Dynamics and instability of a shielded vortex in close proximity of a wall

A dispersion relation preserving optimized upwind compact difference scheme for high accuracy flow simulations

“…14(a) we have shown the variation of mean enstrophy inside complete domain with time. For the periodic boundary case, the mean enstrophy inside a complete domain decays continuously and rapidly as compared to the no-slip boundary case for which there is a continuous interaction between the boundary layer formed on the domain boundaries [35]. During such strong interactions, mean enstrophy inside the domain increases, as also evident from Fig.…”

On the stability of a pair of vortex rings

“…In addition, strain can cause the deformation of a single core into a multipolar structure (van Heijst, Kloosterziel & Williams 1991; Orlandi & van Heijst 1992; Carton & Legras 1994; Sengupta et al. 2012). While such a structure is not visible in the vortex cores in the experiments of McKeown et al.…”

“…While the growth rate is smaller than that of the CI for the cases presently examined, the curvature instability could still excite perturbation growth that contributes to a turbulent transition near Re = 8000. In addition, strain can cause the deformation of a single core into a multipolar structure (van Heijst, Kloosterziel & Williams 1991;Orlandi & van Heijst 1992;Carton & Legras 1994;Sengupta et al 2012). While such a structure is not visible in the vortex cores in the experiments of McKeown et al (2018McKeown et al ( , 2020, core deformations that could cause the formation of multiple poles may be present to an extent which, when coupled with other mechanisms, contributes to transition.…”

“…Although viscous analysis is not applied directly to perturbations, this treatment maintains the applicability of the Biot-Savart law, which cannot strictly be applied to enforce the kinematic constraint on perturbations, (2.3), in a viscous flow (Sengupta 2021). This limitation is demonstrated by a variety of flows including, for example, a vortex in the vicinity of a boundary layer (Lim, Sengupta & Chattopadhyay 2004;Sengupta, Bhumkar & Sengupta 2012). Even when the Reynolds number is high, the Biot-Savart law is insufficient to describe these vortex dynamics, and considering the viscous term in the vorticity transport equation is necessary for an accurate description of the flow profile and its receptivity to perturbation growth (Sengupta 2021).…”