Dynamics of laminar and transitional flows over slip surfaces: effects on the laminar–turbulent separatrix

Variational Nonlinear Optimization in Fluid Dynamics: The Case of a Channel Flow with Superhydrophobic Walls

“…The results provided above indicate that boundary slip may have a strong effect on the energy amplification of nonlinear coherent flow structures such as λ− and hairpin vortices, despite the fact that their overall shape barely changes due to the presence of the slip. These findings confirm the recent conclusions drawn by Davis and Park [68], who investigated the effect of slip surface on the transition dynamics of nonlinear flow structures. In particular, they found that the shape and position of critical-layer vortical structures similar to those typical of K-or H-type transition remain mostly unchanged no matter the slip lengths considered, despite their swirling amplitude may be reduced with slip length.…”

“…However, the amount of energy growth and consequent time to transition appears to be considerably influenced by wall slip, leading to damping effect in the case of hairpin-like structures, while an even more rapid transition is observed for core sinuous flow structures. These results appear to confirm the scenario suggested by [68], in which wall slip stabilizes hairpin-like coherent structures constituted by ejections, while destabilizes sinuous ones located in the core of the channel.…”

“…Whereas, transition triggered by the weakly nonlinear optimal with slip conditions appears to be even faster than that observed in no-slip conditions. This can be easily explained noticing that these vortical perturbations rapidly create sinuous streaks which bear many resemblances with the core structures mentioned by Davis and Park [68], whose transition is promoted by the presence of slip. This may appear in contrast with what found by Picella et al [64], where slip appeared to have no effect at all on the transition behavior of core perturbations such as the linear optimal disturbances.…”

“…Some recent studies have assessed the effect of boundary slip on the optimal growth of perturbations under linearized conditions [66], finding little effect on the linear energy amplification, while linear stability [63,66,67] appears to be much more affected. At the same time, a recent study [68] has assessed the influence of slip at the wall on nonlinear traveling waves solutions of the Navier-Stokes equations. Depending on their structure, the transition to turbulence of these nonlinear solutions can be delayed or advanced.…”

On the Comparison of Flow Physics between Minimal and Extended Flow Units in Turbulent Channels

“…Prior to proceeding to the present work, we aim to provide a brief description of the minimal flow unit and its potential connection to William W. Willmarth's legacy in turbulent flows. Direct numerical simulations (DNSs) based on minimum flow units have been extensively performed for a variety of purposes, including understanding near-wall turbulent dynamics [17][18][19][20] and flow control [21][22][23]. A minimum flow unit involves the periodic computational domain, which has the minimum spanwise length of approximately 100 wall units and the minimum streamwise length of approximately 250-350 wall units [5].…”