The boundary-layer eruption phenomenon caused by a 2D patch of vorticity above a wall was investigated. It is shown that the eruption phenomenon depends on the viscosity (or Reynolds number, Re) of the fluid. There exists a threshold value of Re above which the eruption takes place. The initiation of the eruption goes through the creation of a small recirculation zone near the solid wall, the appearance of the saddle point on streamlines inside it and the tearing off process of the recirculation zone. Further increase of the Reynolds number causes a more complex flow. One can observe that eruption is regenerative and that the vortex patch can produce a cascade of secondary vortices. The vortex-in-cell method was employed to investigate the eruption phenomenon.
In this paper the initial positions of n-point vortices that collapse in finite time are numerically obtained. Examples of the collapsing systems of 3, 15 and 24 vortices are given. How to obtain the collapse positions of the vortices in the configuration space that are parameterized by the Hamiltonian values is described. A solution for the self-similar collapse trajectories of the vortices is derived.
In this study we investigate numerically the vortex wake formation behind the profile performing simple harmonic motion known in the literature as plunging. This research was inspired by the flapping motion which is appropriate for birds, insects and fishes. We assume the two dimensional model of flow. Depending on the parameters such as plunging amplitude, frequency and the Reynolds number, we demonstrate many different types of vortex street behind the profile. It is well known that the type of vortex wake determines the hydrodynamic forces acting on the profile. Dependences of the plunging amplitude, the Strouhal number and various topology vortices are established by constructing the phase transition diagram. The areas in the diagram related to the drag, thrust, and lift force generation are captured. We notice also the areas where the vorticity field is disordered. The disordered vorticity field does not allow maintenance of the periodic forces on the profile. An increase in the Reynolds number leads to the transition of the vortex wake behind the profile. The transition is caused by the phenomenon of boundary layer eruption. Further increase of the Reynolds number causes the vortex street related to the generation of the lift force to vanish.
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