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

Secondary flows in both bounded and unbounded viscous incompressible medium, due to slow uniform rotation of a nearly spherical solid of revolution r=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 ε (Reynolds number) and η (roughness parameter). Expressions for torque and drag acting on the body are given up to O(e{open}sηt)s+t=2. The flow pattern near and far away from the body are analysed for selected cases of F(θ). A large positive integral value of N, when F(θ) is prescribed as Cos (2 N-1) θ, P2N+1(cos θ), Sin 2 Nθ corresponds to distinct axially rough spheres. © 1981 Springer-Verlag.