Unsteady flows at low Reynolds numbers
Most flows in the oceans are unsteady. Formally, that statement means that the time derivative of at least one velocity component is nonzero. Small organisms experience unsteadiness from at least three broadly important mechanisms. One is turbulent dissipation between the Taylor and Kolmogorov scales in transition to viscous dissipation. Because upper mixed and bottom boundary layers are generally turbulent, organisms in these physically and biologically active zones generally experience unsteady flows. Organisms smaller than the Kolmogorov scale in decaying turbulence in a moderately energetic layer will rarely experience constant flow magnitude and direction beyond time scales of a few tens of seconds (Karp-Boss, Jumars and Boss 1996). A second mechanism is entrainment in the flows produced by suspension feeders. These flows are sometimes inherently unsteady due to beating of appendages, but in any case are unsteady from the perspective of an entrained organism being accelerated into the intake stream. A third mechanism is the approach of any other solid particle, living or dead; moving particles produce flow perturbations around themselves that are imposed on neighbors as they get close. Consequently, unsteady flows are important to hydrosol filtration (aka suspension feeding), to prey detection and capture in general, to coagulation, and to fertilization.
Most experiments with flow effects at low Reynolds number, however, have produced steady flows, even when attempting to simulate turbulence effects. We have done things this way ourselves (Karp-Boss and Jumars 1998; Karp-Boss et al. 2000).
Starting with these simpler flows is of course logical, but the time is ripe for moving onward to unsteady flow phenomena because both theory and measurement technology now allow it. Moreover, theory based on steady flow is not up to some important tasks, such as explaining "scan-and-trap" mechanisms of suspension feeding. We have gotten ourselves pretty excited about the possibilities, and have decided to try to work on extensions of our steady-flow experiments, producing unsteady flows that will flex and tumble phytoplankton. The logic is to work in simple unsteady flows with organisms that have no active swimming behavior as perhaps the simplest important case of unsteady, low Reynolds-number flow to tackle.
One of the really interesting aspects of our literature work so far is that the memory integral term was forgotten for a while, whereas the acceleration reaction or added-mass term has entered the biological fluid dynamics literature with a vengeance. For our application, however, the memory integral term has a much larger effect. At low Reynolds numbers, perturbed flow fields are large relative to the objects that create them. Thus, especially for objects in the 0.1 - 10 mm size range when they remain in the low Reynolds-number regime, these wakes can take a long time to form and have major effects on force balances. We have extracted some of these ideas and put them into a review of "Algal biophysics" that we co-authored with Mimi Koehl, who in that review paper concentrated on macroalgal aspects.
We have recently been funded by the National Science Foundation to develop new ways to evaluate effects of turbulence on plankton, focusing on processes in and near dissipation-scale vortices. The work is collaborative with Lisa Fauci of Tulane University, who will numerically model effects of dissipative vortices on plankton. We will then test those effects in tailored laboratory flow chambers. The first phase of the work is to predict the length and velocity scales of the vortices that dominate turbulent dissipation, and we have recently devised a scheme to do so, based on the dynamics of Burgers vortices. The prediction is of vortex radii of a few centimeters and peak azimuthal flow speeds of a few centimeters per second. These vortices also have lifetimes much longer than those of Kolmogorov-scale vortices, making them clearly relevant to issues of planktonic encounter, coagulation and sedimentation (Jumars et al. 2009). The kinds of motions that chains of diatoms experience depend on their mechanical properties (Musielak et al. 2009).
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e-mail: jumars@maine.edu