Linear Perturbation Analysis Research Articles

Nonlinear transient disturbance growth analysis for the compressible external flow and application to a flow around circular cylinder

The property of nonlinear optimal perturbation (NLOP) analysis for the flow around the circular cylinder was investigated with a comparison with the linear optimal perturbation analysis (LOP). Our analysis revealed that NLOP is highly dependent on the initial disturbance norm and highlighted the limitation of linear prediction in triggering instability in the flow field. This NLOP shows an asymmetric and deformed vortex structure on the cylinder wall, with the angle of the maximum wall vorticity shifting in relation to the initial disturbance norm. We also observed that the circulation and disturbance vorticity at the shear layer in boundary layer efficiently contributed to larger disturbance growth of the separation vortex behind the cylinder compared with the LOP.

Mechanochemical modeling of morphogenesis in cell polarization for budding yeast

Cell polarization is a multiphysics problem resulting from coupling protein pathways and cell morphological evolution. The most common example is asexual reproduction in budding yeast through Cdc42 and septin signals. However, how the interaction between the Cdc42-septin systems and the mechanical deformation of the cell surface is not well understood. To explore the interaction, we build a three-dimensional mechanochemical coupling framework to investigate the Cdc42-septin systems and elucidate how morphogenesis at the cell scale enhances the robustness of cell polarization in budding yeast. We utilize the viscous active shell model to describe the moving boundary of the cell surface, and the mechanochemical coupling is achieved through the introduction of cell surface mean curvature and active contraction-growth effects. With a normal effect of septin, numerical results demonstrate the budding processes with different transition shapes of budding profiles. On the other hand, the mechanochemical coupling problem with a weak effect of septin drives the emergence of wrinkles on the cell surface. We also apply linear perturbation analysis of the cell surface deformation to show how cell shape evolution is subjected to active contraction-growth effects. Our results show that a 3D coupled mechanochemical model can reproduce the budding morphology in yeast. Such a model provides a more comprehensive portrait of cell polarity and can be used to characterize both wild-type and mutant phenotypes such as septin mutants.

The Impact of Ambipolar Diffusion on the Rossby Wave Instability in a Protoplanetary Disk

Recent observational and simulation studies have revealed that ambipolar diffusion is an important phenomenon in the outer regions of a protoplanetary disk (PPD). However, numerous simulation studies have found that ambipolar diffusion suppresses the turbulence caused by the magnetorotational instability (MRI) in these regions of a PPD. The aim of this study is to investigate the impact of ambipolar diffusion on the Rossby wave instability (RWI) at large radii of a PPD. To accomplish this, we examine the occurrence of the RWI in a PPD threaded by the magnetic field in the presence of ambipolar diffusion. Additionally, we scale the ambipolar diffusivity with respect to both the toroidal magnetic field and an important parameter known as the Elsässer number. We obtain the growth rate of unstable RWI modes in the outer regions of a PPD using linear perturbation analysis. In our nonaxisymmetric perturbation analysis, we find that the amplitude of the toroidal field oscillates in various modes for small values of the Elsässer numbers. For small Elsässer numbers, the growth rate of unstable modes associated with the RWI decreases. In other words, ambipolar diffusion suppresses the perturbation caused by the RWI. This effect is similar to the effect of ambipolar diffusion on the MRI. In contrast to the MRI, where there is a range around 1 for the Elsässer numbers, the existence of ambipolar diffusion supports the occurrence of RWI. Finally, we compare our findings with those of simulation studies to emphasize the importance of RWI in the outer regions of a PPD.

Robust and accurate Roe-type Riemann solver with compact stencil: Rotated-RoeM scheme

In this study, we aim to develop a robust and accurate Riemann solver to resolve strong shock waves with compact stencil information by applying the rotated hybrid concept to the RoeM scheme. The original RoeM scheme offers good robustness from the perspective of avoiding shock instability, also called the carbuncle phenomenon, in hypersonic flows by introducing Mach-number-based functions. These functions rely on multi-dimensional shock discontinuity sensing terms to capture grid-aligned shock waves, thus necessitating sharing of values of cells adjacent to each vertex. Consequently, constructing a data structure that can handle such a wide stencil is necessary, particularly for implementations on unstructured grids. Moreover, communication of this stencil information on parallel computation can increase computational costs.To overcome these complexities, the rotated hybrid concept is applied to the RoeM scheme, to replace the multi-dimensional terms while still resolving the grid-aligned shock instability. In addition, a Mach-number-based weighting function is introduced to distinguish between the flow around the boundary layer and the onset of shock instability. The damping characteristic of the proposed scheme is compared to that of the original RoeM scheme by conducting a linear perturbation analysis. The findings reveal that the proposed scheme effectively controls spurious oscillations across strong shock waves. Numerous test cases are presented to demonstrate the robustness and accuracy of the proposed approach. Notably, the proposed scheme successfully resolves thermal boundary layers and accurately predicts the heat transfer rate around stagnation points in hypersonic flows.

Braneworld sum rules and positive tension branes in a massive gravity

By taking advantage of the braneworld sum rules, we explore the feasibility of constructing a flat 3-brane scenario consisting solely of positive tension branes in a 5D extension of the Lorentz-violating massive gravity. It is found that the theory supports three distinct brane configurations, one of which is exactly what we expected, consisting solely of two positive tension branes. The cosmological problem of Randall-Sundrum-1 model and the gauge hierarchy problem can be solved in this model simultaneously. Furthermore, the analysis of linear perturbations reveals that the tensor, vector and scalar modes are all massive and share the same mass spectrum, except that the ground state of vector mode is absent. Moreover, the tensor and vector modes are robust, but the scalar mode is ghost-like. Interestingly, even though the Kaluza-Klein gravitons have an extremely small mass splitting scale, an estimation of the effective gravitational potential and production of these gravitons on the brane indicates that the phenomenology of the present model is equivalent to that of the 6D ADD model.

A low diffusion flux-split scheme for all Mach number flows

A low diffusion version of the Harten–Lax–Leer convective pressure split (HLL-CPS) scheme for resolving the shear layers and the flow features at low Mach numbers is presented here. The low diffusion HLL-CPS scheme is obtained by reconstructing the velocities at the cell interface with the face normal Mach number and a pressure function. Asymptotic analysis of the modified scheme shows a correct scaling of the pressure at low Mach numbers and a significant reduction in numerical dissipation. The robustness of the HLL-CPS scheme for strong shock is improved by reducing the contribution of the contact wave in the vicinity of the shock. The improvement in robustness for strong shock is demonstrated analytically through linear perturbation and matrix stability analyses. A set of numerical test cases are solved to demonstrate the efficacy of the proposed scheme over a wide range of Mach numbers.

Effects of Nose Bluntness on Hypersonic Transition over Ogive-Cylinder Forebodies

Ogive cylinders are representative designs of hypersonic forebodies and harbor several flow complexities. This work evaluates the effects of nose bluntness of ogive-cylinder forebodies on their laminar, transitional, and turbulent boundary layers (BLs). Laminar simulations indicate that the thickness of BL and entropy layer (EL) increases with nose bluntness, with the latter displaying a stronger sensitivity to nose radius due to the increased strength and curvature of the leading-edge shock system. Linear perturbation analysis identifies the presence of the second mode, the first mode, and EL modes with increasing bluntness. While the former two are prevalent over a significant streamwise extent, EL modes are limited to the upstream region, well within the swallowing length. Using direct numerical simulations, it is found that transition over the sharpest nose design occurs through the modal fundamental resonance route, driven by second-mode instabilities. Due to weakened BL modes, the blunter geometries undergo transition further downstream in the low-amplitude freestream perturbation environment tested in this study. The transition mechanism in the blunter geometries is intermittent in nature and appears to be driven by turbulent spots generated from streamwise vortices reminiscent of Klebanoff modes.

A simple HLLE-type scheme for all Mach number flows

A simple HLLE-type scheme is proposed for all Mach number flows. In the proposed scheme, no extra wave structure is added in the HLLE scheme to resolve the shear wave while the contact wave is resolved by adding a wave structure similar to the HLLEM scheme. The resolution of the shear layers and the flow features at low Mach numbers is achieved by a velocity reconstruction method based on the face normal Mach number. Robustness against the numerical instabilities is achieved by scaling the velocity reconstruction function in the vicinity of shock with a multi-dimensional pressure sensor. The ability of the proposed scheme to resolve low Mach flow features is demonstrated through asymptotic analysis while the stability of the proposed scheme for strong shock is demonstrated through linear perturbation and matrix stability analyses. A set of numerical test cases are solved to show that the proposed scheme is free from numerical shock instability problems at high speeds and is capable of resolving the flow features at very low Mach numbers.

Optimization of the equilibrium magnetic sensor set for the SPARC tokamak

Accurate reconstruction of the plasma equilibrium is imperative for successful operation of the SPARC tokamak. In order to assess the expected reconstruction accuracy throughout the duration of design-point discharges, the EFIT equilibrium reconstruction code was deployed for SPARC. Reconstructions from SPARC baseline scenarios were compared with free-boundary equilibria generated by FreeGS, Toksys, and the Tokamak Simulation Code. The key geometric areas of interest, where design constraints are imposed, included: the inner and outer midplane gaps, the X-point locations, as well as the strike point locations. Successful reconstructions of various reference discharges, using deviations in these key geometric quantities as metrics, were calculated from synthetic signals considering an optimized equilibrium magnetic sensor set. The optimization process for this sensor set combined a scan of randomized sensor placement with a linear perturbation analysis to determine critical sensor locations, while simultaneously conforming to design constraints on the sensor placement. This optimized set was also successful in performing equilibrium reconstructions with the addition of error to synthetic measurements of magnetic flux and magnetic field, as well as contributions from eddy currents in conducting structures. These methods represent a workflow of optimization and validation that balances the engineering constraints of sensor placement with achieving sufficient reconstruction fidelity for science and operations missions for SPARC.

Surface wrinkling of a film on an anisotropic substrate

This paper presents analytical solution for wrinkling of thin film bonded to anisotropic substrate by complex function method and linear perturbation analysis, which is verified by FEM. Effect of material parameters along principal axes on critical strain is illustrated. Furthermore, due to effective modulus determined by Voigt assumption, a fiber-reinforced substrate is considered, and results indicate that both Young’s modulus perpendicular to wrinkling direction and in-plane shear modulus have significant influence on wrinkling onset point. The most effective fiber layout in resisting wrinkling is at about 45°inclined to wrinkling direction and arranging at the upper area of the substrate.

Self-sustained azimuthal aeroacoustic modes. Part 2. Effect of a swirling mean flow on the modal dynamics

The whistling induced by a low-Mach turbulent flow through a deep axisymmetric cavity in a duct is investigated theoretically and experimentally. The experiments include acoustic measurements and stereoscopic particle image velocimetry (PIV). The paper focuses on the effect of a mean swirl on the dynamics of the azimuthal aeroacoustic modes. The mean swirl in the cavity has two origins: one component is imposed by a controlled tangential air injection upstream of the cavity, and the other component spontaneously arises under the action of the self-sustained azimuthal aeroacoustic mode, as explained in the companion paper, Part 1 (Faure-Beaulieu, Xiong, Pedergnana & Noiray, J. Fluid Mech., vol. 971, 2023, A21). Experiments show that the dynamics of the aeroacoustic wave is influenced by the imposed swirl. In particular, the spinning wave propagating against the swirl is promoted. To explain this, a linear perturbation analysis is performed around an incompressible mean swirling flow obtained from RANS simulations. It reveals that the dominant shear layer modes of azimuthal order 1 and −1 involved in the whistling phenomenon are helical modes winding respectively with and against the swirl, and spinning respectively in counterswirl and co-swirl directions. The counterswirl hydrodynamic mode is the least damped of the two, which is in agreement with the experimental observations. Finally, a low-order model based on the wave equation is derived. With only a few parameters, it fully reproduces the experimental observations for a wide range of imposed swirl intensity in the duct flow, and it allows us to disentangle the mechanisms responsible for this complex aeroacoustic instability.

Self-sustained azimuthal aeroacoustic modes. Part 1. Symmetry breaking of the mean flow by spinning waves

In this paper, we study the aeroacoustic instability which occurs in a deep axisymmetric cavity in a turbulent pipe flow. This phenomenon is the axisymmetric counterpart of the classical whistling of a rectangular deep cavity subject to a grazing flow. The whistling of such axisymmetric cavity originates from the interaction of the coherent fluctuations of the vorticity at the cavity's opening with one of its trapped azimuthal or radial acoustic modes. We focus here on the situation involving the first pure azimuthal mode, which is trapped in the cavity. As a consequence of the rotational symmetry of the configuration, azimuthal modes are actually pairs of degenerate eigenmodes, or almost degenerate in the presence of small asymmetries. Therefore, the aeroacoustic instabilities exhibit more complex mechanisms than in the case of a rectangular deep cavity. In particular, we show that self-sustained spinning modes induce a symmetry breaking of the mean flow and we will elucidate the details of this phenomenon. To that end, simultaneous acoustic and time-resolved stereoscopic particle image velocimetry (PIV) measurements are performed. They reveal that when large-amplitude aeroacoustic waves spin around the cavity, a quasi-steady mean flow starts whirling slowly in the opposite direction to the wave propagation. A linear perturbation analysis around an axisymmetric mean flow confirms the experimental observations: although the incoming pipe flow is not swirling, the hydrodynamic component of the aeroacoustic wave induces such whirling motion of the mean flow because of the forcing from the steady part of the coherent Reynolds stress tensor.

Gravitational Wave Eigenfrequencies from Neutrino-driven Core-collapse Supernovae

Core-collapse supernovae (CCSNe) are predicted to produce gravitational waves (GWs) that may be detectable by Advanced LIGO/Virgo. These GW signals carry information from the heart of these cataclysmic events, where matter reaches nuclear densities. Recent studies have shown that it may be possible to infer the properties of the proto-neutron star (PNS) via GWs generated by hydrodynamic perturbations of the PNS. However, we lack a comprehensive understanding of how these relationships may change with the properties of CCSNe. In this work, we build a self-consistent suite of over 1000 exploding CCSNe from a grid of progenitor masses and metallicities combined with six different nuclear equations of state (EOS). Performing a linear perturbation analysis on each model, we compute the resonant GW frequencies of the PNS, and we motivate a time-agnostic method for identifying characteristic frequencies of the dominant GW emission. From this, we identify two characteristic frequencies, of the early- and late-time signal, that measure the surface gravity of the cold remnant neutron star, and simultaneously constrain the hot nuclear EOS. However, we find that the details of the CCSN model, such as the treatment of gravity or the neutrino transport, and whether it explodes, noticeably change the magnitude and evolution of the PNS eigenfrequencies.

Kelvin–Helmholtz instability at the interface of H ii region and molecular cloud under the influence of ambipolar diffusion: a discontinuous model of the interface

ABSTRACT For typical flow velocities in the interstellar medium (ISM), the Kelvin–Helmholtz instability (KHI) may result in the development of structures in molecular clouds near the interface between the clouds and H ii regions flowing past them (Berné et al. 2010). Ambipolar diffusion (AD) is one of the significant mechanisms considered frequently in the dynamics of molecular clouds. It may play a relevant role in the development of the KHI in the interface of the H ii region and the molecular clouds. Here, we examine the role of AD in the evolution of the KHI, using linear perturbation analysis. We model the interaction of two regions as a planar discontinuity separating two fluids in relative motion. Linear analysis, for a certain range of magnetosonic Mach number of flow ($\mathcal {M}_{sA1}\lt 1$), shows that AD has a destabilizing effect on the KHI and consequently decreases the e-fold time-scale of instability. The results indicate that AD is more effective on the KHI for large magnetosonic Mach numbers than for low magnetosonic Mach numbers. This may give rise to the development of larger numbers of KH structures in high-velocity flows. The results also indicate that AD is more effective for perturbation wavelengths $\lambda _{\rm KH} \ \lt \ 1\rm pc$ than for $\lambda _{\rm KH}\gt 1\rm pc$. This nominates a length-scale ($L=1 \rm \, pc$) above which AD is not important for the formation of KH structures. Conforming to the results, AD is proposed as a triggering factor in the development of the small-scale KH structures in the regions of high-velocity streams in ISM.

Measuring the properties of f−mode oscillations of a protoneutron star by third-generation gravitational-wave detectors

Core-collapse supernovae are among the astrophysical sources of gravitational waves that could be detected by third-generation gravitational-wave detectors. Here, we analyze the gravitational-wave strain signals from two- and three-dimensional simulations of core-collapse supernovae generated using the code fornax. A subset of the two-dimensional simulations has nonzero core rotation at the core bounce. A dominant source of time changing quadrupole moment is the $l=2$ fundamental mode ($f\text{\ensuremath{-}}\mathrm{mode}$) oscillation of the protoneutron star. From the time-frequency spectrogram of the gravitational-wave strain we see that, starting $\ensuremath{\sim}400\text{ }\text{ }\mathrm{ms}$ after the core bounce, most of the power lies within a narrow track that represents the frequency evolution of the $f\text{\ensuremath{-}}\mathrm{mode}$ oscillations. The $f\text{\ensuremath{-}}\mathrm{mode}$ frequencies obtained from linear perturbation analysis of the angle-averaged profile of the protoneutron star corroborate what we observe in the spectrograms of the gravitational-wave signal. We explore the measurability of the $f\text{\ensuremath{-}}\mathrm{mode}$ frequency evolution of a protoneutron star for a supernova signal observed in the third-generation gravitational-wave detectors. Measurement of the frequency evolution can reveal information about the masses, radii, and densities of the protoneutron stars. We find that if the third-generation detectors observe a supernova within 10 kpc, then we can measure these frequencies to within 5 Hz rms error. We can also measure the energy emitted in the fundamental $f\text{\ensuremath{-}}\mathrm{mode}$ using the spectrogram data of the strain signal. We find that the energy in the $f\text{\ensuremath{-}}\mathrm{mode}$ can be measured to within 20% error for signals observed by Cosmic Explorer using simulations with successful explosion, assuming source distances within 10 kpc.

Accurate and Robust Hybrid HLLC Riemann Solver on Triangular Grids

The HLLC scheme is an accurate, approximate Riemann solver. However, it suffers from the carbuncle phenomenon and numerical shock instability problems on both rectangular and triangular grids. In this paper, a hybrid HLLC scheme () is developed by adding some extra computations to the original HLLC scheme in order to achieve a stable and accurate scheme. The idea of the hybrid scheme is straightforward as it uses a simple shock-capturing function with parameter to detect regions where pressure oscillations such as shock waves are significant. In these regions, a less diffusive version of the scheme () is activated with a new weighting function with parameter . This new weighting function is designed to control the stability and accuracy of the hybrid scheme via the ratio of the square of the speed of sound of two adjacent cells. A linear perturbation analysis of an odd–even decoupling problem is used to analyze the effectiveness of the proposed hybrid scheme in damping perturbations. Several numerical examples are given to demonstrate that the new scheme () can obtain accurate solutions and that it is simple and efficient and requires comparable computational time with the original scheme.

Determination of local buckling resistance of Fiber-reinfoced composite column having material imperfection by nonlinear buckling analysis

The pultruded Fiber Reinforced Polymer (PFRP) material manufactured by the “pultrusion” process has many applications in the construction industry. However, the production process involves several difficult-to-control stages, which can lead to material defects. This paper proposes a method to determine the local buckling resistance of FRP composite I column having material imperfection on the flanges and web. The research has shown that the buckling load determined in nonlinear buckling analysis is 15.5% higher than that obtained from eigenvalue solution (linear perturbation analysis). In addition, the post-buckling resistance of the column is 66.4% higher compared to the local buckling load. The author suggests that this modelling and determination method be widely applied to PFRP structures when studying the instability of columns or beams under various loadings and boundary conditions and different combinations of defects.

Boundary Layers of Circumplanetary Disks around Spinning Planets. I. Effects of Rossby Waves

Gas giant planets are believed to accrete from their circumplanetary disks (CPDs). The CPDs usually involve accretion through the boundary layer (BL) in the vicinity of planets. Prior studies have concentrated on the BL of nonspinning planets. We investigate the influence of planetary spin on the wave behaviors within the BL. The rotation profile in such BLs would show a sharp transition from the rigid rotation to the Keplerian rotation. We examine the angular momentum transport in these BLs in terms of linear perturbation analysis. We find that the global inertia-acoustic mode associated with spinning planets would give rise to the inflow of angular momentum and the accretion of gas. In this work, we identify a new kind of global mode, namely the Rossby mode. The Rossby mode can lead to the outflow of angular momentum and the decretion of gas from a spinning planet. The Rossby mode provides a negative feedback that regulates the planetary spin and mass. We compare the growth rate of the two modes as a function of the width of BL, the Mach number, and the spin rate of planets. Our results reveal the underlying hydrodynamic mechanism of terminal spins and asymptotic mass of the giant planets.

Light-induced wrinkling instability of confined annulus liquid crystal elastomer film.

Authors of previous studies have focused on wrinkling phenomena in thin films with relatively large stiffness under mechanical loadings. A liquid crystal elastomer (LCE) is a smart soft material sensitive to various environmental stimuli. In this letter, we investigate the wrinkling instability of a confined LCE film with different inner hole sizes induced by light illumination. The LCE film is clamped at the outer edge and has a free inner edge. Based on linear perturbation analysis, we obtain the critical condition for the onset of wrinkling instability. Whether the film will remain flat or bifurcate into a wrinkled state is determined by the value of expansion coefficient, light intensity, inner hole size, and thickness of the LCE film. We find that a film with a bigger inner hole size corresponds to a large wrinkle number and show that the expansion coefficient of a LCE and light intensity can be used to adjust the wrinkling instability behavior and time consumption for the appearance of wrinkles.

On the stability of scale-invariant black holes

Quadratic scale-invariant gravity non minimally coupled to a scalar field provides a competitive model for inflation, characterized by the transition from an unstable to a stable fixed point, both characterized by constant scalar field configurations. We provide a complementary analysis of the same model in the static, spherically symmetric setting, obtaining two Schwarzschild-de Sitter solutions, which corresponds to the two fixed points existing in the cosmological scenario. The stability of such solutions is thoroughly investigated from two different perspectives. First, we study the system at the classical level by the analysis of linear perturbations. In particular, we provide both analytical and numerical results for the late-time behavior of the perturbations, proving the stable and unstable character of the two solutions. Then we perform a semi-classical, non-linear analysis based on the Euclidean path integral formulation. By studying the difference between the Euclidean on-shell actions evaluated on both solutions, we prove that the unstable one has a meta-stable character and is spontaneously decaying into the stable fixed point which is always favoured.