J.H.G.M. van Geffen, V.V. Meleshko and G.J.F. van Heijst
Physics of Fluids 8, 2393-2399 (1996)
On the other hand, comparitively little has been done to clarify the influence of viscous effects on the motion of initially compact vorticity distributions in a bounded domain. This paper provides a comparative analysis of the motion of a point vortex and of a circular vortex with a non-singular initially axisymmetric vorticity distribution (henceforth referred to as "monopole") in an inviscid and viscous fluid, respectively, confined in a rectangular domain with free-slip walls. Such a rather simple and basic configuration offers a better understanding of the possibilities of both models.
In physical reality, however, free-slip walls are not present since there is always friction at the walls. Hence, one would want to apply a "no-slip" boundary condition: at the wall the velocity of the fluid equals zero. This condition implies generation of oppositely-signed vorticity near the wall, leading to a flow evolution different from the case of free-slip walls (see e.g. Orlandi ; Verzicco et al. ). A no-slip boundary condition cannot be applied to point vortices, but it can be applied in the method used for the computations with the distributed monopole, so that the effect of no-slip walls can be studied too.
In the next section the vortex models used in the numerical simulations are discussed. The results of these simulations for free-slip and no-slip domain boundaries are presented in Sect. III and IV, respectively. The paper ends with some general conclusions.
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