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The prediction of three-dimensional boundary layer transition has long been an important issue in aircraft design. The eN method based on one-dimensional stability theories (LST-eN) is widely used in transition prediction, yet fails to capture transition features of large-scale vortical structures commonly present on the vehicle surface. The vortical structures cause substantial spanwise variations of the base flow and thereby render the one-dimensional stability theories invalid. We in the present study modulate the eN method by exploiting multi-dimensional stability theories, especially the plane-marching parabolized stability equations (PSE3D), to predict the windward transition front of a lifting body under a high-speed flight condition (FLT) and a wind-tunnel condition with two angles of attack (WT1 with 2-degree angle of attack and WT2 with 4-degree angle of attack). The modal instability characteristics for the centerline vortex region in these three cases are similar, featuring the upstream Mack-mode instability and the downstream vortex instabilities. The transition N -factor front qualitatively aligns well with direct numerical simulation (DNS) results for the flight case and the experimental measurements for the wind-tunnel cases. The transition N -factor is correlated to be around 2 for the flight case (based on the DNS data), around 4 for the wind-tunnel case WT1 and around 2 for the wind-tunnel case WT2. Intriguingly, the WT2 case experiences an earlier transition than the WT1 case although the former turns out to be more stable as predicted by the modal stability analysis. Preliminary non-modal analysis shows that non-modal growth is stronger in the WT2 case than in the WT1 case, implying that non-modal disturbances may play a role in the transition process. The cross-flow instability is also addressed for the flight case, focusing on the comparison of results from the one- and multi-dimensional stability analyses.

The stability and behavior of jet flows are critical in various engineering applications, yet many aspects remain insufficiently understood. Previous studies predominantly relied on modal methods to describe small perturbations on jet flow surfaces through the linear superposition of modal waves. However, these approaches largely neglected the interaction between different modes, which can lead to transient energy growth and significantly impact jet stability. This work addresses this gap by focusing on the transient growth of disturbances in jet flows through a comprehensive non-modal analysis, which captures the short-term energy evolution. Unlike modal analysis, which provides insights into the overall trend of energy changes over longer periods, non-modal analysis reveals the instantaneous dynamics of the disturbance energy. This approach enables the identification of transient growth mechanisms that are otherwise undetectable using modal methods, which treat disturbance waves as independent and fail to account for their coupling effects. The results demonstrate that non-modal analysis effectively quantifies the interplay between disturbance waves, capturing the nonlinearity inherent in transient energy growth. This method highlights the short-term amplification of disturbances, providing a more accurate understanding of jet flow stability. Furthermore, the impact of dimensionless parameters such as the Reynolds number, Weber number, and initial wave number on transient energy growth is systematically analyzed. Key findings reveal the optimal conditions for maximizing energy growth and elucidate the mechanisms driving these phenomena. By integrating non-modal analysis, this study advances the theoretical framework of transient energy growth, offering new insights into jet flow stability and paving the way for practical improvements in fluid dynamic systems.

This paper devotes to the approximation of spectral and boundary-value problems arising in the stability analysis of incompressible boundary layers. As an alternative to the collocation method with mappings, the Galerkin–collocation method based on Laguerre functions is adopted. A robust numerical implementation of the latter method is discussed. The methods are compared within the stability analysis of the Blasius and Ekman layers. The Galerkin–collocation method demonstrates an exponential convergence rate for scalar stability characteristics, and has a number of advantages.

We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a space–time variational formulation and associated generalized singular value decomposition of the (linearized) Navier–Stokes equations. We first introduce a linear framework applicable to a wide variety of stationary- or time-dependent base flows: we consider arbitrary disturbances in both the initial condition and the dynamics measured in a ‘data’ space–time norm; the theory provides a rigorous, sharp (realizable) and efficiently computed bound for the velocity perturbation measured in a ‘solution’ space–time norm. We next present a generalization of the linear framework in which the disturbances and perturbation are now measured in respective selected space–time semi-norms; the semi-norm theory permits rigorous and sharp quantification of, for example, the growth of initial disturbances or functional outputs. We then develop a (Brezzi–Rappaz–Raviart) nonlinear theory which provides, for disturbances which satisfy a certain (rather stringent) amplitude condition, rigorous finite-amplitude bounds for the velocity and output perturbations. Finally, we demonstrate the application of our linear and nonlinear hydrodynamic stability theory to unsteady moderate Reynolds number flow in an eddy-promoter channel.

We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a spacetime variational formulation and associated generalized singular value decomposition of the (linearized) NavierStokes equations. We first introduce a linear framework applicable to a wide variety of stationary- or time-dependent base flows: we consider arbitrary disturbances in both the initial condition and the dynamics measured in a data spacetime norm; the theory provides a rigorous, sharp (realizable) and efficiently computed bound for the velocity perturbation measured in a solution spacetime norm. We next present a generalization of the linear framework in which the disturbances and perturbation are now measured in respective selected spacetime semi-norms; the semi-norm theory permits rigorous and sharp quantification of, for example, the growth of initial disturbances or functional outputs. We then develop a (BrezziRappazRaviart) nonlinear theory which provides, for disturbances which satisfy a certain (rather stringent) amplitude condition, rigorous finite-amplitude bounds for the velocity and output perturbations. Finally, we demonstrate the application of our linear and nonlinear hydrodynamic stability theory to unsteady moderate Reynolds number flow in an eddy-promoter channel.

We present a brief overview of the probable velocity-shear induced phenomena in solar plasma flows. Shear-driven MHD wave oscillations may be the needed mechanism for the generation of solar Alfven waves, for the transmission of fast waves through the transition region, and for the acceleration of the solar wind.

Traditional stability tools have done much in the last few decades to demonstrate the significance of modal instabilities as a pathway for laminar to turbulent transition in hypersonic flows, but are less effective at predicting transition in flows with significant streamwise variation and strong shock waves. Because of this, most stability analyses over blunt cones tend to focus on the growth of instabilities in regions of the flow away from the blunt tip and downstream of any strong shock waves. We develop a new shock-kinematic boundary condition which is compatible with both the finite-volume method and input–output analysis. This boundary condition enables analysis of the receptivity of blunt cones to disturbances in the free stream by careful treatment of linear interactions of small disturbances with the shock. In particular, a Mach 5.8 flow over a 7∘ half-angle cone with a 0.15\" nose radius is analyzed, showing significant amplification of disturbances along the cone frustum in a 5–15 kHz bandwidth due to the destabilization of a slow acoustic boundary layer mode, and significant amplification of entropy layer instabilities between 100 and 180 kHz due to rotation/deceleration of entropy/vorticity waves. These mechanisms are receptive to free-stream disturbances in very localized positions upstream of the bow shock.

This article provides a detailed examination of voice quality in word-final vowels in Spanish. The experimental task involved the pronunciation of words in two prosodic contexts by native Spanish speakers from diverse dialects. A total of 400 vowels (10 participants × 10 words × 2 contexts × 2 repetitions) were analyzed acoustically in Praat. Waveforms and spectrograms were inspected visually for voice, creak, breathy voice, and devoicing cues. In addition, the relative amplitude difference between the first two harmonics (H1–H2) was obtained via FFT spectra. The findings reveal that while creaky voice is pervasive, breathy voice is also common, and devoicing occurs in 11% of tokens. We identify multiple phonation types (up to three) within the same vowel, of which modal voice followed by breathy voice was the most common combination. While creaky voice was more frequent overall for males, modal voice tended to be more common in females. In addition, creaky voice was significantly more common at the end of higher prosodic constituents. The analysis of spectral tilt shows that H1–H2 clearly distinguishes breathy voice from modal voice in both males and females, while H1–H2 values consistently discriminate creaky and modal voice in male participants only.

Layered flows that are commonly observed in stratified turbulence are susceptible to the Taylor–Caulfield Instability. While the modal stability properties of layered shear flows have been examined, the non-modal growth of perturbations has not been investigated. In this work, the tools of Generalized Stability Theory are utilized to study linear transient growth within a finite time interval of two-dimensional perturbations in an inviscid, three-layer constant shear flow under the Boussinesq approximation. It is found that, for low optimization times, small-scale perturbations utilize the Orr mechanism and achieve growth equal to that in the case of an unstratified flow. For larger optimization times, transient growth is much larger compared to growth for an unstratified flow as the Kelvin–Orr waves comprising the continuous spectrum of the dynamical operator and the gravity edge-waves comprising the discrete spectrum interact synergistically. Maximum growth is obtained for perturbations with scales within the region of instability, but significant growth is maintained for modally stable perturbations as well. For perturbations with scales within the unstable region, the unstable normal modes are excited at high amplitude by their bi-orthogonals. For perturbations with modally stable scales, the Orr mechanism is utilized to excite at high amplitude neutral propagating waves resembling the neutral Taylor–Caulfield modes.

A non-modal transient disturbances growth in a stably stratified mixing layer flow is studied numerically. The model accounts for a density gradient within a shear region, implying a heavier layer at the bottom. Numerical analysis of non-modal stability is followed by a full three-dimensional direct numerical simulation (DNS) with the optimally perturbed base flow. It is found that the transient growth of two-dimensional disturbances diminishes with the strengthening of stratification, while three-dimensional disturbances cause significant non-modal growth, even for a strong, stable stratification. This non-modal growth is governed mainly by the Holmboe modes and does not necessarily weaken with the increase of the Richardson number. The optimal perturbation consists of two waves traveling in opposite directions. Compared to the two-dimensional transient growth, the three-dimensional growth is found to be larger, taking place at shorter times. The non-modal growth is observed in linearly stable regimes and, in slightly linearly supercritical regimes, is steeper than that defined by the most unstable eigenmode. The DNS analysis confirms the presence of the structures determined by the transient growth analysis.