Taylor halos and Taylor spears in odd viscous liquids

Abstract

A body placed in a rigidly-rotating fluid becomes circumscribed by a fictitious cylinder with generators parallel to the axis of rotation, a Taylor column. Slowly-moving liquid impinging on the body will swerve around the cylinder. Thus, Taylor columns may form when a breeze impinges on a mountain or when slowly-moving oceanic water impinges on a seamount, both due to the Earth's rotation. Here we show that classical non-rotating liquids endowed with an odd or Hall coefficient of viscosity, exhibiting nondissipative behavior, also give rise to Taylor column structures resembling halos or spears. Steady three-dimensional flow of such a liquid becomes effectively two dimensional, swirling around the Taylor column imitating its rigidly-rotating counterparts. Formation of Taylor halos and spears is attributed to the propagation of data along characteristics that may be parallel or oblique to a center axis, respectively.