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The receptivity process by which two-dimensional, time-harmonic freestream disturbances generate instability waves in the incompressible Blasius boundary layer is investigated analytically. The importance of the leading edge region and the linear nature of the receptivity process are discussed, and Goldstein's (1983a, 1983b) theoretical framework for the leading edge receptivity problem is reviewed. His approach utilizes asymptotic matching of a region close to the leading edge, which is governed by the linearized unsteady boundary layer equation, with a region further downstream, which is described by an Orr-Sommerfeld type equation. The linearized unsteady boundary layer equation is solved numerically, using the slip velocity and pressure gradient obtained from the inviscid interaction of the freestream disturbance with the semi-infinite plate. A new method is developed to extract the receptivity coefficient from this numerical solution. The receptivity coefficient determines the amplitude of the instability wave--a quantity not available from classical stability theory. The freestream disturbances investigated are oblique plane acoustic waves, vortical gusts of various orientations convected downstream with freestream speed U(∞), and a Karman vortex street passing above the plate surface with speed U(p). In addition, the case of a semi-infinite plate in a channel of finite width subject to an upstream traveling acoustic wave on the upper plate surface is considered. For oblique acoustic waves, the dominant receptivity mechanism is related to scattering of the waves by the leading edge. In contrast, for vortical gusts the receptivity produced by leading edge scattering is very small. The boundary layer receptivity to a Karman vortex street is found to be a strong function of the speed ratio U(p)/U(∞). A pronounced influence of channel walls, which is related to the alternate cut-on of higher modes in the upstream and downstream channel halves, is found. A comparison of the present results with available experiments shows good qualitative and quantitative agreement.

The nonlinear transition regime of supersonic boundary layers at low to moderate supersonic Mach numbers (Mach 2-3:5) under wind-tunnel conditions is studied using linear stability theory (LST) and direct numerical simulations (DNS). Two main flow configurations are chosen, a flat-plate boundary layer and a cone boundary layer. Previous investigations of the early nonlinear transition regime have mainly focused on two nonlinear mechanisms, the so-called "oblique breakdown" mechanism and "asymmetric subharmonic resonance". The first mechanism has only been investigated numerically while the second mechanism was first observed in experiments. This dissertation discusses three open questions related to both mechanisms: (i) Can oblique breakdown be identified in old wind-tunnel experiments published in the literature, (ii) what is the most dominant breakdown mechanism for a supersonic boundary layer, oblique breakdown or asymmetric subharmonic resonance, and (iii) does oblique breakdown lead to a fully developed turbulent boundary layer? By adopting the flow conditions and the disturbance generation of a specific experiment from the literature, in which asymmetric subharmonic resonance in a wave train was studied, it was possible to show that oblique breakdown might also have been present in the experiment, although oblique breakdown was not reported by the experimentalists. Hence, this experiment might provide the first experimental evidence of oblique breakdown for a supersonic boundary layer. The second question was addressed by performing DNS of a wave packet. A wave packet is typically used as a model of a broadband disturbance environment. If a nonlinear mechanism is dominant, it should leave strong imprints in the disturbance spectrum of the wave packet. In the DNS of the wave packet, oblique breakdown was visible in the disturbance spectrum while subharmonic resonance played only a minor role. To study the last question, a set of DNS of the entire transition path from the linear regime to the turbulence stage was conducted. Some of these simulations demonstrated that the ow reached turbulence near the downstream end of the computational domain.

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The purpose of the current study was to answer several questions related to hypersonic, low Reynolds number, turbulent boundary layers, of which available data related to turbulence quantities is scarce. To that end, a unique research facility was created, instrumentation was developed to acquire data in the challenging low Reynolds number (low density) domain, and meaningful data was collected and analyzed. The low Reynolds number nature of the boundary layer (Re_theta = 3700) allows for tangible DNS computations/validations using the current geometry and conditions. The boundary layer examined in this experiment resembled other, higher Reynolds number boundary layers, but also exhibited its own unique characteristics. The Van Driest equivalent velocity scaling method was found to perform well, and the log layer of the law of the wall plot matched expected theory. Noticeably absent from the data was an overlap region between the two layers, which suggests a different profile for the velocity profiles at these low Reynolds number, hypersonic conditions. The low density effects near the wall may be having an effect on the turbulence that modifies this region in a manner not currently anticipated. The Crocco-Busemann relation was found to provide satisfactory results under its general assumptions. When compared to available data, the Morkovin scaled velocity fluctuations fell almost an order of magnitude short. Currently, it is not known if this deficit is due to inadequacies with the Strong Reynolds Analogy, or the Morkovin scaling parameters. The trips seem to promote uniformity across the span of the model, and the data seems to generally be in agreement across the spanwise stations. However, additional information is needed to determine if two-dimensional simulations are sufficient for these boundary layers. When the turbulent boundary layer power spectra is analyzed, the result is found to follow the traditional power law. This result verifies that even at low Reynolds numbers, the length scales still follow the behavior described by Kolmogorov. Moving downstream of the trips, the peak RMS disturbance value grows in amplitude until it reaches a critical value. After this point, the peak begins to decrease in amplitude, but the affected region spreads throughout the boundary layer. Once the influenced region covers a significant portion of the boundary layer, transition occurs.

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