Rossby Number

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) approx (v2/r)/(v f) = (v/r)/f = U/(f0 · L)

For the GRS, hurricanes, etc.

Ro = (Vt a/b2/eta3)/f

eta2 = [ cos2(theta) + (a4/b4) · sin2(theta) ] / [ cos2(theta) + (a2/b2) · sin2(theta) ]

where Vt is the tangential velocity, a is the semimajor axis, b is the semiminor axis, and theta is the angle between the semi-major axis and the direction of motion. Mitchell et al. 1981 JGR 86 p.8751.



terrestrialRed SpotFA/BC/DEsmall spots
Vt110 m/s120 m/s
a1.1E7 m4.9E6 m
Ro(0).36.36
Ro(90).04.08
g.lat22 S33 S40.5 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)