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 B

A rotating weather system's balance can be determined by examining the forces at play. Given parameters: tangential velocity \(v_t = 100~\mathrm{m/s}\), diameter \(d = 1~\mathrm{km} = 1000~\mathrm{m}\), Coriolis parameter \(f = 10^{-4}~\mathrm{s^{-1}}\).

• Radius \(r\) is half the diameter: \(r = \frac{1000}{2} = 500~\mathrm{m}\). 
• Coriolis Force: \(\mathrm{CF} = f \cdot v_t\). Substitution gives \(\mathrm{CF} = 10^{-4} \times 100 = 0.01~\mathrm{m/s^2}\).
• Centripetal Force: Needed for circular motion: \(\mathrm{CP} = \frac{v_t^2}{r} = \frac{100^2}{500} = 20~\mathrm{m/s^2}\).
• Pressure Gradient Force (PGF): For gradient wind balance, the forces equate: \[\mathrm{PGF} + \mathrm{CF} = \mathrm{CP}\]\(0.01 < 20\), which implies PGF must counterbalance the larger centripetal force, supporting a pressure gradient typical in gradient wind situations.
• In geostrophic balance, CF balances PGF, neglecting centripetal force, unrealistic here due to high velocity.
  In cyclostrophic balance, CF is negligible, focusing on CP and PGF, viable for small-scale, not large-scale weather systems.
  Without further information on pressure, identifying high/low-pressure systems isn't determined.

Thus, the correct choice is: It is in gradient wind balance.