Discussion
Estimate the Rossby number for \( U = 10 \) m/s, \( L = 10^{6} \) m and \( f = 10^{-4} \) per second.
Answer: C
Substituting gives \( Ro = 10/(10^{-4} \times 10^{6}) = 0.1 \), a value small enough that the geostrophic approximation is good to about ten per cent, which is the basis of quasi-geostrophic theory. A value near one would indicate that inertia and rotation compete, as in a tropical cyclone core, and a much larger value would describe a tornado or a laboratory flow where rotation is irrelevant. Making this estimate before choosing an approximation is a habit worth acquiring early.
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