Two dimensional immersed boundary simulations of swimming jellyfish

The swimming behavior of jellyfish, driven by the periodic contraction of body muscles,can be modeled using a two dimensional bell-shaped membrane immersed in fluid with aperiodic contraction force exerted along the membrane. We aim to use a simple two dimensional elastic membrane to simulate the swimming behavior without imposing any given membrane configuration, in which the swimming behavior is driven naturally by the interaction between the elastic membrane and fluid and solved by the immersed boundary (IB) method. We begin by describing our implementation of stretching and bending forces in the IB formulation, and then study the relative importance of the stretching and bending forces for an idealized closed membrane. We then develop a two dimensional model of a jellyfish whose bell resists any deformation from a given target shape. The swimming dynamics are driven by a muscle contraction force that is fit to experimental data. Numerical simulations demonstrate an emergent swimming behavior that is consistent with experimentally observed jellyfish.