Secondary flows due to slow viscous rotating of rough or nearly spherical solids

Abstract

Secondary flows in both bounded and unbounded viscous incompressible medium, due to slow uniform rotation of a nearly spherical solid of revolutionr=a+ηF(θ), 0≦θ≦π, about its axis is studied. The stream function is expanded as a double power series involving two small parameters e (Reynolds number) and η (roughness parameter). Expressions for torque and drag acting on the body are given up toO(ɛ s η t ) s+t=2. The flow pattern near and far away from the body are analysed for selected cases ofF(θ). A large positive integral value ofN, whenF(θ) is prescribed as Cos (2N-1) θ,P 2N+1 (cos θ), Sin 2Nθ corresponds to distinct axially rough spheres.