Turbulent dissipation

Before proceeding to the comparison of (u*) with sinking velocities of plankters (us), it is helpful to grasp how the turbulent energy runs down through the eddy spectrum and how this, in turn, sets the environmental grain. In truly open turbulence, the largest eddies generated should propagate smoothly into smaller ones, having progressively lesser velocities as well as lesser dimensions. Momentum is lost until the residual inertia is finally overcome once again by viscosity and order returns. In the absence of any constraining solid surfaces (shores or bottom) or density gradients, it is possible to envisage a structure in which the largest eddies are adjacent to the source of their mechanical forcing (such as wind stress on the water surface) and a layer of active, propagating turbulence (in this case, from the surface downwards), until the turbulence is finally overwhelmed some distance away (in this case, its lower base). The entire structure might then be regarded as a single boundary layer, separating the energy source from the non-energised water. The mechanical properties of the boundary layer then relate to the sizes of the dimensions of the largest eddies (ie) and the gradient with which their velocities are dimin ished. For the wind-stirred boundary layer, with a vertical velocity gradient, (du/dz),

Even in the open ocean, the wind-mixed layer rarely extends more than 200-250 m from the surface (Nixon, 1988; Mann and Lazier, 1991). It is clear that so long as the inputs remain steady, the boundary-layer structure serves to dissipate the input of kinetic energy through the spectrum of subsidiary eddies. The rate of energy dissipation, E, also turns out to be an important quantity in plankton ecology. Dimensionally, it is equivalent to the product of the turbulent intensity and the velocity gradient. Thus,

By rearranging Eq. (2.9) for (du/dz) and substituting for it in Eq. (2.10), it follows that:

Where the vertical dimension is constrained, however, either because the basin is considerably less deep than 250 m in depth or because density gradients resist the downward eddy propagation, the smaller surface mixed layer must still dissipate the turbulent kinetic energy within the space available. Were this not so, the motion would have to spill out of the containing structure in, for instance, breaking waves or some rapid erosion of the perimeter shoreline. What happens is that the residual energy reaches into smaller eddies before it is overcome by viscosity. Thus it is that the most relevant feature of the

Table 2.2 Shear velocity of turbulence (u*j, mixed-layer thickness (hm), dissipation rate (E) and smallest eddy size (lm) for various kinetic systems. Abstracted from the compilation of Reynolds (1994a).

Site

(u*) (m

s-1)

hm (m)

E (m2 s~

-3)

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