, p is density and g is the acceleration due to gravity. It can be shown that the reciprocal of hydrostatic balance also applies. That is Equation -2 дz Əz Әр =-pg, 1 pg Use the ideal gas law (p= pRT, where Ra is the gas constant for dry air and T is temperature) to eliminate p from (2). (2) Under geostrophic balance, the following balance is approximately satisfied Equation -3 fu=-g ¹(³), ду where f is the Coriolis parameter, u is the zonal wind, y is meridional distance and z is altitude. (Note that the derivative on the right hand side is taken at constant pressure.) Differentiate (3) with respect to p, and use your expression from part 1 to obtain an expression relating du/ap and T/ay. This expression is called "thermal wind balance".
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Transcribed Image Text:(1) Hydrostatic balance states
Әр
Equation -1
-Pg,
where p is pressure, z is altitude, pis density and g is the acceleration due to gravity.
It can be shown that the reciprocal of hydrostatic balance also applies. That is
Equation -2
Əz
Əz
Әр
1
pg
Use the ideal gas law (p = pRT, where R is the gas constant for dry air and T is
temperature) to eliminate p from (2).
(2) Under geostrophic balance, the following balance is approximately satisfied
Equation -3
fu = -g
(³3),
ду
where f is the Coriolis parameter, u is the zonal wind, y is meridional distance and
z is altitude. (Note that the derivative on the right hand side is taken at constant
pressure.) Differentiate (3) with respect to p, and use your expression from part
1 to obtain an expression relating du/ap and OT/oy. This expression is called
"thermal wind balance".
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