Engineering & Science
Rossby Number (Ro), Coriolis Parameter (f) & Geostrophic Wind Speed
Calculate the planetary Coriolis parameter f = 2 * Omega * SIN(phi), atmospheric/oceanic Rossby number Ro = U / (|f| * L), and geostrophic wind speed Ug = (dP / dn) / (rho * |f|).
Diagnose when Earth’s rotation locks synoptic pressure gradients into geostrophic balance!
Synoptic meteorologists and physical oceanographers separate rotation-dominated cyclones from small-scale convective storms using Carl-Gustaf Rossby’s dimensionless Rossby Number Ro = U / (|f| * L), comparing inertial advection U / L against Earth’s local Coriolis frequency f = 2 * Omega * sin(phi) (where sidereal rotation rate Omega = 7.2921e-5 rad/s and phi is latitude)!
When Ro << 1 (for example, mid-latitude latitude phi = 45°, characteristic wind U = 20 m/s, synoptic length scale L = 1,000 km -> f = 1.0313e-4 s^-1 and Ro = 0.194), horizontal pressure gradients dP / dn balance the Coriolis deflection to produce Geostrophic Wind Ug = (dP / dn) / (rho * |f|)! For a 150 Pa pressure drop per 100 km (1.5 hPa / 100 km) at air density rho = 1.225 kg/m^3, Ug = 11.87 m/s at 45° latitude—and jumps to 32.44 m/s near the tropics at 15° latitude where |f| weakens, before breaking down completely right on the equator (phi = 0° -> f = 0)!
| Latitude Scenario (U = 20 m/s, L = 1000 km, dP/100km = 150 Pa) | Coriolis |f| (x 10^-4 s^-1) | Rossby Number Ro | Geostrophic Wind Ug (m/s) |
|---|---|---|---|
| Mid-Latitude Extratropical Cyclone (45° N) | 1.0313 | 0.194 (Quasi-Geostrophic) | 11.87 m/s |
| Subtropical Flow (15° N) | 0.3775 | 0.530 (Ageostrophic Drift) | 32.44 m/s |
| Exact Equator (0° Latitude) | 0.0000 | Singularity Guard | "Equatorial / Invalid Inputs" |
Dimensionless Atmospheric / Oceanic Rossby Number Ro = U / (|f| * L)
Converts latitude B2 (degrees) via RADIANS and length scale B4 from km to meters (* 1000).
=IF(OR(B2 = 0, ABS(B2) > 90, B3 <= 0, B4 <= 0, B6 <= 0), "Equatorial / Invalid Inputs", ROUND(B3 / ((2 * 0.000072921 * ABS(SIN(RADIANS(B2)))) * (B4 * 1000)), 3))Geostrophic Wind Speed Ug (m/s) = (dP_100km / 100000) / (rho * |f|)
Divides horizontal pressure gradient (Pa per 100 km / 100,000 m) by air density B6 and local Coriolis frequency |f|.
=IF(OR(B2 = 0, ABS(B2) > 90, B5 < 0, B6 <= 0), "Equatorial / Invalid Inputs", ROUND((B5 / 100000) / (B6 * (2 * 0.000072921 * ABS(SIN(RADIANS(B2))))), 2))Try the example
Use the original values or change them to test your understanding.