The Fluid Dynamics of Mayfly Naiads

Abstract

During their aquatic phase, mayflies Centroptilum triangulifer use a series of tracheal gills to facilitate gas exchange. Recent experimental studies on nymphal mayflies have identified two coupled features associated with the ontogenic progression of their ventilatory kinematics: 1) there is an abrupt shift from a rowing mechanism in small instars to a flapping mechanism in larger instars, and 2) the flapping mechanism is associated with the development of a flexural hinge that permits the passive movement of a distal flap. The primary role of the tracheal gills is tied to ventilation rather than locomotion. As such, it is not yet understood why such a transition happens and which performance metric is improved, if any. Hence, the goal of the current research is to investigate both features using numerical simulations. First, a computational model of the mayfly is built from a dissected animal. Then, a 3-level prescribed kinematic chain is introduced to a previously in-house developed and in-house validated explicit parallel Navier-Stokes solver where both the advective and diffusive terms are advanced explicitly using a third-order, low-storage, Runge-Kutta scheme. Finally, an immersed boundary method based on a moving least squares reconstruction is implemented to enforce the correct moving boundary conditions. Two different parametric spaces are constructed. The first one investigates the transition from rowing to flapping kinematics, the morphological effects on the flow field and on the proposed performance parameters while the second aims to provide an explanation for the hinge development. Two metrics based on control volume analysis are proposed to quantify the performance of each numerical case. The first metric is simply the mechanical efficiency of the energy transfer from the moving gills to the surrounding flow field while the second incorporates the mass flow rate across the control surface. The second metric is promising because it is able to provide a plausible explanation of both features by showing that the rate of work done by the mayfly is diminished throughout ontogeny with respect to the induced mass flow rate.