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We use large-eddy simulations (LES) to investigate the impact of stable stratification on gravity-wave excitation and energy extraction in a large wind farm. To this end, the development of an equilibrium conventionally neutral boundary layer into a stable boundary layer over a period of 8 h is considered, using two different cooling rates. We find that turbulence decay has considerable influence on the energy extraction at the beginning of the boundary-layer transition, but afterwards, energy extraction is dominated by geometrical and jet effects induced by an inertial oscillation. It is further shown that the inertial oscillation enhances gravity-wave excitation. By comparing LES results with a simple one-dimensional model, we show that this is related to an interplay between wind-farm drag, variations in the Froude number and the dispersive effects of vertically-propagating gravity waves. We further find that the pressure gradients induced by gravity waves lead to significant upstream flow deceleration, reducing the average turbine output compared to a turbine in isolated operation. This leads us to the definition of a non-local wind-farm efficiency, next to a more standard wind-farm wake efficiency, and we show that both can be of the same order of magnitude. Finally, an energy flux analysis is performed to further elucidate the effect of gravity waves on the flow in the wind farm.

Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state. Originally developed in numerical studies of parallel shear flows with a linearly stable base flow, this concept is adapted here to the case of a spatially developing Blasius boundary layer. Longer time horizons fundamentally change the nature of the problem due to the loss of stability of the base flow due to Tollmien–Schlichting (TS) waves. We demonstrate, using a moving box technique, that efficient long-time tracking of edge trajectories is possible for the parameter range relevant to bypass transition, even if the asymptotic state itself remains out of reach. The flow along the edge trajectory features streak switching observed for the first time in the Blasius boundary layer. At long enough times, TS waves co-exist with the coherent structure characteristic of edge trajectories. In this situation we suggest a reinterpretation of the edge as a manifold dividing the state space between the two main types of boundary layer transition, i.e. bypass transition and classical transition.

Stability analyses based on the rates of change of perturbations were performed to study the growth mechanisms of second-mode instability in hypersonic boundary layers. The results show that the streamwise velocity perturbation is strengthened by the concurrence of the momentum transfer due to the wall-normal velocity fluctuation and the streamwise gradient of the pressure perturbation near the wall, while the wall-normal velocity perturbation is dominated by the wall-normal gradient of the pressure perturbation. Meanwhile, the change of fluctuating internal energy is sustained by the advection of perturbed thermal energy in the vicinity of the critical layer and by the dilatation fluctuation near the wall. The energy transport by the wall-normal velocity fluctuation accounts for the growth of second-mode instability, and the growth rate depends on the relative phase of the energy transport by the wall-normal velocity fluctuation to the total time rate of change of fluctuating internal energy in the vicinity of the critical layer. Moreover, this relative phase is associated with the mutual interaction between the critical-layer fluctuation and the near-wall fluctuation. Porous walls recast this mutual interaction by delaying the phase of the wall-normal energy transport near the wall, resulting in the stabilization of the second mode.

High-speed boundary layer transition is dominated by the modal, exponential amplification of the oblique Mack’s first mode waves in two-dimensional boundary layers from Mach 1 up to freestream Mach numbers of 4.5 to 6.5 depending on the wall-to-adiabatic temperature ratio. At higher Mach numbers, the acoustic, planar Mack’s second mode waves become dominant. Although many theoretical, computational and experimental studies have focused on the supersonic boundary layer transition due to the oblique Mack’s first mode, several fundamental questions about the source of this instability and the reasons for its obliqueness remain unsolved. Here, we perform an inviscid energetics investigation and classify disturbances based on their energetics signature on a Blasius boundary layer for a range of Mach numbers. This approach builds insight into the fundamental mechanisms governing various types of instability. It is shown that first mode instability is distinct from Tollmien–Schlichting instability, being driven by a phase shifting between streamwise velocity and pressure perturbations in the vicinity of the generalized inflection point and insensitive to the viscous no-slip condition. Further, it is suggested that the obliqueness of the first mode is associated with an inviscid flow invariant.

An experimental study is performed to determine the mechanisms by which a forward-facing step impacts the growth and breakdown to turbulence of the stationary cross-flow instability. Particle image velocimetry measurements are obtained in the boundary layer of a$30^{\\circ }$swept flat plate with a pressure body. Step heights range from 53 % to 71 % of the boundary-layer thickness. The critical step height is approximately 60 % of the boundary-layer thickness for the current study, although it is also shown that the critical step height depends on the initial amplitude of the stationary cross-flow vortices. For the critical cases, the stationary cross-flow amplitude grows sharply downstream of the step, decays for a short region and then grows again. The initial growth region is linear, and can be explained primarily through the impact of the step on the mean flow. Namely, the step causes abrupt changes to the mean flow, resulting in large values of wall-normal shear, as well as highly inflectional profiles, due to either cross-flow reversal, separation or both. These inflectional profiles are highly unstable for the stationary cross-flow. Additionally, the reversed flow regions are significantly modulated by the stationary cross-flow vortices. The second region of growth occurs due to the stationary-cross-flow-induced modulation of the shear layer, which leads to multiple smaller wavelength streamwise vortices. High-frequency fluctuations indicate that the unsteady transition mechanism for the critical cases relates to the shedding of vortices downstream of reattachment of the modulated separated regions.

The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite-amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output analysis, in which the environment noise is modelled as distributed body forces. The most ‘dangerous’ perturbations in a time frame until flow reversal are found to be arranged as counter-rotating streamwise-constant vortices. One of these vortex configurations is then selected and deployed to nonlinear equations, and streaks of various amplitudes are generated via the lift-up mechanism. By means of secondary stability analysis and direct numerical simulations, the dual role of streaks in the boundary-layer transition is shown. When the amplitude of streaks remains moderate, these elongated features remain stable until the adverse-pressure-gradient stage and have a dampening effect on the instabilities developing thereafter. In contrast, when the low-speed streaks reach high amplitudes exceeding 15 % of the free stream velocity at the respective phase, they become highly unstable to secondary sinuous modes in the outer shear layers. Consequently, a subcritical transition to turbulence, i.e. bypass transition, can be initiated already in the favourable-pressure-gradient region ahead of the wave crest.

Stability theory offers a practical method on parametric studies that encompass scales in the boundary layer typically not captured in Large Eddy (LES) or Reynolds-Averaged Navier–Stokes (RANS) simulations. We investigated the transition modes of a Low-Pressure Turbine (LPT) with Linear Stability Theory (LST) and Linear Parabolized Stability Equations (LPSEs) over a wider parametric space. A parametric study was done to examine the wall-shear stress, shape factor, momentum thickness, as well as the growth rate and N-factor envelope. Additionally, the methodology was applied to active control techniques like suction and blowing. The results are consistent with the expected physical behavior and initial observations, while also offering a quantitative description of trends in frequencies, amplitude growth, and wavelengths. This confirms the suitability of the two stability theories, laying the base for their future validation to ensure accuracy and reliability.

The intrinsic uncertainty of fluid properties, including the equation-of-state, viscosity and thermal conductivity, on boundary layer stability has scarcely been addressed. When a fluid is operating in the vicinity of the Widom line (defined as the maximum of isobaric specific heat) in supercritical state, its properties exhibit highly non-ideal behavior, which is an ongoing research field leading to refined and more accurate fluid property databases. Upon crossing the Widom line, new mechanisms of flow instability emerge, feasibly leading to changes in dominating modes that yield turbulence. The present work investigates the sensitivity of three-dimensional boundary layer modal instability to these intrinsic uncertainties in fluid properties. The uncertainty, regardless of its source and the fluid regimes, gives rise to distortions of all profiles that constitute the inputs of the stability operator. The effect of these distortions on flow stability is measured by sensitivity coefficients, which are formulated with the adjoint operator and validated against linear modal stability analysis. The results are presented for carbon dioxide at a representative supercritical pressure of approximately 80 bar. The sensitivity to different inputs of the stability operator across various thermodynamic regimes shows an immense range of sensitivity amplitude. A balancing relationship between the density gradient and its perturbation leads to a quadratic effect across the Widom line, provoking significant sensitivity to distortions of the second derivative of the pressure with respect to the density,$\\partial ^2 p/\\partial \\rho ^2$. From an application-oriented point of view, one important question is whether the correct baseflow profiles can be meaningfully analysed by the simplified ideal-fluid model. The integrated modal disturbance growth – the N factor calculated with different partly idealised models – indicates that the answer depends strongly on the thermodynamic regime investigated.

The present work was devoted to an experimental study of small angles of attack and cone nose bluntness on the efficiency of stabilization of high-frequency disturbances in hypersonic boundary layer with a passive porous coating. The experiments were carried out on a cone with an apex half-angle 7° and nose bluntness radii R = 0.03, 0.5 and 1 mm installed under angles of attack α = 0–1° at the freestream Mach number M∞ = 5.8. High-frequency pressure fluctuations on the sides of the cone with the solid and porous surfaces were measured. It is shown that at all angles of attack and cone bluntness, the passive porous coating permits an efficient suppression of disturbances in hypersonic boundary layer both on the windward and leeward sides of the cone.

Strongly influenced by thermodynamic stability, the planetary boundary layer (PBL) is key to the exchange of heat, momentum, and moisture between the ground surface and free troposphere. The PBL with different thermodynamic stability across the whole of China, however, is not yet well understood. In this study, the occurrence frequency and spatial distribution of the convective boundary layer (CBL), neutral boundary layer (NBL), and stable boundary layer (SBL) were systematically investigated, based on intensive summertime soundings launched at 1400 Beijing time (BJT) throughout China’s radiosonde network (CRN) for the period 2012 to 2016. Overall, the occurrences of CBL, NBL, and SBL account for 70%, 26%, and 4%, respectively, suggesting that CBL dominates in summer throughout China. In terms of the spatial pattern of PBL height, a prominent north–south gradient can be found with higher PBL height in northwest China. In addition, the PBL heights of CBL and NBL were found to be positively (negatively) associated with near-surface air temperature (humidity), whereas no apparent relationship was found for SBL. Furthermore, clouds tend to reduce the occurrence frequency, irrespective of PBL type. Roughly 70% of SBL cases occur under overcast conditions, much higher than those for NBL and CBL, indicating that clouds govern to some extent the occurrence of SBL. In contrast, except for the discernible changes in PBL height under overcast conditions relative to those under clear-sky conditions, the changes in PBL height under partly cloudy conditions are no more than 170m for both NBL and CBL types.