The detailed fluid mechanics of sperm propulsion are fundamental to our understanding of reproduction. In this paper, we aim to model a human sperm swimming in a microscope slide chamber. We model the sperm itself by a distribution of regularized stokeslets over an ellipsoidal sperm head and along an infinitesimally thin flagellum. The slide chamber walls are modelled as parallel plates, also discretized by a distribution of regularized stokeslets. The sperm flagellar motion, used in our model, is obtained by digital microscopy of human sperm swimming in slide chambers. We compare the results of our simulation with previous numerical studies of flagellar propulsion, and compare our computations of sperm kinematics with those of the actual sperm measured by digital microscopy. We find that there is an excellent quantitative match of transverse and angular velocities between our simulations and experimental measurements of sperm. We also find a good qualitative match of longitudinal velocities and computed tracks with those measured in our experiment. Our computations of average sperm power consumption fall within the range obtained by other authors. We use the hydrodynamic model, and a prototype flagellar motion derived from experiment, as a predictive tool, and investigate how sperm kinematics are affected by changes to head morphology, as human sperm have large variability in head size and shape. Results are shown which indicate the increase in predicted straight-line velocity of the sperm as the head width is reduced and the increase in lateral movement as the head length is reduced. Predicted power consumption, however, shows a minimum close to the normal head aspect ratio.

Many wake flows exhibit self-excited flow oscillations which are sustained by the flow itself and are not caused by amplification of external noise. The archetypal example of a self-excited wake flow is the low Reynolds number flow past a circular cylinder. This flow exhibits self-sustained periodic vortex shedding above a critical Reynolds number. In general, control of such flows requires stabilization of many globally unstable modes; the present work describes a multiple-sensor control strategy for the cylinder wake which succeeds in controlling a simplified wake model at a Reynolds number above that at which single-sensor schemes fail.Representation of the flow field by a finite set of coherent structures or modes, which are extracted by proper orthogonal decomposition and correspond to the large-scale wake components, allows the efficient design of a closed-loop control algorithm. A neural network is used to furnish an empirical prediction of the modal response of the wake to external control forcing. This model avoids the need for explicit representation of the control actuator-wake interaction. Additionally, the neural network structure of the model allows the design of a robust nonlinear control algorithm. Furthermore the controller does not necessarily require velocity field information, but can control the wake using other quantites (for example flow visualization pictures) which characterize the structure of the velocity field. Successful control of a simplified cylinder wake model is used to demonstrate the feasibility of the low-dimensional control strategy.

No abstract

Measurements of the flow field around a model rotor descending axially into its own vortex wake have been performed using particle image velocimetry (PIV). At low descent rates, the expected cylindrical down-flow structure below the rotor is observed. At slightly higher descent rate, the flow enters the so-called vortex ring state (VRS) where the vorticity from the rotor accumulates into a toroidal structure near the rotor tips, and a large recirculation zone forms above the rotor disk. In the VRS, the flow below the rotor shows a significant upwards component, with a small up-flow zone penetrating right up to the rotor disk. Measurements show there to be a range of descent rates just before the onset of the VRS over which the flow may be interpreted to be in an incipient VRS condition. In this range, analyses of individual PIV measurements indicate that the flow near the rotor intermittently switches between the down-flow topology found at lower descent rates and the flow topology found in the fully developed VRS. The frequency of excursions of the flow into the VRS topology increases as the descent rate of the rotor is increased until, at high enough descent rate, the flow remains locked within its toroidal state.

No abstract