  We introduce a new concept for the manipulation of fluid flow around
three-dimensional bodies. Inspired by transformation optics, the concept is
based on a mathematical idea of coordinate transformations and physically
implemented with anisotropic porous media permeable to the flow of fluids. In
two situations - for an impermeable object placed either in a free-flowing
fluid or in a fluid-filled porous medium - we show that the object can be
coated with an inhomogeneous, anisotropic permeable medium, such as to preserve
the flow that would have existed in the absence of the object. The proposed
fluid flow cloak eliminates downstream wake and compensates viscous drag,
hinting us at the possibility of novel propulsion techniques.
