The fluid is supposed to have initially, at infinity, a uniform axial component of velocity together with a uniform angular velocity about a parallel axis. Its motion is supposed to be governed by Os�en's equations and their appropriate form for steady inviscid motion, together with associated boundary conditions, is obtained by investigating the double limit t →∞.eint; and v →0 ( v is the kinematic viscosity). By this means a steady state problem can be posed which looks physically reasonable and (probably) has a unique mathematical solution. The flow properties are investigated when the inverse Rossby number α is both small and large. When $$\alpha \ll 1$$ a weak wake is found both upstream and downstream of the body and even if free to rotate zthe body remains virtually at rest. Curiously the drag decreases slightly as a increases from zero. When $$\alpha \gg 1$$ strong wakes are set up both upstream and downstream of the body, that upstream being almost like a plug, while the downstream wake contains a strong oscillatory element. Further, the body, if free to rotate, rotates with the undisturbed fluid. The conclusions, so far as they can be tested, are consistent with experiment.
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