Fabre, David; Tchoufag, Joël; Magnaudet, Jacques The steady oblique path of buoyancy-driven disks and spheres. (English) Zbl 1275.76064 J. Fluid Mech. 707, 24-36 (2012). Summary: We consider the steady motion of disks of various thicknesses in a weakly viscous flow, in the case where the angle of incidence \({\alpha}\) (defined as that between the disk axis and its velocity) is small. We derive the structure of the steady flow past the body and the associated hydrodynamic force and torque through a weakly nonlinear expansion of the flow with respect to \({\alpha}\). When buoyancy drives the body motion, we obtain a solution corresponding to an oblique path with a non-zero incidence by requiring the torque to vanish and the hydrodynamic and net buoyancy forces to balance each other. This oblique solution is shown to arise through a bifurcation at a critical Reynolds number \({Re}^{{SO}}\) which does not depend upon the body-to-fluid density ratio and is distinct from the critical Reynolds number \({Re}^{{SS}}\) corresponding to the steady bifurcation of the flow past the body held fixed with \({\alpha} = 0\). We then apply the same approach to the related problem of a sphere that weakly rotates about an axis perpendicular to its path and show that an oblique path sets in at a critical Reynolds number \({Re}^{{SO}}\) slightly lower than \({Re}^{{SS}}\), in agreement with available numerical studies. Cited in 10 Documents MSC: 76D05 Navier-Stokes equations for incompressible viscous fluids 76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics Keywords:bifurcation; flow-structure interactions; wakes PDFBibTeX XMLCite \textit{D. Fabre} et al., J. Fluid Mech. 707, 24--36 (2012; Zbl 1275.76064) Full Text: DOI HAL References: [1] DOI: 10.1016/j.jfluidstructs.2011.03.013 · doi:10.1016/j.jfluidstructs.2011.03.013 [2] DOI: 10.1146/annurev-fluid-120710-101250 · Zbl 1355.76019 · doi:10.1146/annurev-fluid-120710-101250 [3] DOI: 10.1017/S0022112010004878 · Zbl 1225.76090 · doi:10.1017/S0022112010004878 [4] DOI: 10.1017/jfm.2011.419 · Zbl 1241.76238 · doi:10.1017/jfm.2011.419 [5] DOI: 10.1016/j.ijmultiphaseflow.2007.05.002 · doi:10.1016/j.ijmultiphaseflow.2007.05.002 [6] DOI: 10.1063/1.2909609 · Zbl 1182.76238 · doi:10.1063/1.2909609 [7] DOI: 10.1017/S0022112009007290 · Zbl 1183.76721 · doi:10.1017/S0022112009007290 [8] DOI: 10.1017/S0022112004009164 · Zbl 1065.76068 · doi:10.1017/S0022112004009164 [9] DOI: 10.1017/S0022112009993934 · Zbl 1189.76152 · doi:10.1017/S0022112009993934 [10] DOI: 10.1017/S0022112006003685 · Zbl 1108.76310 · doi:10.1017/S0022112006003685 [11] DOI: 10.1017/S0022112093002150 · Zbl 0780.76027 · doi:10.1017/S0022112093002150 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.