The dynamic characteristics of the pressure and velocity fields of the unsteady incompressible laminar wake behind a circular cylinder are investigated numerically and analysed physically. The governing equations, written in a velocity-pressure formulation and in conservative form, are solved by a predictor-corrector pressure method, a finite-volume second-order-accurate scheme and an alternating-directionimplicit (ADI) procedure. The initiation mechanism for vortex shedding and the evaluation of the unsteady body forces are presented for Reynolds-number values of 100,200 and 1000.The vortex shedding is generated by a physical perturbation imposed numerically for a short time. The flow transition becomes periodic after a transient time interval. The frequency of the drag and lift oscillations agree well with the experimental data.The study of the interactions of the unsteady pressure and velocity fields shows the phase relations between the pressure and velocity, and the influence of different, factors : the strongly rotational viscous region, the convection of the eddies and the almost inviscid flow.The interactions among the different scales of structures in the near wake are also studied, and in particular the time-dependent evolution of the secondary eddies in relation to the fully developed primary ones is analysed.

The transition and the development of turbulence in the near wake of a circular cylinder are investigated using hot-wire anemometry and flow visualization. The formation zone of the large regular vortices is studied in the subcritical regime (2000 < U0 D/v < 60000). with and without the introduction of a splitter plate. Two different regimes are identified in the interaction between the von Kármán vortices and those of the shear layer emerging from the separated boundary layer. Experimental evidence is given in support of the strong coupling at low Reynolds numbers characterized by phase modulations between the two types of structures. The interaction is weaker at high Reynolds numbers where the small-scale vortices are disconnected from the regular vortex shedding, giving rise to an intermittent pattern. Spectral properties are used to describe the different stages of the interaction between the shear-layer vortices and the alternating ones. Physical properties of the interaction are examined separately in a numerical simulation using a pressure-velocity formulation. Both unexcited and excited two-dimensional plane mixing layers are studied using streakline maps and time traces of the dynamical properties. The main features of the simulated vortex development are in agreement with the experimental results.

A direct numerical simulation of the viscous incompressible flow around a circular cylinder is carried out in the Reynolds number range 2000–10 000 by solving the two-dimensional time-dependent Navier–Stokes equations, using a pressure–velocity finite-volume method. Apart from the vortex shedding phenomenon, it is shown that transition waves develop in the separated shear layers and lead to mixing layer eddies. The ratio of the computed transition wave frequency over Strouhal number is in good agreement with experimental results. This allows the supposition that the instability leading to mixing layer eddies has a predominant two-dimensional origin and is predicted by the Navier–Stokes equations.

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