Discussion
Which scale does the ratio of the Coriolis parameter to the buoyancy frequency define?
Answer: D
The ratio \( f/N \) is about one in a hundred in the troposphere, and multiplying it by a horizontal scale gives the depth over which a disturbance of that width can influence the flow. It is therefore the natural aspect ratio of balanced motion and explains why weather systems a thousand kilometres wide are about ten kilometres deep. The Rossby, Richardson and Burger numbers are formed from different combinations of the same quantities. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.
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