AbstractsEarth & Environmental Science

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…