The effect of aspect ratio on the meridional circulation of a homogeneous fluid is analyzed. Aspect ratio is allowed to range between zero and unity. Relationships between possible horizontal and vertical length scales are obtained by length scale analysis as well as by solving an idealized problem. It is found that whenE1/2 ≪ Z ≪ E1/2/δ, whereE is the Ekman number, the stream lines are closely packed near the sidewall within a thickness ofO(E1/2). The effect of stratification is unimportant within this depth range. In the depth rangeE1/2/δ ≪ Z ≪ 1/Eδ the vertical boundary layer in which the streamlines are packed is ofO(EZδ)1/3. WhenZ ≫ 1/Eδ it is shown that the circulation decays algebraically with depth as 1/Z.
Volume 131, 2021
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