Hydrodynamic rotational amplifiers with direction controllability, rotational hysteresis, nonreciprocity, and venturi...

Hydrodynamic metamaterials provide a transformation-based route for manipulating low-Reynolds-number flows, but many existing designs rely on spatially inhomogeneous and anisotropic material parameters that are difficult to realize and integrate in practical fluidic systems. Here, we propose a body-force-based design strategy for hydrodynamic rot-amplifiers. By mapping coordinate transformations to an equivalent body-force distribution, the proposed method reproduces target transformed flow fields in a homogeneous background fluid without physically constructing complex anisotropic viscosity tensors. Numerical simulations show that the designed rot-amplifiers can simultaneously redirect the central flow direction and enhance the central velocity, leading to Venturi amplification while keeping the external background flow unperturbed. We further reveal that the transformation sequence controls the coupling between rotation and amplification: amplification followed by rotation induces Venturi amplification attenuation and rotational hysteresis, whereas rotation followed by amplification separates the dominant functional regions, eliminating the coupled attenuation and maintaining both target rotation and velocity amplification. The different responses under the two transformation sequences demonstrate transformation-order-induced nonreciprocity and a magnetism-analogous rotational hysteresis response associated with body-force redistribution, pressure-gradient lag, and viscous dissipative driving. Under inhomogeneous incoming flow, body force manipulation locks the central average flow direction to the prescribed direction in the fixed Cartesian frame, with angular deviations below 0.3° for the tested preset angles, whereas viscosity manipulation is passively deflected by the background inflow and shows deviations of approximately 23°. These results establish body-force manipulation and transformation-sequence control as design principles for active multifunctional hydrodynamic metamaterials with Venturi amplification, nonreciprocity, rotational hysteresis, and direction-locking capability.