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Computational and Analytical Perspectives on the Drift Paradox Problem in a Freshwater Embayment
Small, planktonic organisms in a variety of fresh and saltwater environments with primarily unidirectional flow often manage to avoid washout into a larger, often inhospitable body of water, a phenomenon commonly termed the `drift paradox.' We investigate the drift paradox in the case of vertically migrating zooplankton in a long, narrow embayment emptying into a colder lake by means of a three-dimensional hydrodynamic model, SI3D, along with an accompanying (modified) particle tracking module. Chapter 1 describes tests of SI3D designed to insure that the basic advection and scalar (temperature) transport behave as expected in the embayment regime. Chapter 2 describes simulations using different migration types, zooplankton cloud sizes, start times, and background flow speeds. Largely due to its interaction with exchange flow between lake and embayment, background flow speed emerged as the most important factor influencing the residence time of the zooplankton, with smaller flow speeds, normal migration, and larger zooplankton clouds typically leading to higher residence times. Chapter 3 discusses similar smulations, with the addition of rooted macrophytes, which are represented in SI3D by changing the amount and height of drag in the channel. Flow rate was again the single most important variable, with the interaction between flow and zooplankton cloud size also significant. Chapter 4 describes the results of attempts to represent the advection of zooplankton undergoing vertical migration by a relatively simple partial differential equation, with the goal of approximating the results of Chapters 2 and 3. The equation contains advective and diffusive terms with the velocity term encompassing the water flow as well as zooplankton vertical position in the embayment. Background water flow, assumed homogeneous in time and longitudinally, is obtained by averaging output velocities from SI3D. A simple distance/rate approximation was also investigated. While the analytical models can be useful in situations involving a simple flow field, when more accuracy is needed, or in case of a vegetated channel, using the full computational model is advisable.
drift paradox; zooplankton; exchange flow; vertical migration