A small Rossby number indicates that the geostrophic
approximation is valid ( i.e., du/dt = dv/dt = 0) and
that the Coriolis acceleration, v · f, is greater than
the horizontal fluid acceleration, du/dt.
Ro = (du/dt)/(v f) (v2/r)/(v f)
= (v/r)/f = U/(f0 · L)
For the GRS, hurricanes, etc.
Ro = (Vt a/b2/3)/f
2 = [ cos2() + (a4/b4) · sin2() ] /
[ cos2() + (a2/b2) · sin2() ]
where Vt is the tangential velocity, a is the semimajor axis,
b is the semiminor axis, and is the angle between the semi-major
axis and the direction of motion.
Mitchell et al. 1981 JGR 86 p.8751.
|terrestrial||Red Spot||FA/BC/DE||small spots|
|Vt||110 m/s||120 m/s|
|a||1.1E7 m||4.9E6 m|
|g.lat||22 S||33 S||40.5 S|
Great Red Spot
40000 x 13000 km (1879-1882)
20-60 m/s velocity around spot, 6 day period
bounded by Jets at -19.5 (-60 m/s) and -27.0 (+50 m/s) graphic latitude
long drift = -3.4 m/s
± 1/2 degree longitude oscillation with 90 day period
anticyclonic (counterclockwise in southern hemisphere)