ON INVISCID FLOW OF A ROTATING FLUID PAST AN AXIALLY-SYMMETRIC BODY USING OSEENS EQUATIONS

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 Oséen'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 α≪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 α≫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. © 1968 Oxford University Press.