The work reported in this thesis is an experimental and theoretical investigation of the so-called sink flow boundary layers. These are two-dimensional (in the mean), favourable-pressure-gradient (FPG) boundary layer flows where the boundary layers experience stream-wise acceleration inside a two-dimensional convergent channel with smooth and plane walls. The boundary layers studied are mainly turbulent with few cases that may be identified as reverse-transitional. The sink flow turbulent boundary layers (TBLs) are the only smooth-walled layers that are in ‘perfect equilibrium’ or ‘exact self-preservation’ in the sense of Townsend (1976) and Rotta (1962). The present boundary layer experiments were conducted in an open-return low-speed wind tunnel. The sink flow conditions were established on the test-plate by using a contoured test-section ceiling for creating a convergent channel with smooth and plane walls. The strength of the streamwise FPG was varied by changing the freestream speed in the test-section. Few zero-pressure-gradient (ZPG) turbulent boundary layers were also measured in the same tunnel for which the contoured ceiling was replaced by a straight one. The velocity measurement techniques used include conventional Pitot-tubes for mean flow measurements and hotwire/crosswire probes for turbulence measurements. For measurement of skin friction in ZPG flows, Preston-tube was used while for the sink flows the so-called surface hotwire method was employed. Static pressures were measured on the test-surface using an alcohol-based projection manometer. Boundary layers were tripped at the beginning of the test-plate to ensure quick transition to turbulence. The mean velocity scaling in sink flow TBLs in the presence of strong FPG has been studied systematically, especially in view of the apparent pressure-gradient-dependence of the logarithmic laws reported in the literature (Spalart & Leonard, 1986; Nickels, 2004; Chauhan et al., 2007). The experimental study of sink flow TBLs carried out over a wide range of streamwise FPGs has shown that the mean velocity profiles (in inner coordinates) exhibit systematic departures from the universal logarithmic law as the pressure gradient parameter ∆p is varied. Even so, each of these profiles exhibits a logarithmic region, albeit non-universal, whose constants are functions of the pressure gradient. Systematic dependence of these constants on the pressure gradient parameter ∆p is observed. Moreover, the wake region is uniformly absent in all these profiles. In other words, each profile looks like a ‘pure wall-flow’, in the sense of Coles (1957), only if it is viewed in relation to its own non-universal logarithmic law. To support the experimental observation of the pressure-gradient-dependence of logarithmic laws in sink flow TBLs, a theory based on the method of matched asymptotic expansions has been applied to sink flow TBLs and this theory reveals a systematic dependence of inner and outer logarithmic laws on the pressure gradient parameter ∆p. This dependence is essentially a higher-order effect and therefore becomes significant only in the presence of relatively strong pressure gradients. Comparison of the theory with the experimental data demonstrates that the disappearance of the universal logarithmic law in strong FPG situations does not necessarily imply the absence of classical inner-outer overlap region. The overlap may still manifest itself as a logarithmic functional form with constants that are strongly influenced by the magnitude of the FPG. An immediate use of the non-universal log laws is towards the estimation skin friction in strong-pressure-gradient equilibrium and near-equilibrium TBL flows and this issue has been studied in some detail. It is shown that the conventional Clauser-chart method for estimation of skin friction (which gives fairly accurate results for ZPG or mild-pressure-gradient flows), originally proposed by Clauser (1954), can be modified to deal with the situations involving strong streamwise pressure gradients, provided that the equilibrium or near-equilibrium TBL under consideration is not very close to relaminarization or separation. In such cases, the overlap layer manifests itself in the form of non-universal logarithmic laws that are dependent on the local strength of the pressure gradient. Using these non-universal log laws in conjunction with the measured pressure distribution (necessary for obtaining the acceleration parameter K) and a measured mean velocity profile, it is possible to obtain the local skin friction coefficient to an accuracy which is typical of skin friction measurements. This modified Clauser-chart method (MCCM) employs a two-fold iterative procedure (one iteration on Cf and the other on ∆p) in contrast to the conventional method that involves only one iteration (on Cf alone). As a by-product of this MCCM, one obtains the local pressure gradient parameter ∆p and the slope 1/κ and intercept C of the non-universal log law for that profile. It is also demonstrated that the arm´MCCM is quite robust to the changes in the universal values of K´arman constant κ0 and intercept C0 for the ZPG turbulent boundary layer. Various aspects of the large-scale structure in turbulent and reverse-transitional sink flow boundary layers subjected to streamwise FPGs have also been investigated. The use of sink flow configuration allows systematic characterization of the large-scale structure with the strength of the FPG as a parameter where the characterization is not contaminated by the upstream history effects. The large-scale structure is identified by cross-correlating the wall-shear stress fluctuation with the streamwise velocity fluctuation. The structure orientation is found to be linear over a large wall-normal extent typically extending from y/δ of 0.1 to 0.6. Beyond y/δ =0.6, the correlation under consideration becomes very weak to allow any conclusive results. The average structure inclination angle αavg is found to decrease systematically with increase in the streamwise FPG. This result is important and has implications towards modeling of the near-wall region. Further it is found that the structure gets elongated considerably as the FPG is increased, i.e. the streamwise spatial extent of the structure increases. Taken together, it is observed that the structure becomes flatter and longer with the increase in FPG. Structural models are proposed for sink flow TBLs in the form of either the shape of individual hairpin vortices or the possible structural self-organization. These models are then discussed in the light of present experimental results. It is also shown that the process of relaminarization of a TBL by strong FPG may be better appreciated by appealing to these structural models. The validity of Taylor’s hypothesis for structure angle measurements in the present study has been established experimentally. This exercise is important since the flows under consideration are highly accelerated and sometimes even reverse-transitional. In most of the previous work on the validity of Taylor’s hypothesis, at least for the measurements similar to the present work, the emphasis has been on ZPG turbulent boundary layers. The present exercise is therefore crucial for accelerating flows. Possible reasons for the observed validity of Taylor’s hypothesis have also been identified − specifically it is seen that the condition ∆xp/L << 1 needs to be met for Taylor’s hypothesis to be valid in pressure gradient flows. Investigation of the structure convection velocity from the space-time correlations has revealed that the convection velocity of a typical structure in the present sink flow boundary layers is almost equal to the local mean velocity (more than 90%). This implies that the structure gets convected downstream almost along with the mean flow. Near-wall ‘active’ and ‘inactive’ motions in sink flow TBLs have been studied, discussed and compared with the corresponding results for ZPG turbulent boundary layers from five different aspects: (i) turbulent diffusion of TKE, (ii) quadrant statistics, (iii) profiles of the streamwise turbulence intensity, (iv) event correlation length scales obtained from conditional sampling on the instantaneous flux signal and (v) profiles of the Townsend parameter Tp =(−uv) /u2. Near-wall inactive motion is seen to be related to the strength of the large-eddy structure in the outer region of TBL flow. For APG flows the near-wall inactive motion is known to be more intense (Bradshaw, 1967b) than the ZPG flows, say at the same K´arman number δ+. This observation is consistent with a stronger large-eddy structure that may be perceived from the stronger wake component in the mean velocity variation and the larger mean entrainment in an APG turbulent boundary layer as compared to the ZPG flow at same δ+. In sink flow TBLs, the large-eddy structure is much weaker in comparison to the ZPG flow at same δ+ which is consistent with the absence of wake component in the mean velocity profile as well as the zero mean entrainment into the layer. A sink flow TBL represents, a state of weakest large-eddy structure and hence minimum intensity of inactive motion compared to any other equilibrium or near-equilibrium TBL flow having the same K´arman number δ+. All the analysis of the relevant experimental data seems to support this.

This thesis explores the effects of favourable pressure gradient on the structure of turbulent boundary layers (TBL). In this context, the structure of three types of boundary layers namely a zero-pressure-gradient boundary layer, equilibrium boundary layers under favourable pressure gradient and relaminarising boundary layers is investigated mostly from the point of view of large-scale dynamics. This covers a whole range of flows on the so-called Reynolds number - pressure gradient diagram - from turbulent zero pressure gradient flows to relaminarising flows at relatively low Reynolds numbers. The study of turbulent and relaminarising boundary layers is carried out primarily using direct numerical analyses and some limited experiments in this thesis. The direct numerical simulations (DNS) of a zero-pressure-gradient turbulent boundary layer (ZPG TBL) is validated against the experimental and DNS data available in the literature. Furthermore, the important question of time-averaged signature of a large scale vortex structure and its relation with the two-point correlations in the context of ZPG TBL is addressed. In this context, a synthetic flow consisting of hairpin vortex structures is generated. The two-point correlations in the synthetic TBL and a real TBL are found to be qualitatively similar. This shows that the vortex structure leaves a time-averaged footprint in the form of correlations of velocity and vorticity. A study of two-point correlations in a real TBL shows that the structure angle deduced from two-point correlations varies with wall-normal location. The structure angle is small near the wall and increases away from the wall in agreement with the previous studies. The small angle close to the wall signifies the presence of streamwise structure. Away from the wall, this streamwise coherence is lost and the correlation contours become more isotropic. The presence of the wall and the mean shear affects smaller scales making them anisotropic close to the wall. Towards the edge of the boundary layer, smaller scales tend to become isotropic leading to -5/3 law in the energy spectrum. Further, a relation between a passive scalar in a flow and vorticity is explored. It is found that the scalar product of vorticity and scalar gradient is conserved in a non-diffusive situation. This assertion is demonstrated under various flow conditions. Despite the differences in Schmidt numbers, the structures observed in the outer layer are similar in both numerical and experimental flow visualisations. Further, the equilibrium turbulent boundary layers under favourable pressure gradient are studied. The numerical simulations of equilibrium sink flow TBL are validated against the experimental results of Dixit (2010). A study of two-point correlations reveals that the near-wall structure angle decreases with a favourable pressure gradient in sink flow TBLs. In the outer region, the loss of streamwise coherence occurs at a wall-normal location closer to the wall than in an ZPG TBL. Edge intermittency study reveals that the flow is non-turbulent beyond y/δ = 0.8 inside the mean boundary layer edge. The variation of the ratio of pressure gradient to Reynolds shear stress gradient shows that this ratio is very large (> 50) beyond y/δ = 0.8. The dominance of pressure gradient makes this part of sink flow TBL to behave like a Euler-region. Small scales in sink flow TBL tend to be isotropic near the edge of the boundary layer and spectra shows -5/3 law akin to ZPG TBL, albeit at lower Reynolds numbers. The concept of equilibrium is extended to flows with wall transpiration. The sink flow TBL is a special case of more generalised equilibrium TBLs with wall transpiration. Conditions required for the flow with wall transpiration are derived. It is observed that there is a systematic variation of various statistical properties with wall velocity. Further, it is observed that the motion in these equilibrium flows is purely active like in sink flow TBL. In equilibrium TBL, the Reynolds shear stress is directly related to mean velocity. So we have at our disposal an exact relation between the Reynolds shear stress and the mean velocity gradient without the need to do any ad-hoc modelling for the sink flow. This is an interesting observation from the point of view of modelling TBLs using eddy-viscosity. Eddy-viscosity model derived from sink flow TBL data is found to predict the mean velocity profiles in flows with wall transpiration with a sufficient accuracy. Similarly, it is plausible that any general non-equilibrium flow may be treated as a departure from equilibrium. With suitable modifications, eddy viscosity obtained from equilibrium TBL may be used to model them without invoking ad-hoc assumptions. Finally, the effect of initial Reynolds number on the process of relaminarisation is studied numerically and experimentally. ZPG TBLs with two different initial Reynolds number are subjected to different degrees of acceleration. However, the pressure gradient history is same in both the cases. It is observed that the flow with a higher initial Reynolds number relaminarises at a lower pressure gradient value than the flow with a lower initial Reynolds number. Assessment of different parameter criteria reveals that the criterion proposed by Narasimha & Sreenivasan (1973) is appropriate for the prediction of the onset of relaminarisation. Further, the structures in relaminarising flows are studied. The near-wall structure angle is found to decrease with the increasing FPG and the streamwise length of the structure also increases. The low and high speed streaks in the near-wall region are found to become longer and less undulating with an increase in the spanwise spacing. A stabilisation mechanism of near-wall streaks is also presented which suggests that the kinematic effect of mean vertical velocity directed towards the wall is responsible for the stabilisation of streaks.