Swimming Organisms: Coupling Internal Mechanics with External Fluid Dynamics

tion with laboratory experiment, can provide valuable insight into complex biological systems that involve the interaction of an elastic structure with a viscous, incompressible fluid. This biological fluid-dynamics setting presents several more challenges than those traditionally faced in computational fluid dynamics—specifically, dynamic flow situations dominate, and capturing time-dependent geometries with large structural deformations is necessary. In addition, the shape of the elastic structures is not preset: fluid dynamics determines it. The Reynolds number of a flow is a dimensionless parameter that measures the relative significance of inertial forces to viscous forces. Due to the small length scales, the swimming of microorganisms corresponds to very small Reynolds numbers (10–6 – 10–2). Faster and larger organisms such as fish and eels swim at high Reynolds numbers (102 – 105), but organisms such as nematodes and tadpoles experience inertial forces comparable to viscous forces: they swim at Reynolds numbers of order one. Modern methods in computational fluid dynamics can help create a controlled environment in which we can measure and visualize the fluid dynamics of swimming organisms. Accordingly, we designed a unified computational approach, based on an immersed boundary framework,1 that couples internal force-generation mechanisms of organisms and cells with an external, viscous, incompressible fluid. This approach can be applied to model low, moderate, and high Reynolds number flow regimes. Analyzing the fluid dynamics of a flexible, swimming organism is very difficult, even when the organism’s waveform is assumed in advance.2,3 In the case of microorganism motility, the low Reynolds number simplifies mathematical analysis because the equations of fluid mechanics in this regime are linear. However, even at low Reynolds numbers, a microorganism’s waveform is an emergent property of the coupled nonlinear system, which consists of the organism’s force-generation mechanisms, its passive elastic structure, and external fluid dynamics. In the immersed boundary framework, the force-