Question

The Rossby number of a synoptic system with a length scale of 1000 km, characteristic velocity scale of 10 m s$^{-1}$ at a latitude where the Coriolis parameter equals $10^{-4}$ s$^{-1}$, is _________ (rounded off to two decimal places).

Hint:

The Rossby number is a dimensionless number that characterizes the relative importance of inertial forces to Coriolis forces in geophysical flows.

Answer 1

Correct Answer: 0.08

The Rossby number is given by the formula: \[ Ro = \frac{U}{f L} \] Where:
- \( U = 10 \ \text{m/s} \) (velocity scale),
- \( f = 10^{-4} \ \text{s}^{-1} \) (Coriolis parameter),
- \( L = 1000 \ \text{km} = 10^6 \ \text{m} \) (length scale).
Substituting the values into the formula: \[ Ro = \frac{10}{10^{-4} \times 10^6} = \frac{10}{100} = 0.10 \] Thus, the Rossby number is: \[ \boxed{0.10} \]