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This thesis studies the effect of controlling separately the buffer and logarithmic layers in wall-bounded turbulent flows. In the case of buffer-layer control, we examine the effect on near-wall turbulence of displacing the apparent, virtual origins perceived by different components of the overlying flow. This mechanism is commonly reported for drag-altering textured surfaces of small size. For the particular case of riblets, it has been proposed that their effect on the overlying flow could be reduced to an offset between the origins perceived by the streamwise and spanwise velocities, with the latter being the origin perceived by turbulence. Later results, particularly in the context of superhydrophobic surfaces, suggest that this effect is not determined by the apparent origins of the tangential velocities alone, but also by the one for the wall-normal velocity. To investigate this, we conduct direct simulations of turbulent channels imposing different virtual origins for all three velocity components using Robin, slip-like boundary conditions. The results of our simulations support the idea that the relevant parameter is the offset between the virtual origins perceived by the mean flow and turbulence. When using Robin, slip-like boundary conditions, the virtual origin for the mean flow is determined by the streamwise slip length. Meanwhile, the virtual origin for turbulence results from the combined effect of the wall-normal and spanwise slip lengths. The slip experienced by the streamwise velocity fluctuations, in turn, has a negligible effect on the virtual origin for turbulence, and hence the drag, at least in the regime of drag reduction. This suggests that the origin perceived by the quasi-streamwise vortices, which induce the cross-flow velocities at the surface, is key in determining the virtual origin for turbulence, while that perceived by the near-wall streaks, which are associated with the streamwise velocity fluctuations, plays a secondary role. In this framework, the changes in turbulent quantities typically reported in the flow-control literature are shown to be merely a result of the choice of origin, and are absent when using as origin the one experienced by turbulence. Other than this shift in origin, we demonstrate that turbulence thus remains essentially smooth-wall-like. A simple expression can predict the virtual origin for turbulence in this regime. The effect can also be reproduced a priori by introducing the virtual origins into a smooth-wall eddy-viscosity framework. We also present exploratory results that suggest that the effect on the flow of opposition control, an active flow-control technique, can also be interpreted in terms of virtual origins. In the second part of this thesis, we investigate the effect of controlling the flow within the logarithmic layer alone, without directly modifying the flow elsewhere, and assess how this effect varies with Reynolds number. In contrast to buffer-layer control strategies, controlling the logarithmic layer has the potential to provide a reduction in turbulent drag that does not diminish with increasing Reynolds number. We first consider the effect of an idealised, hypothetical control strategy that is able to remove all of the Reynolds shear stress in all or part of the logarithmic layer, while leaving the rest of the flow unaltered. The idea is that this would serve as a theoretical prediction for the maximum turbulent drag reduction achievable by strategies that target the logarithmic layer alone. We quantify the effect of this control strategy on the flow and find that by relaminarising the whole logarithmic layer or a fixed portion of it in outer units, it is theoretically possible to produce a reduction in drag that improves with increasing Reynolds number. We also conduct a series of direct numerical simulations of turbulent channel flows at friction Reynolds numbers in the range 360 ≲ Reτ ≲ 2000, and artificially remove certain streamwise and spanwise wavelengths of the wall-normal velocity across a range of heights primarily within the logarithmic layer. The aim is to inhibit the dynamics of the self-similar, wall-attached sweep and ejection motions and their associated vortex clusters that reside in the logarithmic layer, while modifying the near-wall dynamics as little as possible. When these wavelengths are removed, we observe a positive, outward shift in the mean velocity profile, due to a local reduction in Reynolds shear stress, and subsequent increase in viscous stress, within the controlled region. When a fixed proportion of the uncontrolled Reynolds shear stress is removed across the whole logarithmic layer in our simulations, we show that it is possible to generate a reduction in drag that improves with Reynolds number, although the idealised control strategy grossly over-predicts the actual performance. This occurs because the majority of the energy originally contained in the removed scales in the control region is redistributed to even larger scales, rather than eradicated. This suggests that the flow in the logarithmic layer is very robust, even to this kind of targeted control strategy. Therefore, even though controlling the logarithmic layer has significant potential in theory, our results suggest that actual performance may be limited.

Using a series of direct numerical simulations, the individual and cumulative effects of various disturbance environments existing in a low pressure turbine (LPT) are investigated. In particular, the effects of free-stream turbulence (FST), unsteady wakes, roughness and blade oscillations on the separation-induced transition on the suction surface of a low pressure turbine blade are analyzed. Two configurations are considered: (i) a flat plate subjected to streamwise pressure gradient representative of the suction surface of a low pressure turbine blade, (ii) a flat plate subjected to a convecting free-stream vortex of fixed strength and at a fixed height over the plate. The first configuration represents the ‘ultra high-lift’ blades for the next generation low pressure turbine. The local pressure gradient induced by the convecting vortex in the second configuration is representative of the adverse pressure gradient on the suction surface of a low pressure turbine blade. The results are validated against existing experimental or numerical data and it is demonstrated that the numerical framework has captured most of the phenomena to a reasonable level of accuracy. A kernel experiment for bypass transition is simulated for the vortex-induced instability. The effect of the convection speed and strength of the vortex are discussed and the paths of transition adopted are distinguished. At low disturbance levels, the transition to turbulence is primarily due to the breakdown of ‘Kelvin-Helmholtz’ roll up vortices. In the presence of aeroelastic blade oscillations, unsteady wakes, free-stream turbulence and roughness, transition takes the bypass route and the results show evidence of streamwise streaks. These streaks impart spanwise waviness to the separated shear layer and cause early destabilisation. The blade oscillation has an effect in reducing the separated region and hence, the profile loss, which is further accentuated in the presence of free-stream turbulence. A blade fluctuating at higher reduced frequency is found to be more effective in shrinking the separation region. Blade vibration is found to increase the level of pre-transitional fluctuations, without having a significant influence on the growth beyond separation. There is a cumulative effect in suppressing the separation region when blade oscillation and free-stream turbulence are studied in conjunction, although the additional effect of free-stream turbulence is marginal. A secondary separation bubble, noted in the unperturbed flow, is reduced in size with blade oscillation and further reduced in the presence of free-stream turbulence. The vortex-induced instability has been proposed to be a unit process of free-stream turbulence, the effect of which is studied in the presence of a discrete roughness element (similar in functionality to a trip wire). The roughness element triggers early transition by destabilizing the mean flow. Streaks are observed in the presence of the convecting and rotating cylinder, generating a vortex of fixed strength, and are enhanced by the presence of roughness in the pre-transitional zone. Enhanced spanwise waviness is noted with the roughness, leading to earlier breakdown to turbulence. The route of transition and the origin of three-dimensionality marked by the prominence of the vortex stretching is shown. An optimum range of convection speeds of the free-stream vortex is obtained and the maximum receptivity is noted at a speed of 0.386, which concurs with prior experiments on a periodic convecting vortex (Kendall, 1987). The unsteady wake has a direct effect on the velocity profile. A lag is noted between the wake passing and transition. While the wake convects at the local free-stream velocity, its impression in the boundary layer convects much slower, between 50% and 70% of the local free-stream velocity. Both unsteady wakes and blade oscillation promote near-wall mixing. The unsteady wakes and blade oscillations have a conjunctive effect on reducing the size of separation bubble. The secondary separation bubble observed in the unperturbed flow is reduced with the presence of wakes and is completely suppressed with the addition of the blade oscillation. Turbulent kinetic energy production increases with increasing perturbation levels, with the maximum effect seen for the combination of wakes and oscillation. A receptivity method based on disturbance enstrophy transport equation (DETE) is proposed. The disturbance enstrophy is evaluated as the difference between the instantaneous and mean enstrophies, and while these are positive definite quantities, the difference may not be so. This aspect of disturbance enstrophy has been used meaningfully to obtain new information about the flow instability, such as segmenting regions of flow instabilities into those dictated by positive growth rates of disturbance enstrophy, and those due to its negative counterpart. The positive growth rates are associated with large scale coherence in the free-stream whereas the negative growth rates are found to be arising in near-wall viscous structures (Sengupta et al., 2019a,b). The extension of this method to structure detection and comparison against existing vortex identification methods, indicates the ability of the DETE method to capture small-scale structures induced by the viscous term of the Navier- Stokes equation. DETE has been used for the two configurations operating with varying perturbation levels and valuable insight pertaining to the flow dynamics has been attained with respect to its budget terms. In particular, the role of vortex stretching in leading the flow to three-dimensionality is highlighted. The global and local spatio-temporal receptivity analysis of flows perturbed by plate oscillations, wakes and free-stream excitation yields a spatio-temporal wave front to be the causal mechanism for flow transition. This is essentially representative of the nonmodal part of the disturbance spectrum. While this flow instability has already been established for geophysical flows such as tsunami and other fluid dynamical problems such as for zero pressure gradient boundary layer formed over a semi-infinite flat plate excited from inside the shear layer, its role for pressure gradient dominated flows (such as in LPTs) is shown for the first time. The importance of nonlinearity and its dispersion effects is shown, specifically for flows excited at the free stream, even when the onset of disturbances follows a linear mechanism. The need for using a global, nonlinear, spatio-temporal setup is established in order to capture all pertinent flow physics.

In this thesis, turbulent flows over canopies in the sparse and dense regimes are examined using direct numerical simulation. The term 'canopy' is used to refer to tall roughness elements in the flow. Sparse canopies typically have large element spacings and allow turbulent eddies to penetrate between the elements, whereas dense canopies have small spacings and preclude the penetration of turbulent eddies within them. In sparse canopies, we consider layouts with rigid elements and spacings larger than the characteristic scales of near-wall turbulence, $s^+ \gtrsim 100$. We focus on the effect of the canopy on the background turbulence, the part of the flow that remains once the element-induced flow is filtered out. In channel flows, the distribution of the total stress is linear with height. Over smooth walls, the total stress is only the 'fluid stress' $\tau_f$, the sum of the viscous and the Reynolds shear stresses. In canopies, in turn, there is an additional contribution from the canopy drag, which can dominate within. We find that, for sparse canopies, the ratio of the viscous and the Reynolds shear stresses in $\tau_f$ at each height is similar to that over smooth-walls, even within the canopy. From this, a height-dependent scaling based on $\tau_f$ is proposed. Using this scaling, the background turbulence within the canopy shows similarities with turbulence over smooth walls. This suggests that the background turbulence scales with $\tau_f$, rather than with the conventional scaling based on the total stress. This effect is essentially captured when the canopy is substituted by a drag force that acts on the mean velocity profile alone, aiming to produce the correct $\tau_f$, without the discrete presence of the canopy elements acting directly on the fluctuations. The proposed mean-only forcing is shown to produce better estimates for the turbulent fluctuations compared to a conventional, homogeneous-drag model. The present results thus suggest that a sparse canopy acts on the background turbulence primarily through the change it induces on the mean velocity profile, which in turn sets the scale for turbulence, rather than through a direct interaction of the canopy elements with the fluctuations. The effect of the element-induced flow, however, requires the representation of the individual canopy elements. The dense canopies studied consist of rigid, prismatic filaments with small spacings. The effect of the height and spacing of the canopy elements on the flow is studied. The flow is composed of an element-coherent, dispersive flow and an incoherent flow, which includes contributions from the background turbulence and from the flow arising from the Kelvin--Helmholtz-like, mixing-layer instability typically reported over dense canopies. For the present canopies, with spacings $s^+ \approx 3$--$50$, the background turbulence is essentially precluded from penetrating within the canopy. As the elements are 'tall', with height-to-spacing ratios $h/s \gtrsim 1$, the roughness sublayer of the canopy is determined by their spacing, extending to $y \approx 2$--$3s$ above the canopy tips. The dispersive velocity fluctuations are observed to also depend mainly on the spacing, and are small deep within the canopy, where the footprint of the Kelvin--Helmholtz-like instability dominates. The instability is governed by the canopy drag, which sets the shape of the mean velocity profile, and thus the shear length near the canopy tips. For the tall canopies considered here, this drag is governed by the element spacing and width, that is, the planar layout of the canopy. The mixing length, which determines the lengthscale of the instability, is essentially the sum of its height above and below the canopy tips. The former remains roughly the same in wall-units and the latter is linear with $s$ for all the canopies considered. For very small element spacings, $s^+ \lesssim 10$, the elements obstruct the fluctuations and the instability is inhibited. Within the range of $s^+$ of the present canopies, the obstruction decreases with increasing spacing and the signature of the Kelvin--Helmholtz-like rollers intensifies. For sparser canopies, however, the intensification of the instabilities ceases as the assumption of a spatially homogeneous mean flow breaks down. For the present, dense configurations, the canopy depth also has an influence on the development of the instability. For shallow canopies, $h/s \sim 1$, the lack of depth blocks the Kelvin--Helmholtz-like rollers. For deep canopies, $h/s \gtrsim 6$, the rollers do not perceive the bottom wall and the effect of the canopy height on the flow saturates. Two approaches based on linear stability analysis are proposed to capture the Kelvin--Helmholtz-like instability over dense canopies. The first approach models the canopy as an anisotropic permeable substrate whose wall-normal permeability, $K_y$, is larger than its streamwise permeability, $K_x$. This model predicts that the instability over canopies is governed by the geometric mean of the two permeabilities, $\sqrt{K_x^+ K_y^+}$. We also use this model to study the effect of the mean inclination of the canopy elements on the instability. The second approach models the canopy using a drag force in the momentum equation. This model shows that two competing effects, originating from the canopy drag, govern the growth of the instability. Increasing the canopy drag results in a stronger inflection point in the mean velocity profile, which enhances the instability, while at the same time, it also inhibits fluctuations within the canopy, suppressing the instability. We also analyse the stability of the mean profiles obtained from the DNS of dense canopy flows. Using this analysis, we show that the shear-layer thickness within the canopy, which determines the streamwise wavelength of the instability, also scales with the element spacing.

The objective of the present thesis is to answer the question: 'can anisotropic permeable substrates reduce turbulent skin-friction drag?' The first part of the thesis aims to extend the existing understanding on how complex surfaces of small texture size can reduce drag. We show that the effect of these surfaces can be reduced to an offset between the apparent, virtual smooth wall perceived by the mean flow and that perceived by the overlying turbulence, but turbulence remains otherwise smooth-wall-like. The drag reduction produced by these surfaces is therefore proportional to the difference between the two virtual origins. In the second part of the thesis, we study the influence that anisotropic permeable substrates have on the overlying turbulence and show the potential of these substrates to reduce drag. For this, we conduct direct numerical simulations of channel flows bounded by permeable substrates. For small permeabilities, we observe a linear regime, where drag reduction is proportional to the aforementioned offset between the virtual origin perceived by the mean flow and that perceived by turbulence. For the substrates under study, the former is governed by the streamwise permeability and the latter by the spanwise permeability. This linear regime breaks down as spanwise-coherent structures begin to appear, which increase the turbulent mixing and consequently increase the drag. These structures are attributed to a Kelvin-Helmholtz-like instability of the mean flow, a common feature to a variety of obstructed flows, and their onset can be predicted using a linear stability analysis. This analysis shows, and the simulations corroborate, that the governing parameter for the breakdown is the wall-normal permeability. As this permeability increases, the drag-increasing, spanwise-coherent structures become prevalent in the flow, outweighing the drag-reducing effect of the virtual origins and eventually leading to an increase of drag. Based on the virtual-origin theory and the linear stability analysis, we build a predictive model for the behaviour of drag-reducing substrates, which estimates, with good accuracy, the drag reduction observed in the simulations. The present results and the models we subsequently developed provide guidelines for the design of drag-reducing permeable substrates. For the substrate configurations considered, the largest drag reduction observed is ≈ 20-25% at a friction Reynolds number δ⁺ = 180, which is at least twice that obtained for riblets.

Superhydrophobic surfaces are able to entrap gas pockets in-between surface roughness elements when submerged in water. These entrapped gas pockets give these surfaces the potential to reduce drag due to the overlying flow being able to locally slip over the gas pockets, resulting in a mean slip at the surface. This thesis investigates the different effects that slip and the texturing of the surface have on turbulence over superhydrophobic surfaces. It is shown that, after filtering out the texture-induced flow, the background, overlying turbulence experiences the surface as a homogeneous slip boundary condition. For texture sizes, expressed in wall units, up to $L^+ \lesssim 20$ the only effect of the surface texture on the overlying flow is through this surface slip. The direct effect of slip does not modify the dynamics of the overlying turbulence, which remains canonical and smooth-wall-like. In these cases the flow is governed by the difference between two virtual origins, the virtual origin of the mean flow and the virtual origin experienced by the overlying turbulence. Streamwise slip deepens the virtual origin of the mean flow, while spanwise slip acts to deepen the virtual origin perceived by the overlying turbulence. The drag reduction is then proportional to the difference between the two virtual origins, reminiscent of drag reduction using riblets. The validity of slip-length models to represent textured superhydrophobic surfaces can resultantly be extended up to $L^+ \lesssim 20$. However, for $L^+ \gtrsim 25$ a non-linear interaction with the texture-coherent flow alters the dynamics of the background turbulence, with a reduction in coherence of large streamwise lengthscales. This non-linear interaction causes an increase in Reynolds stress up to $y^+ \lesssim 25$, and decreases the obtained drag reduction compared to that predicted from homogeneous slip-length models.