On the Quasi-Geostrophic Drag on a Rising Sphere in a Rotating Fluid

Summary

The angular velocity profile and the drag on a spherical solid particle which rises slowly in a rapidly rotating fluid in a non-long container are estimated via the finite-difference solution of a quasi-geostrophic approximation model. In contrast with the classic geostrophic approach, the radial motion in the slightly inviscid core (including the outer Stewartson layer) is incorporated—in addition to the Ekman layers transport—and shown to affect strongly the results when $\varepsilon = {\left( {\frac{1}{2}H{T^ - }^{\frac{1}{2}}} \right)^{\frac{1}{2}}}$ is not very small, where H is the dimensionless particle-to-wall distance and T is the Taylor number. Comparisons with the disk particle and with experimental results are discussed and the limitations of the present approximation are pointed out.