## Sinking floating and entrainment

Preceding sections of this chapter have reviewed the scales of the quantities of the two key components of plankton entrainability - the velocities of the intrinsic tendency of plankton to sink, swim or float and the velocities of motion in the medium. Both typically cover several orders of magnitude. The sinking rates of diatoms span something like 1 ¡m s-1 to 6mms-1. The flotation rates of buoyant colonies of the Cyanobacteria such as Anabaena and Aphani-zomenon may reach 40-60 ¡m s-1, typical colonies

Ranges of sinking ('DOWN') and floating ('UP') velocities of freshwater phytoplankters, or, where appropriate of vertical swimming rates of motile species, plotted against unit volume. The algae are: An flo, Anabaena flos-aquae; Aphan, Aphanizomenon flos-aquae; Ast, Asterionella formosa; Aul, Aulacoseira subarctica; Cer h, Ceratium hirundinella; Chlm, Chlorococcum; Chlo, Chlorella; Clo ac, Closterium aciculare; Cycl, Cyclotella meneghiniana; Fra c, Fragilaria crotonensis; Mic; Microcystis aeruginosa; Pla ag, Planktothrix agardhii; Sta p, Staurastrum pingue; Ste r, Stephanodiscus rotula; Volv, Volvox aureus. Redrawn with permission from Reynolds (1997a).

of Gloeotrichia and Microcystis may achieve 100-300 ¡m s-1, while some of the largest aggregations achieve 3-4 mm s-1 (Reynolds et al., 1987; Oliver, 1994). Among motile organisms, reported 'swimming speeds' range between 3-30 ¡m s-1 for the nanoplanktic flagellates to 200-500 ¡m s-1 for the larger dinoflagellates, such as freshwater Cer-atium and Peridinium (Talling, 1971; Pollingher, 1988) and marine Gymnodinium catenatum and Lin-gulodinium spp. (see Smayda, 2002). Large colonies of Volvox can attain almost 1mms-1 (Sommer and Gliwicz, 1986) while the ciliate Mesodinium is reported to have a maximum swimming speed of 8 mm s-1 (Crawford and Lindholm, 1997).

At the other end of the motility spectrum, solitary bacteria and picoplankters probably sink no faster than 0.01-0.02 ¡m s-1 (data collected in Reynolds, 1987a). The data plotted in Fig. 2.15 show that, despite the compounding of several factors in the modified Stokes equation (2.16), the intrinsic rates at which phytoplankton move (or potentially move) in relation to the adjacent medium are powerfully related to their sizes. Smaller algae sink or 'swim' so slowly that the motion of the water is supposed to keep them in suspension. Larger species potentially move faster or farther but they need to be either flagellate or to govern their own buoyancy to counter the tendency to sink. Indeed, there is a strong indication that their ability to overcome elimination from the plankton, at least in the extant vegetative stages of their life cycles, depends upon the amplification of motility that large size confers. In essence, phytoplankton motility can be differentiated among those that can do little to stop themselves from sinking (mostly diatoms), the very large, which self-regulate their movements, and the very small for which it seems to matter rather little.

Even so, when the comparison is made, the range of intrinsic rates of sinking (ws), floating (-ws) and flagellar self-propulsion (us) represented in Fig. 2.15 (mostly <10-3 ms-1) are 1-6 orders of magnitude smaller than the sample turbulent velocities cited in Table 2.2 (mostly >10-2 ms-1). Generally speaking, the deduction is that ws ^ u*. This does not mean that the sinking potential (or the floating or migratory potential) is overcome, just that gravitating plankters are constantly being redistributed. What really matters to sinking particles is the relative magnitudes of ws and the upward thrusts of the turbulent eddies W (see Section 2.3.1). If ws > w', nothing prevents the particle from sinking. While, however, ws < W some particles can be transported upwards faster than they gravitate downwards - and their sinking trajectories are reinitiated at a higher point in the turbulence field. Of course, there are, other things being equal, downward eddy thrusts which add to rate of vertical descent of the particles. Given that the upward and downward values of W are self-cancelling, ws is not affected. However, the greater is the magnitude of w relative to ws, the more dominant is the redistribution and the more delayed is the descent of the particles.

In this way, the ability of fluid turbulence to maintain sinking particles in apparent suspension depends on the ratio of sinking speed to the vertical turbulent velocity fluctuations. Empirical judgement suggested that this entrainment threshold occurs at 1-2 orders of magnitude greater than the intrinsic motion of the particle. In a detailed consideration of this relationship, Humphries and Imberger (1982) introduced a quotient (herein referred to as ^) to represent the boundary between behaviour dominated by turbulent diffusivity of the medium and behaviour dominated by particle buoyancy:

Figure 2.16

The entrainment criterion, as expressed in Eq. (2.19). In essence, the larger is the alga and the greater its intrinsic settling (or flotation) velocity, then the greater is the turbulent intensity required to entrain it. Redrawn with permission from Reynolds (1997a).

### Figure 2.16

The entrainment criterion, as expressed in Eq. (2.19). In essence, the larger is the alga and the greater its intrinsic settling (or flotation) velocity, then the greater is the turbulent intensity required to entrain it. Redrawn with permission from Reynolds (1997a).

Noting that, in open turbulence, the magnitude of u* is not dissimilar from [(w')2]1'2 (see Eq. (2.4)), Reynolds (1994a) proposed that substitution of u* in Eq. (2.19) gave a useful approximation to the value of ^. The main line drawn into Fig. 2.16 (^ = 1) against axes representing sinking rate (ws) and turbulent velocity (u*), is proposed as the boundary between effective entrainment (diffusivity dominates distribution) and effective disentrainment (particle properties dominate distribution).

The adjective 'effective' is important, because entrainment is never complete while ws has finite value; neither is disentrainment total while there is any possibility that motion in the water can deflect the particle from its intrinsic vertical trajectory. However, the main point requiring emphasis at this point is that, in lakes, rivers and oceans, u* is a highly variable quantity (see, e.g., Table 2.2), with the variability being often expressed over high temporal frequencies (from the order of a few minutes) and, sometimes, over quite short spatial scales. Whilst in near-surface layers even the lower values u* may often still be an order of magnitude greater than the intrinsic particle properties, the entrainment condition is not necessarily continuous in the vertical direction. Just taking the example of the transfer of the momentum of wind stress on the water surface and the propagation of turbulent eddies in the water column below (Eq. 2.5), it is clear that the loss of velocity through the spectrum of diminishing eddies will continue downwards into the water to the point where the residual energy is overcome by viscosity. As the penetrating turbulence decays with depth, the entraining capacity steadily weakens towards a point where neither u* nor [(w')2]1'2 can any longer satisfy the particle-entrainment condition. In other words, the turbulence field is finite in extent and is open to the loss of sedimenting particles (and, equally, to the recruitment of buoyant ones).

This leads us to a significant deduction about the suspension and continued entrainment of phytoplankton in lakes and the sea. It is the extent of the turbulence, rather than its quantitative magnitude, that most influences the persistence or otherwise of various types of organism in the plankton. For the same reason, the factors that influence the depth of the turbulent mixed layer and its variability are important in the survival, seasonality and succession of phytoplankton in natural waters. These are reviewed briefly in later sections but it is first necessary to consider their behaviour within the mixed layer itself.

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