Question

A rotating weather system has a tangential velocity of \(100~\mathrm{m/s}\), diameter of \(1~\mathrm{km}\), and located at a latitude where the Coriolis parameter is \(10^{-4}~\mathrm{s^{-1}}\). Which one of the following statements is true about this weather system?

• A. It is in geostrophic balance.
• B. It is in gradient wind balance.
• C. It is a high-pressure system.
• D. It is in cyclostrophic balance.

Hint:

Rossby number is the key: small → geostrophic, order 1 → gradient, very large → cyclostrophic (e.g., tornadoes, small vortices).

Answer 1

The Correct Option is D

Step 1: Define Rossby number.
Rossby number measures the importance of inertial (centrifugal) force vs. Coriolis force: \[ Ro = \frac{U}{fL} \] where \(U = 100~\mathrm{m/s},\ f = 10^{-4}~\mathrm{s^{-1}},\ L = \text{radius} = 500~\mathrm{m}. \]

Step 2: Compute Rossby number.
\[ Ro = \frac{100}{(10^{-4})(500)} = \frac{100}{0.05} = 2000. \]

Step 3: Interpret.
- If \(Ro \ll 1\), Coriolis dominates → geostrophic balance.
- If \(Ro \sim 1\), Coriolis and centrifugal both matter → gradient wind balance.
- If \(Ro \gg 1\), centrifugal dominates → cyclostrophic balance.
Since \(Ro=2000 \gg 1\), the system is in cyclostrophic balance. Final Answer:
\[ \boxed{\text{It is in cyclostrophic balance.}} \]