Ekman flow

L. Juncheng, J. Wanqi. Modelling Ekman flow during the ACRT process with marked particles. J Cryst Growth 7 5 140, 1998. 

Figure 11.5 shows the ACRT rotation sequence used and Fig. 11.6 depicts the various flows as seen in water simulation trials. AU three predicted flow patterns were seen and showed quahtative agreement with the parameters given in Eqs. (11.2)-(11.9). The most vigorous stirring arose due to Ekman flow for distances of R to 2R from the container base (Ekman volume), particularly when a flat-based container was used. 

The conservation equations for momentum, assuming horizontally homogeneous flow, need to be solved for each sub-basin. In straits or channels the boundary layer considered could often be represented by a channel flow model with wind stress, while in larger sub-basins an Ekman flow model can be applied. 

Although the detailed flow-structure in the vessel is unknown and can be predicted by numerical means, only the basic features of the flame-flow interaction can now be depicted. The interaction is shown schematically in Figure 6.4.7. Each of the Ekman layers formed at the sidewalls by the angular velocity perturbation of the flow induces two recirculation cells—one in front of the flame and one behind it, separated by the flame. The recirculation cell in front of fhe flame is of less importance, as the flow velocities there do not affect the flame. 

Flame-flow interaction in a rotating vessel, showing the generation by the sidewall of two recirculation cells before and after the flame driven by the Ekman layers. 

Figure 13-9 Schematic views of (A) meridional and vertical transport of nitrate in the upper Atlantic basin and (B) associated horizontal transport pathways. Nitrate-rich Circumpolar Deep Water (CDW) upwells in the Southern Hemisphere and the residual mean flow transports some of this upwelled water across the polar front into the regions of intermediate and mode water formation. Nitrate-rich Sub-Antarctic Mode Water (SAMW) and Antarctic Intermediate Water move northward in the thermocline, ultimately outcropping in the subpolar North Atlantic. Ekman transfer provides a source of nitrate to the subtropical gyre along with lateral and vertical eddy transport processes.

The dynamics behind the Kelvin wave front changes completely. The divergence of the Ekman offshore transport is balanced by the divergence of the coastal jet in the surface layer and the divergence of the Ekman compensation current in the sub-thermocline layer is balanced by the longshore divergence of a coastal undercurrent flowing in opposite direction to the upper layer coastal jet. 

The theoretically predicted dual cascade with two power-law regimes in the kinetic energy spectrum (Fig. 1.4) has been reproduced in numerical simulations and confirmed by laboratory experiments. In some of the experiments spectra steeper than k 3 was observed in the enstrophy cascade range. This deviation can be related to the presence of additional damping at large scales, the so-called Ekman friction. Since the theoretical description of this regime is very similar to the problem of chemical decay in smooth flows we will return to this later in Chapter 6. 

Figure 6.9 Comparison of power spectra of decaying scalar (x) and vorticity (+) from numerical simulation of a two-dimensional turbulent flow with Ekman friction. Inset shows the ratio Z(k)/Eg(k), which is roughly constant for large k. (From Boffetta et al. (2002))...

The induced surface flow also gives rise to secondary bulk fluid motion, in the same way that bulk meridional vortices are generated in a fluid trapped between rotating and stationary disks in Batchelor flows [19], as depicted in Fig. 12. In this flow recirculation mode, particles dispersed in the flow are convected to the bottom by the bulk meridional recirculation. However, due to the inward radial velocity in the Ekman boundary layer (see Fig. 13), the particles begin to swirl in a helical-like manner toward the center of the base [19]. Although the flow recirculates back up a central spinal coluirm, the gravitational... 

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