STARTING AND STEADY QUADRUPOLAR FLOW

Planar flow induced in a viscous fluid by a small cylinder oscillating in the direction normal to its axis is modeled theoretically and repr oduced experimentally. In the model, a line force dipole (force double t) was used as the source of motion. In an initially quiescent unbound ed fluid this source produces zero net momentum and generates symmetri cal quadrupolar flow consisting of two dipolar vorticity fronts propag ating in opposite directions from the source. For starting flow at low Reynolds numbers, a second-order unsteady solution is obtained in ter ms of a power series of the Reynolds number, Re=Q/4 pi nu(2), where Q is the forcing amplitude and nu is the kinematic viscosity. This solut ion demonstrates that, as time t-->infinity, the flow in the vicinity of the source becomes steady and radial. To describe this steady asymp tote, the Jeffery-Hamel nonlinear solution for radial flow is used. A particular solution is derived using the nondimensional intensity Re o f the force dipole as a governing parameter. It is shown that the prob lem permits a similarity solution for all values of Re when a mass sin k of prescribed intensity q=q(Re) is added to the flow. This steady as ymptote is reproduced experimentally, using a vertical porous cylinder that oscillates horizontally in the shallow upper layer of a two-laye r fluid and sucks fluid through its porous walls. (C) 1996 American In stitute of Physics.