Stratified drift

Vertical migration of zooplankton has been suggested as a major contributor to ocean mixing. The original hypothesis is based on estimates of the Darwinian drift of fluid parcels due to the motion of passive particles in a viscous stably stratified ambient. This suggestion is highly debated, however, with there being subsequent suggestions to the contrary. In this study, we attempt to quantify the drift volume associated with a sphere moving vertically in a viscous stably stratified ambient. For the case where viscous and buoyancy forces are in balance, we first describe the flow field around the particle, emphasizing the existence of non-trivial features on length scales much larger than the primary screening length. Next, we trace the pathlines of individual fluid elements, in an initial material plane surrounding the sphere, over a range of viscous Richardson numbers. We show that the drift volume, for long times, is finite, unexpectedly small in relation to naive scaling estimates, and has a negative sign due to the Lagrangian reflux of parcels induced by the ambient stratification. We then examine both the flow field and drift volume for the oceanically more relevant scenario where inertial and buoyancy forces are of comparable magnitude.