Thin airfoil dynamic stall at moderate Reynolds numbers is typically linked to the sudden bursting of a small laminar separation bubble close to the leading edge. Given the strong sensitivity of laminar separation bubbles to external disturbances, the onset of dynamic stall on a NACA0009 airfoil section subject to different levels of low-amplitude free stream disturbances is investigated using direct numerical simulations. The flow is practically indistinguishable from clean inflow simulations in the literature for turbulence intensities at the leading edge of Tu = 0.02 %. At slightly higher turbulence intensities of Tu = 0.05 %, the bursting process is found to be considerably less smooth and strong coherent vortex shedding from the laminar separation bubble is observed prior to the formation of the dynamic stall vortex (DSV). This phenomenon is considered in more detail by analysing its appearance in an ensemble of simulations comprising statistically independent realisations of the flow, thus proving its statistical relevance. In order to extract the transient dynamics of the vortex shedding, the classical proper orthogonal decomposition method is generalised to include time in the energy measure and applied to the time-resolved simulation data of incipient dynamic stall. Using this technique, the dominant transient spatiotemporally correlated features are distilled and the wave train of the vortex shedding prior to the emergence of the main DSV is reconstructed from the flow data exhibiting dynamics of large-scale coherent growth and decay within the turbulent boundary layer.

The linear temporal stability of the fully developed pulsatile flow in a torus with high curvature is investigated using Floquet theory. The baseflow is computed via a Newton-Raphson iteration in frequency space to obtain basic states at supercritical Reynolds numbers in the steady case for two curvatures, δ=0.1 and 0.3, exhibiting structurally different linear instabilities for the steady flow. The addition of a pulsatile component is found to be overall stabilizing over a wide range of pulsation amplitudes, in particular for high values of curvature. The pulsatile flows are found to be at most transiently stable with large intracyclic growth rate variations even at small pulsation amplitudes. While these growth rates are likely insufficient to trigger an abrupt transition at the parameters in this work, the trends indicate that this is indeed likely for higher pulsation amplitudes, similar to pulsatile flow in straight pipes. At the edge of the considered parameter range, subharmonic eigenvalue orbits in the local spectrum of the time-periodic operator, recently found in pulsating channel flow, have been confirmed also for pulsatile flow in toroidal pipes, underlining the generality of this phenomenon.

The long-term trend of increasing natural organic matter (NOM) in boreal and north European surface waters represents an economic and environmental challenge for drinking water treatment plants (DWTPs). High-frequency measurements from absorbance-based online spectrophotometers are often used in modern DWTPs to measure the chromophoric fraction of dissolved organic matter (CDOM) over time. These data contain valuable information that can be used to optimise NOM removal at various stages of treatment and/or diagnose the causes of underperformance at the DWTP. However, automated monitoring systems generate large datasets that need careful preprocessing, followed by variable selection and signal processing before interpretation. In this work we introduce AbspectroscoPY (“Absorbance spectroscopic analysis in Python”), a Python toolbox for processing time-series datasets collected by in situ spectrophotometers. The toolbox addresses some of the main challenges in data preprocessing by handling duplicates, systematic time shifts, baseline corrections and outliers. It contains automated functions to compute a range of spectral metrics for the time-series data, including absorbance ratios, exponential fits, slope ratios and spectral slope curves. To demonstrate its utility, AbspectroscoPY was applied to 15-month datasets from three online spectrophotometers in a drinking water treatment plant. Despite only small variations in surface water quality over the time period, variability in the spectrophotometric profiles of treated water could be identified, quantified and related to lake turnover or operational changes in the DWTP. This toolbox represents a step toward automated early warning systems for detecting and responding to potential threats to treatment performance caused by rapid changes in incoming water quality. 

The laminar separation bubble (LSB) forming on a symmetric NACA0009 airfoil at a steady pitch angle of 8 degrees and Reynolds number Re = 2.0 · 10^5 under theinfluence of free-stream disturbances is computed using high-fidelity large-eddy simulations. Two disturbance levels are considered corresponding to cruiseconditions achievable in low free-stream turbulence wind tunnels and higher disturbance levels typical of larger, conventional wind tunnels. The extracted flow fields are Fourier transformed in the spanwise direction and then eachspanwise mode is analysed using Spectral Proper Orthogonal Decomposition to extract the dominant structures in the flow exhibiting spatio-temporal coherence. Since LSBs are known to be sensitive to external disturbances as well as self-excited absolute instabilities, the analysis of the effect of free-stream disturbances on the separation bubble is crucial for understanding the bubble dynamics and to relate results from simulations to experiments in applications where certain levels of inflow disturbance are unavoidable.

Spectral degeneracies where eigenvalues and eigenvectors simultaneously coalesce, also known as exceptional points, are a natural consequence of the strong non-normality of the Orr-Sommerfeld operator describing the evolution of infinitesimal disturbances in parallel shear flows. While the resonances associated with these points give rise to algebraic growth, the development of non-modal stability theory exploiting specific perturbation structures with much larger potential for transient energy growth has led to waning interest in spectral degeneracies. The appearance of subharmonic eigenvalue orbits, recently discovered in the periodic spectrum of pulsating Poiseuille flow, can be traced back to the coalescence of eigenvalues at exceptional points. We present a thorough analysis of the spectral properties of the linear operator to identify exceptional points and accurately map the prevalence of subharmonic eigenvalue orbits for a large range of pulsation amplitudes and frequencies. This information is then combined with solutions of the linear initial value problem to analyse the impact of the appearance of these orbits on the temporal evolution of linear disturbances in pulsating Poiseuille flow. The periodic amplification phases are shown to be heralded by repeated non-normal growth bursts that are intensified by the formation of subharmonic orbits involving the leading eigenvalues. These bursts are associated with the change of alignment of the perturbation from the decaying towards the amplified branch of the subharmonic eigenvalue orbits in a so-called branch transition process.

Time-dependent flows are notoriously challenging for classical linear stability analysis. Most progress in understanding the linear stability of these flows has been made for time-periodic flows via Floquet theory focusing on time-asymptotic stability. However, little attention has been given to the transient intracyclic linear stability of periodic flows since no general tools exist for its analysis. In this work, we explore the potential of using the recent framework of the optimally time-dependent (OTD) modes (Babaee & Sapsis, Proc. R. Soc. Lond. A, vol. 472, 2016, 20150779) to extract information about both the transient and the time-asymptotic linear stability of pulsating Poiseuille flow. The analysis of the instantaneous OTD modes in the limit cycle leads to the identification of the dominant instability mechanism of pulsating Poiseuille flow by comparing them with the spectrum and the eigenmodes of the Orr-Sommerfeld operator. In accordance with evidence from recent direct numerical simulations, it is found that structures akin to Tollmien-Schlichting waves are the dominant feature over a large range of pulsation amplitudes and frequencies but that for low pulsation frequencies these modes disappear during the damping phase of the pulsation cycle as the pulsation amplitude is increased beyond a threshold value. The maximum achievable non-normal growth rate during the limit cycle was found to be nearly identical to that in plane Poiseuille flow. The existence of subharmonic perturbation cycles compared with the base flow pulsation is documented for the first time in pulsating Poiseuille flow.

This study analyses the main characteristics of the fully developed laminar pulsatile flow in a toroidal pipe as the governing parameters vary. A novel computational technique is developed to obtain time-periodic solutions of the Navier--Stokes equations. They are computed as fixed points of the system in the frequency domain via the Newton-Raphson method. Drawbacks and advantages of the adopted methodology with respect to a time-stepping technique are discussed. The unsteady component of the driving pressure gradient is found to change linearly with the pulsation amplitude, with a proportionality coefficient dependent on the pulsation frequency. Although the time-averaged streamwise wall shear stress is very close to the value in the steady case, very large fluctuations are observed within the period. Flow reversal occurs during certain time intervals in the period for high pulsation amplitudes. The analysis of the spatial structure of the unsteady component of the velocity field shows that three different flow regimes can be identified, depending on the pulsation frequency, termed quasi-steady, intermediate and plug-flow regimes.

Thin airfoil dynamic stall at moderate Reynolds numbers is typically linked to the sudden bursting of a small laminar separation bubble close to the leading edge. Given the strong sensitivity of laminar separation bubbles to external disturbances, the onset of dynamic stall on a NACA0009 airfoil section subject to different levels of low-amplitude freestream disturbances is investigated using direct numerical simulations. For turbulence intensities at the leading edge of Tu = 0.02 %, the flow is practically indistinguishable from clean inflow simulations in literature. For Tu = 0.05 %, the bursting process is found to be considerably less smooth and strong coherent vortex shedding from the laminar separation bubble is observed prior to the formation of the dynamic stall vortex. The non-linear simulations are complemented with a transient linear stability analysis of the time-dependent evolution of the laminar shear layer in the bursting separation bubble using a spatially localised formulation of the Optimally Time-Dependent (OTD) framework, with which the most unstable part of the instantaneous tangent space of the non-linear trajectory is tracked over time. The resulting modes reveal intermittent switching between two regimes. Rapid growth of the Kelvin--Helmholtz rolls on the separated shear layer and complicated secondary instabilities on the transitional part of the separation bubble. The appearance of the latter is linked to large spikes in the instantaneous growth rate within the linear subspace and more rapid transition in the non-linear baseflow. These intense growth spikes are well correlated with the subsequent shedding of energetic vortices from the laminar separation bubble.