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The manner by which external vortical disturbances penetrate the laminar boundary layer and induce transition is explored. Linear theory suggests that the well-known Klebanoff mode precursor to transition can be understood as a superposition of Squire continuous modes. Shear sheltering influences the ability of free-stream disturbances to generate a packet of Squire modes. A coupling coefficient between continuous spectrum spectrum Orr–Sommerfeld and Squire modes is used to characterize the interaction. Full numerical simulations with prescribed modes at the inlet substantiate this approach. With two weakly coupled modes at the inlet, the boundary layer is little perturbed; with two strongly coupled modes, Klebanoff modes are produced; with one strongly coupled and one weakly coupled high-frequency mode, the complete transition process is simulated.

The secondary instability of a zero-pressure-gradient boundary layer, distorted by unsteady Klebanoff streaks, is investigated. The base profiles for the analysis are computed using direct numerical simulation (DNS) of the boundary-layer response to forcing by individual free-stream modes, which are low frequency and dominated by streamwise vorticity. Therefore, the base profiles take into account the nonlinear development of the streaks and mean flow distortion, upstream of the location chosen for the stability analyses. The two most unstable modes were classified as an inner and an outer instability, with reference to the position of their respective critical layers inside the boundary layer. Their growth rates were reported for a range of frequencies and amplitudes of the base streaks. The inner mode has a connection to the TollmienSchlichting (T-S) wave in the limit of vanishing streak amplitude. It is stabilized by the mean flow distortion, but its growth rate is enhanced with increasing amplitude and frequency of the base streaks. The outer mode only exists in the presence of finite amplitude streaks. The analysis of the outer instability extends the results of Andersson et al. (J. Fluid Mech. vol. 428, 2001, p. 29) to unsteady base streaks. It is shown that base-flow unsteadiness promotes instability and, as a result, leads to a lower critical streak amplitude. The results of linear theory are complemented by DNS of the evolution of the inner and outer instabilities in a zero-pressure-gradient boundary layer. Both instabilities lead to breakdown to turbulence and, in the case of the inner mode, transition proceeds via the formation of wave packets with similar structure and wave speeds to those reported by Nagarajan, Lele & Ferziger (J. Fluid Mech., vol. 572, 2007, p. 471).

The secondary instability of boundary layer streaks is investigated by means of direct stability analysis. The base flow is computed in direct simulations of bypass transition. The random nature of the free-stream perturbations causes the formation of a spectrum of streaks inside the boundary layer, with breakdown to turbulence initiated by the amplification of localized instabilities of individual streaks. The capability of the instability analysis to predict the instabilities which are observed in the direct numerical simulation is established. Furthermore, the analysis is shown to identify the particular streaks that break down to turbulence farther downstream. Two particular configurations of streaks regularly induce the growth of these localized instabilities: low-speed streaks that are lifted towards the edge of the boundary layer, and the local overlap between high-speed and low-speed streaks inside the boundary layer. It is established that the underlying modes can be ascribed to the general classification of inner and outer modes which was introduced by Vaughan & Zaki (J. Fluid Mech., vol. 681, 2011, pp. 116-153). Statistical evaluations show that Blasius boundary layers favour the amplification of outer instabilities. Adverse pressure gradient promotes breakdown to turbulence via the inner mode.

The flow through a compressor passage without and with incoming free-stream grid turbulence is simulated. At moderate Reynolds number, laminar-to-turbulence transition can take place on both sides of the aerofoil, but proceeds in distinctly different manners. The direct numerical simulations (DNS) of this flow reveal the mechanics of breakdown to turbulence on both surfaces of the blade. The pressure surface boundary layer undergoes laminar separation in the absence of free-stream disturbances. When exposed to free-stream forcing, the boundary layer remains attached due to transition to turbulence upstream of the laminar separation point. Three types of breakdowns are observed; they combine characteristics of natural and bypass transition. In particular, instability waves, which trace back to discrete modes of the base flow, can be observed, but their development is not independent of the Klebanoff distortions that are caused by free-stream turbulent forcing. At a higher turbulence intensity, the transition mechanism shifts to a purely bypass scenario. Unlike the pressure side, the suction surface boundary layer separates independent of the freestream condition, be it laminar or a moderate free-stream turbulence of intensity T u ∼ 3 %. Upstream of the separation, the amplification of the Klebanoff distortions is suppressed in the favourable pressure gradient (FPG) region. This suppression is in agreement with simulations of constant pressure gradient boundary layers. FPG is normally stabilizing with respect to bypass transition to turbulence, but is, thereby, unfavourable with respect to separation. Downstream of the FPG section, a strong adverse pressure gradient (APG) on the suction surface of the blade causes the laminar boundary layer to separate. The separation surface is modulated in the instantaneous fields of the Klebanoff distortion inside the shear layer, which consists of forward and backward jet-like perturbations. Separation is followed by breakdown to turbulence and reattachment. As the free-stream turbulence intensity is increased, T u ∼ 6.5 %, transitional turbulent patches are initiated, and interact with the downstream separated flow, causing local attachment. The calming effect, or delayed re-establishment of the boundary layer separation, is observed in the wake of the turbulent events.

Non-equilibrium molecular dynamics simulations of boundary-driven sheared Lennard-Jones liquids at variable pressure up to 5 GPa (for argon) reveal a rich out-of-equilibrium phase behavior with a strong degree of shear localization. At the lowest apparent shear rate considered (wall speed ~1 m s(-1)) the confined region is an homogeneously sheared solid (S) with no slip at the walls. This transforms at higher shear rates to a non-flowing plug with slip at the walls, referred to as the plug slip (PS) state. At higher shear rate a central localized (CL) state formed in which the shear gradient was localized in the center of the film, with the rest of the confined sample in a crystalline state commensurate with the wall lattice. The central zone liquidlike region increased in width with shear rate. A continuous rounded temperature profile across the whole system reflects strong dynamical coupling between the wall and confined region. The temperature rise in the confined film is consistent with the Brinkman number. The transition from the PS to CL states typically occurred at a wall speed near where the shear stress approached a critical value of ~3% of the shear modulus, and also near the peak in the traction coefficient, μ. The peak traction coefficient values computed, ~0.12-0.14 at 1000 MPa agree with those found for traction fluids and occur when the confined liquid is in the PS and CL states. At low wall speeds slip can occur at one wall and stick at the other. Poorly wetting liquids manifest long-lived asymmetries in the confined liquid properties across the system, and a shift in solid-liquid phase co-existence to higher shear rates. A non-equilibrium phase diagram based on these results is proposed. The good agreement of the tribological response of the Lennard-Jones fluid with that of more complicated molecular systems suggests that a corresponding states scaling of the tribological behavior could apply.

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Direct numerical simulations of turbulent flow in a channel with superhydrophobic surfaces (SHS) were performed, and the effects of the surface texture on the turbulence and skin-friction coefficient were examined. The SHS is modeled as a planar boundary comprised of spanwise-alternating regions of no-slip and free-slip boundary conditions. Relative to the reference no-slip channel flow at the same bulk Reynolds number, the overall mean skin-friction coefficient is reduced by 21.6%. A detailed analysis of the turbulence kinetic energy budget demonstrates a reduction in production over the no-slip phases, which is explained by aid of quadrant analysis of the Reynolds shear stresses and statistical analysis of the turbulence structures. The results demonstrate a significant reduction in the strength of streamwise vortical structures in the presence of the SHS texture and a decrease in the Reynolds shear-stress component ⟨R12⟩ which has a favorable influence on drag over the no-slip phases. A secondary flow which is set up at the edges of the texture also effects a beneficial change in drag. Nonetheless, the skin-friction coefficient on the no-slip features is higher than the reference levels in a simple no-slip channel flow. The increase in the skin-friction coefficient is attributed to two factors. First, spanwise diffusion of the mean momentum from free-slip to no-slip regions increases the local skin-friction coefficient on the edges of the no-slip features. Second, the drag-reducing capacity of the SHS is further reduced due to additional Reynolds stresses, ⟨R13⟩.