Hydrodynamic cloaks with isotropic and homogeneous viscosity for multi-object in collaborative operations

Although significant efforts have been devoted to advancing hydrodynamic cloaks for a single object, limited exploration has focused on cloaking multiple objects. By cloak, we mean a state of hydrodynamic invisibility achieved by eliminating flow disturbances caused by intrusive objects in the surrounding fluids. These gaps in understanding present challenges in developing effective strategies for achieving hydrodynamic stealth for multiple objects in collaborative operations. To address these issues, we propose a multi-object hydrodynamic cloak with isotropic and homogeneous fluid viscosity in viscous potential flows through a combination of neutral inclusion theory and convection-diffusion-balance method. By effectively transforming the intrusive objects into one single object while maintaining the overall invasive volume unchanged—a critical factor in flow disturbances—we successfully derive the analytical solution of fluid viscosity for multi-object hydrodynamic cloaks. Numerical simulations demonstrate the proposed cloaks considerably minimize the hydrodynamic perturbations generated by objects in groups with symmetric or asymmetric distributions, various sizes, and even arbitrary shapes. In addition, we reveal that the antagonism between the defined boundary effect of flow disturbances and vorticity magnitudes primarily determines the effectiveness of the proposed cloaks, laying the foundation for the future development of multi-object hydrodynamic cloaks involving interactions among objects. Hopefully, this research will advance the fields of hydrodynamic metamaterials for multiple objects in collaborative settings and contribute to the broader understanding of complexity science.