Bénard–von Kármán–Taylor–Proudman phantom wakes

The Bénard–von Kármán wake is a canonical phenomenon in fluid mechanics, readily identified by its alternating vortex street forming behind a bluff body. Seemingly unrelated, rapidly rotating fluids give rise to elongated, quasi-two-dimensional structures known as Taylor columns. The Taylor–Proudman theorem indeed enforces an invariance of the flow along the rotation axis when inertial and viscous effects are small compared with Coriolis forces. Here, we combine these two seemingly distinct phenomena by studying the formation of what we call phantom wakes: a rotating fluid appears to flow around a non-existent solid obstacle, namely a Taylor column. We address the question of whether a Bénard–von Kármán-type wake can spontaneously emerge under such conditions. To do so, we perform direct numerical simulations of an imposed flow in a rotating channel containing a small cylindrical cavity on one wall, which generates a Taylor column. By systematically varying the Rossby and Reynolds numbers, we analyze the progressive emergence of a wake behind the column and its convergence toward the classical vortex street. As in the non-rotating case, vortex shedding occurs through a Hopf bifurcation, which we characterize for a fixed Rossby number. However, the transition threshold varies non-monotonically with rotation. For intermediate Rossby numbers, elliptical streamlines and a shorter recirculation region are observed, resulting in a critical Reynolds number exceeding the classical value of 47. These findings not only reveal unexpected wake dynamics, but also suggest a mechanism for Taylor column formation that depends sensitively on the cavity geometry.