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Bénard–von Kármán–Taylor–Proudman phantom wakes
[Sillages fantômes de Bénard–von Kármán–Taylor–Proudman]
Benjamin Favier1 orcid   ; Patrice Le Gal1 orcid
1Aix Marseille Univ., CNRS, Centrale Med, IRPHE, Marseille, France
Comptes Rendus. Mécanique, Volume 354 (2026), pp. 783-800

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.

Le sillage de Bénard–von Kármán est un phénomène classique de la mécanique des fluides, facilement reconnaissable à sa rangée de tourbillons alternés qui se forme derrière un corps non profilé. À première vue sans rapport, les fluides en rotation rapide donnent naissance à des structures allongées, quasi bidimensionnelles, appelées “colonnes de Taylor”. Le théorème de Taylor–Proudman impose en effet une invariance de l’écoulement le long de l’axe de rotation lorsque les effets d’inertie et de viscosité sont faibles par rapport aux forces de Coriolis. Ici, nous combinons ces deux phénomènes apparemment distincts en étudiant la formation de ce que nous appelons des sillages fantômes : un fluide en rotation semble s’écouler autour d’un obstacle solide inexistant, à savoir une colonne de Taylor. Nous nous demandons si un sillage de type Bénard–von Kármán peut émerger spontanément dans de telles conditions. Pour ce faire, nous réalisons des simulations numériques directes d’un écoulement imposé dans un canal en rotation contenant une petite cavité cylindrique sur l’une de ses parois, qui génère une colonne de Taylor. En faisant varier systématiquement les nombres de Rossby et de Reynolds, nous analysons l’émergence progressive d’un sillage derrière la colonne et sa convergence vers l’allée de tourbillons classique. Comme dans le cas non-tournant, le détachement de tourbillons se produit par le biais d’une bifurcation de Hopf, que nous caractérisons pour un nombre de Rossby fixe. Cependant, le seuil de l’instabilité varie de manière non monotone avec la rotation. Pour des nombres de Rossby intermédiaires, on observe des lignes de courant elliptiques et une zone de recirculation plus courte, ce qui conduit à un nombre de Reynolds critique supérieur à la valeur classique de 47. Ces résultats révèlent non seulement une dynamique inattendue du sillage, mais suggèrent également un mécanisme de formation des colonnes de Taylor qui dépend fortement de la géométrie de la cavité.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmeca.379
Keywords: Rotating flows, Taylor column, wakes, stability, bifurcation
Mots-clés : Écoulements tournants, colonne de Taylor, sillage, instabilité, bifurcation

Benjamin Favier  1   ; Patrice Le Gal  1

1 Aix Marseille Univ., CNRS, Centrale Med, IRPHE, Marseille, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Benjamin Favier; Patrice Le Gal. Bénard–von Kármán–Taylor–Proudman phantom wakes. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 783-800. doi: 10.5802/crmeca.379
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     pages = {783--800},
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