Prandtl–Batchelor Flow in a Cylindrical Domain

In this paper, the classical problem of two-dimensional flow in a cylindrical domain, driven by a nonuniform tangential velocity imposed at the boundary, is reconsidered in straightforward manner. When the boundary velocity is a pure rotation Ω plus a small perturbation ηΩfθ and when the Reynolds number based on Ω is large (Re >> 1), this flow is of Prandtl-Batchelor type, namely, a flow of uniform vorticity Ω in a core region inside a viscous boundary layer of thickness O(Re)-1/2. The O(n2) contribution to \omegac is determined here by asymptotic analysis up to O(Re-1). The result is in good agreement with numerical computation for Re ≳ 400.