Realizing the thinnest hydrodynamic cloak in porous medium flow

Abstract

Transformation mapping theory offers us great versatility to design invisible cloaks for the physical fields whose propagation equations remain invariant under coordinate transformations. Such cloaks are typically designed as a multi-layer shell with anisotropic material properties, which makes no disturbance to the external field. As a result, an observer outside the cloak cannot detect the existence of this object from the field disturbances, leading to the invisible effect in terms of field prorogation. In fact, for many prorogating fields, at a large enough distance, the field distortion caused by an object is negligible anyway; thus, a thin cloak is desirable to achieve near-field invisibility. However, a thin cloak typically requires more challenging material properties, which are difficult to realize due to the huge variation of anisotropic material parameters in a thin cloak region. For a flow field in a porous medium, by applying the bilayer cloak design method and integrating the inner layer with the obstacle, we successfully reduce the anisotropic multi-layer cloak into an isotropic single-layer cloak. By properly tailoring the permeability of the porous medium, we realize the challenging material parameters required by the ultrathin cloak and build the thinnest shell-shaped cloak of all physical fields up to now. The ratio between the cloak’s thickness and its shielding region is only 0.003. The design of such an ultrathin cloak may help to achieve the near-field invisibility and concealment of objects inside a fluid environment more effectively.