Discussion
What will happen to the speed of a balanced flow as one moves across the isobar along a particular latitude?
Answer: B
The key gives The speed remains constant for a geostrophic flow and changes for a cyclostrophic flow.
In geostrophic balance the pressure gradient force is balanced by the Coriolis force:
\[ V_{g} = \frac{1}{\rho f}\frac{\partial p}{\partial n} \]
Along a fixed latitude the Coriolis parameter \(f\) is the same, so for a given pressure gradient the speed does not depend on the position across the isobars. In cyclostrophic balance the pressure gradient is balanced by the centripetal acceleration of curved flow:
\[ \begin{aligned} \frac{V^{2}}{r} &= \frac{1}{\rho}\frac{\partial p}{\partial n} \\ \Rightarrow V &= \sqrt{\frac{r}{\rho}\frac{\partial p}{\partial n}} \end{aligned} \]
The speed depends on the radius \(r\), which changes as one moves across the circular isobars, so the speed changes. The other options reverse this or treat both balances alike.
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