  We have developed a minimal model of a swimmer without body deformation based
on force and torque dipoles which allows accurate 3D Navier-Stokes
calculations. Our model can reproduce swimmer propulsion for a large range of
Reynolds numbers, and generate wake vortices in the inertial regime,
reminiscent of the flow generated by the flapping tails of real fish. We
performed a numerical exploration of the model from low to high Reynolds
numbers and obtained universal laws using scaling arguments. We collected data
from a wide variety of micro-organisms, thereby extending the experimental data
presented in (M. Gazzola et al., Nature Physics 10, 758, 2014). Our theoretical
scaling laws compare very well with experimental data across the different
regimes, from Stokes to turbulent flows. We believe that this model, due to its
relatively simple design, will be very useful for obtaining numerical
simulations of collective effects within fish schools composed of hundreds of
individuals.
