Pressure and vorticity scaling in anguilliform and carangiform swimming

The scaling of pressure and vorticity in aquatic swimming can provide insights into the mechanisms of propulsion. This is investigated through self-propelled, wall-resolved, large-eddy simulations of a lamprey (an anguilliform swimmer) and a mackerel (a carangiform swimmer) using the curvilinear immersed boundary method. It is observed that the pressure around the swimmers scales with theoretical fluid acceleration, which includes both local body and the convective acceleration, for anguilliform swimmers, whereas it scales with both acceleration and the angle of attack (AoA) for carangiform swimmers. This indicates that the main mechanism for propulsion in anguilliform swimmers is added mass (unsteady), whereas both lift-based (steady) and added mass (unsteady) are at play for carangiform swimmers. Furthermore, it is observed that the vorticity in the boundary layer of the swimmer initially follows the body rotation at low speeds but not at high speeds during the quasisteady swimming. This is explained by identifying the scaling of vorticity components: one due to body rotation and the other due to shear, which scale with Strouhal number ( $St$ ) and Reynolds number ( $\sqrt {Re}$ ), respectively. Here $St$ (body rotation) dominates at low speeds, but $\sqrt {Re}$ (shear) dominates at high speeds. Finally, it is observed that the pressure decreases as the swimming speed increases. This counterintuitive observation is explained by showing that both fluid acceleration and AoA decrease as swimming speed increases. This suggests that for efficient swimming, the pressure difference across the body should be minimised, but high enough to overcome the viscous drag.