Lagrangian drift near a wavy boundary in a viscous oscillating flow

Abstract

The formation of sand ripples in oscillating flows is thought to be due to a steady streaming current which near the bottom is towards the crests. We present quantitative observations of this mean flow over self-formed and artificial ripples, by observing the displacement of a coloured filament after a number of oscillations in the simple situation of viscous Couette flow. Confusingly, the filament moves in the ‘wrong’ direction, because it follows the Lagrangian mean flow. We calculate the Lagrangian mean flow. A complication is that the amplitudes of the oscillations in the experiments are not small. We compare the predictions with the experimental observations of displacements of the filament, showing good agreement.

Steady streaming: A key mixing mechanism in low-Reynolds-number acinar flows

“…36 More recently, Larrieu et al observed Lagrangian drift for oscillatory flow over a wavy wall due to streaming. 34 Wang and Ottino observed that increasing K C increases disorder in tracer motion in a lid-driven cavity flow. 43 The present finding is unique to low-Re open cavity flows directly applicable to dispersion in acinar airways with a large displacement parameter, K C .…”

“…27,[31][32][33][34][35][36][37] In an oscillatory flow setting, a nonzero mean flow averaged over one time period may be observed. This nonzero mean flow can result in significant drift of particles at end cycle called steady streaming.…”

“…37 Larrieu et al presented an analytical treatment of drift in a simple setting of Couette flow weakly perturbed by a wavy bottom. 34 For any given passive particle under the assumption of small displacement, 37 Eq. ͑1͒ with x͑t =0͒ = x 0 may be expanded in a Taylor series.…”

“…34 Because the magnitude of the Eulerian mean velocity u E is small, to assess the sensitivity of u E on mesh size we present in Appendix B the comparison of the observed maximum Eulerian mean velocities for three different mesh sizes. The results show that a mesh-independent solution is ensured.…”

Mean mass transport in an orbitally shaken cylindrical container

“…Because of the identical scaling of the two contributions u str and u Sto , it is difficult in general to anticipate which of streaming or Strokes drift contribute more to this Lagrangian mean flow [22]. Predicting the structure of the Lagrangian mean flow in the orbital sloshing configuration is a difficult task, not only because of the non-trivial viscous boundary layers that generate the streaming, but also because of the complex dynamics near the contact line.…”