Structure and particle transport in second-order stokes flow
Second-order streaming in a thin fluid layer driven by one or two opposed, tangentially oscillating wavy walls is theoretically investigated. In contrast to the well-studied problem of oscillatory flow past a stationary boundary, the present problem is subject to a nonhomogeneous second-order boundary velocity condition. A combination of steady Reynolds stresses and boundary forcing thus drives the streaming flow; indeed, under most conditions, boundary-forced flow dominates Reynolds-stress-driven flow. The first part of the paper examines parametric effects on second-order flow structure. Under low-Reynolds-stress conditions and during single-boundary forcing, flow structure remains essentially independent of all parameters, including the Stokes layer thickness, the fluid layer thickness, and the forcing wave form. Three approximations to the full second-order solution, valid under low-Reynolds-stress conditions, are used to explain these results. In the case of dual-boundary forcing, no corresponding universal behaviors are observed; flow structure exhibits sensitivity to all problem parameters. The second part of the paper investigates particle transport during quasistatic second-order streaming. Here, slow, superposed, large-amplitude oscillations of one wall produce the time-dependent, quasisteady flows of interest. Collective particle motion in the direction of large-scale boundary displacement and filamentary motion in the opposite direction, features consistent with transport in traveling waves [E. Moses and V. Steinberg, Phys. Rev. Lett. 60, 2030 (1988)], characterize short-time transport. Long-time or asymptotic transport, in contrast, is characterized by particle attraction or repulsion to or from period-one elliptic points and attraction toward limit cycles on the Poincare map.
Keanini
RG
Department of Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, North Carolina 28223, USA.