On burst-and-coast swimming performance in fish-like locomotion

Burst-and-coast swimming performance in fish-like locomotion is studied via two-dimensional numerical simulation. The numerical method used is the collocated finite-volume adaptive Cartesian cut-cell method developed previously. The NACA00xx airfoil shape is used as an equilibrium fish-body form. Swimming in a burst-and-coast style is computed assuming that the burst phase is composed of a single tail-beat. Swimming efficiency is evaluated in terms of the mass-specific cost of transport instead of the Froude efficiency. The effects of the Reynolds number (based on the body length and burst time), duty cycle and fineness ratio (the body length over the largest thickness) on swimming performance (momentum capacity and the mass-specific cost of transport) are studied quantitatively. The results lead to a conclusion consistent with previous findings that a larval fish seldom swims in a burst-and-coast style. Given mass and swimming speed, a fish needs the least cost if it swims in a burst-and-coast style with a fineness ratio of 8.33. This energetically optimal fineness ratio is larger than that derived from the simple hydromechanical model proposed in literature. The calculated amount of energy saving in burst-and-coast swimming is comparable with the real-fish estimation in the literature. Finally, the predicted wake-vortex structures of both continuous and burst-and-coast swimming are biologically relevant.