On the use of an annulus to study mixed-layer entrainment

An annulus covered by a rotating screen (or surface) which imparts stress and turbulence to the upper of two fluid layers has been shown by Scranton & Lindberg (1983) and Jones & Mulhearn (1983) to produce mixed-layer entrainment that is dependent on annulus curvature and geometry. This general result is confirmed here, where photographs of the mixed-layer interface indicate that turbulent entrainment rapidly diminishes away from the outer wall. The problem is explained as a damping of the turbulence within the bulk of the mixed layer by inertial stability associated with angular momentum increasing rapidly with radius except very close to the outer wall. Through hot-film-anemometer measurements, a shallow turbulent Ekman layer is found to exist immediately underneath the rotating screen, having a depth of order $ 0.4u_{*}r/\overline{v}$, where u_* is the friction velocity, $\overline{v}$ is the mean circumferential flow speed within the layer and r is the radius. For r of order 1 m, this depth is typically only a small fraction of the mixed-layer depth determined from the density profile.When the stress input is placed near the inner wall, the mean-flow radial profile is much more nearly irrotational and the turbulence-damping problem becomes minimal. The entrainment is then much more uniform with radius, and local interfacial scaling can be used to relate the entrainment rate to one or more local Richardson numbers containing a turbulent velocity scale rather than u_* or $\Delta\overline{v}$, where Δ signifies the change across the interface. Although u_* and $\Delta\overline{v}$ are proper ‘external’ scales for entrainment in a horizontally homogeneous mixed layer that is turbulent throughout, a local internal turbulent velocity scale can alternatively be used. Entrainment rates thus scaled are presented and compared with Turner's (1973) locally scaled entrainment.