Reorienting External Fields

This chapter explores the impact of external fields, which add a rotational constraint to the microswimmer motion by reorienting them in a certain direction. First, we analyze the emerging patterns in the full model on the basis of numerical results and linear stability analysis. For intermediate field strength, the external field induces anisotropic stripe-like patterns that move in the direction of the field and exhibit numerous defects, whereas for higher values, the mesoscale-turbulent state is suppressed completely. In the second part, we consider the reduced minimal model as it is easier to tackle analytically but still exhibits the basic mechanisms of the pattern formation. Performing a weakly nonlinear analysis, we derive an amplitude equation that is characterized by intriguing features such as anisotropic diffusion coefficients and advective transport of modulations.