Description of the transitional wake behind a strongly streamwise rotating sphere

• Published in: Journal of fluid mechanics 2020-08, Vol.896, Article A18
• Main Authors: Lorite-Díez, M., Jiménez-González, J. I.
• Format: Article
• Language: English
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2020.342

Direct numerical simulations are performed to study the flow regimes at the wake behind a strongly streamwise rotating sphere, covering the range of rotation parameters $0\leqslant \unicode[STIX]{x1D6FA}\leqslant 3$ and laminar and transitional Reynolds numbers $Re=250$ , 500 and 1000. The wake dynamics is investigated in terms of flow topology, dominant modes and force coefficients. A higher wake complexity is found for growing values of the rotation parameter $\unicode[STIX]{x1D6FA}$ for all the Reynolds numbers investigated. In particular, at low and intermediate $Re$ , successive bifurcations entail the development of periodic, quasi-periodic and irregular regimes, constituting a classical scenario of route to chaos, through the destabilization of different structures associated to incommensurate frequencies, which have been analysed by means of flow decomposition techniques. At low $Re$ and high rotation rates, the flow is governed by double-threaded structures due to the destabilization of helical symmetries of azimuthal wavenumber $m=2$ , which are not dominant at larger $Re$ . Interestingly, at intermediate values of $\unicode[STIX]{x1D6FA}$ and $Re=500$ , a bistable dynamics is observed whereby the wake undergoes a random switching between a modulated quasi-periodic regime and an irregular regime, which is associated to a sudden increase of the drag coefficient, on account of the development of a double-celled recirculating bubble. Finally, for $Re=1000$ , the flow is already chaotic at $\unicode[STIX]{x1D6FA}=0$ , and the evolution with the rotation rate of the flow dynamics is simpler, with wake regimes being characterized by the rotation and massive shedding of vortex loops, that are a continuous deformation through axial rotation of the irregular wake behind the static sphere.