Fluid dynamics of moving fish in a two-dimensional multiparticle collision dynamics model

The fluid dynamics of animal locomotion, such as that of an undulating fish, are of great interest to both biologists and engineers. However, experimentally studying these fluid dynamics is difficult and time consuming. Model studies can be of great help because of their simpler and more detailed analysis. Their insights may guide empirical work. Particularly the recently introduced multiparticle collision dynamics method may be suitable for the study of moving organisms because it is computationally fast, simple to implement, and has a continuous representation of space. As regards the study of hydrodynamics of moving organisms, the method has only been applied at low Reynolds numbers (below 120) for soft, permeable bodies, and static fishlike shapes. In the present paper we use it to study the hydrodynamics of an undulating fish at Reynolds numbers 1100-1500, after confirming its performance for a moving insect wing at Reynolds number 75. We measure (1) drag, thrust, and lift forces, (2) swimming efficiency and spatial structure of the wake, and (3) distribution of forces along the fish body. We confirm the resemblance between the simulated undulating fish and empirical data. In contrast to theoretical predictions, our model shows that for steadily undulating fish, thrust is produced by the rear 2/3 of the body and that the slip ratio U/V (with U the forward swimming speed and V the rearward speed of the body wave) correlates negatively (instead of positively) with the actual Froude efficiency of swimming. Besides, we show that the common practice of modeling individuals while constraining their sideways acceleration causes them to resemble unconstrained fish with a higher tailbeat frequency.