Shear Flow Profile Research Articles

Numerical investigation on the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow

Vortex-induced vibration (VIV) of flexible cylinders is an important phenomenon in ocean structures, which may cause fatigue damage and structural failure of offshore structures. Much literature has extensively explored VIV of flexible cylinders under various flow conditions, such as uniform and linearly varying shear flow. However, real scenarios in most cases involve non-uniform, non-linearly varying shear flow profiles. Hence, it is important to investigate the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow profiles. This study employs a wake oscillator model (WOM) that simulates the VIV response of the flexible cylinder under the action of non-linearly varying shear flow velocity profiles. The flexible cylinder subjected to linearly varying sheared flow velocity profiles not only overpredicts but also underpredicts the VIV responses compared to the non-linearly varying sheared flow profile, which represents the real scenario. The VIV mode number for the flexible cylinder subjected to non-linear shear flow was found to have a non-linear relationship with that of linear shear flow. The VIV response of the flexible cylinder subjected to a linearly varying shear flow profile exhibits more travelling wave behaviour compared to non-linear shear flow. The location of the maximum VIV response of the structure having the same aspect ratio (L/D) and shear parameter (β), was different for linear and non-linear flow profiles across the span. The time and frequency domain responses showed a shift in the frequency band. The results obtained from the numerical simulations give better insights into the vibrational behaviour of flexible cylinders in realistic flow environments.

Effects of turbulence on the blade root load of the tandem wind turbine in neutral atmospheric boundary layer

Abstract A model characterizing a turbulent wind field, consistent with neutral atmospheric boundary layer attributes, was developed for a field-based experimental wind turbine using stochastic processes combined with shear flow profiles. By incorporating interactions of vertical thermal exchange, terrain-induced surface roughness, and Coriolis forces, the model simulates environmental impacts. A sequence of wind turbines situated within the atmospheric wind field underwent computational analysis leveraging Large Eddy Simulation (LES) alongside an Actuator Line Model (ALM) to examine atmospheric turbulence alterations both preceding and following the turbines. Analysis of the power spectra concerning wind velocity, turbulence intensity, and components of Reynolds stress upwind and downwind demonstrated the turbines’ blade effects on surrounding turbulence patterns. The research demonstrated that turbulence kinetic energy experienced enhancement in downwind turbines as a result of the upwind turbine’s impact, particularly evident in the lower-frequency spectrum. Augmenting the distance between turbines initially aids in the wake’s turbulent structure restoration, with a marked effect on tip vortices that hold greater amounts of high-frequency energy.

Drag, lift, and torque correlations for axi-symmetric rod-like non-spherical particles in linear wall-bounded shear flow

This paper presents novel correlations to predict the drag, lift, and torque coefficients of axi-symmetric non-spherical rod-like particles in a wall-bounded linear shear flow. The particle position and orientation relative to the wall are varied to systematically investigate the influence of the wall on the hydrodynamic forces. The newly derived correlations for drag, lift, and torque on the particle depend on various parameters, including the particle Reynolds number, the orientation angle between the major axis of the particle and the main local flow direction, the aspect ratio of the particle, and the dimensionless distance from the particle centre to the wall. The impact of the wall on the hydrodynamic forces is accounted for as a function of a multiplication factor on the drag force in case of locally uniform flow, and an additional force contribution for the lift and the torque, modifying the resultant forces experienced by a particle in a locally uniform flow. The changes in the hydrodynamic forces prove to be substantial, emphasizing the necessity of accounting for wall effects across all particle types and flow conditions investigated in this study. The coefficients of the correlations are determined through a fitting process utilizing the data generated from our previous study on the interaction forces between a locally uniform flow and an axi-symmetric non-spherical rod-like particles, as well as from data of novel direct numerical simulations (DNS) performed in this work of flow past axi-symmetric rod-like particles near a wall. The proposed correlations exhibit a good agreement compared to the DNS results, with median errors of 2.89%, 5.37%, and 11.00%, and correlation coefficients of 0.99, 0.99, and 0.96 for the correlations accounting for the drag, lift, and torque coefficients of a non-spherical particle in wall-bounded linear shear flow profile, respectively. These correlations can be used in large-scale simulations using an Eulerian–Lagrangian or a CFD/DEM framework to predict the behaviour of axi-symmetric rod-like non-spherical particles in wall-bounded shear flow to locally uniform flow conditions.

On the role of unsteadiness in impulsive-flow-driven shear instabilities: precursors of fragmentation

Shear instabilities at the interface of two fluids, such as classical Kelvin–Helmholtz instability (KHI), is the precursor of interface destabilization, leading to fluid fragmentation critical in a wide range of applications. While many insights into such instabilities are derived for steady background forcing flow, unsteady impulse flows are ubiquitous in environmental and physiological processes. Yet, little is understood on how unsteadiness shapes the initial interface amplification necessary for the onset of its topological change enabling subsequent fragmentation. In this combined theoretical, numerical and experimental study, we focus on an air-on-liquid interface exposed to canonical unsteady shear flow profiles. Evolution of the perturbed interface is formulated theoretically as an impulse-driven initial value problem using both linearized potential flow and nonlinear boundary integral methods. We show that the unsteady airflow forcing can amplify the interface's inherent gravity–capillary wave, up to wave-breaking transition, even if the configuration is classically KH stable. For impulses much shorter than the gravity–capillary wave period, it is the cumulative action, akin to total energy, that determines amplification, independent of the details of the impulse profile. However, for longer impulses, the details of the impulse profile become important. In this limit, akin to a resonance, it is the entangled history of the interaction of the forcing, i.e. the impulse, that changes rapidly in amplitude, and the response of the oscillating interface that matters. The insights gained are discussed and experimentally illustrated in the context of interface distortion and destabilization relevant for upper respiratory mucosalivary fluid fragmentation in violent exhalations.

Studying X-ray spectra from large-scale jets of FR II radio galaxies: application of shear particle acceleration

ABSTRACT Shear particle acceleration is a promising candidate for the origin of extended high-energy emission in extra-galactic jets. In this paper, we explore the applicability of a shear model to 24 X-ray knots in the large-scale jets of FR II radio galaxies and study the jet properties by modelling the multiwavelength spectral energy distributions (SEDs) in a leptonic framework including synchrotron and inverse Compton–CMB processes. In order to improve spectral modelling, we analyse Fermi-LAT data for five sources and reanalyse archival data of Chandra on 15 knots, exploring the radio to X-ray connection. We show that the X-ray SEDs of these knots can be satisfactorily modelled by synchrotron radiation from a second, shear-accelerated electron population reaching multi-TeV energies. The inferred flow speeds are compatible with large-scale jets being mildly relativistic. We explore two different shear flow profiles (i.e. linearly decreasing and power law) and find that the required spine speeds differ only slightly, supporting the notion that for higher flow speeds the variations in particle spectral indices are less dependent on the presumed velocity profile. The derived magnetic field strengths are in the range of a few to 10 µG and the required power in non-thermal particles is typically well below the Eddington constraint. Finally, the inferred parameters are used to constrain the potential of FR II jets as possible ultra-high-energy cosmic-ray accelerators.

Nonlinear interaction between double tearing mode and Kelvin–Helmholtz instability with different shear flows

The nonlinear interaction between the double tearing mode (DTM) and Kelvin–Helmholtz (KH) instabilities with different shear flow profiles has been numerically investigated via the use of a compressible magnetohydrodynamics (MHD) model. We focus on KH instabilities in weak and reversed magnetic shear plasmas with strong stabilizing effect of field line bending. Results show that KH instabilities coupled with DTMs occur in these plasmas and the KH mode dominates the instability dynamics, suggesting the crucial role of weak magnetic shear in the formation of high-mode harmonics. For symmetric flows, an asymmetric forced magnetic reconnection configuration is maintained during the growth phase, leading to interlocking of the modes. Additionally, this investigation of the DTM-KH instability interaction contributes to our understanding of the nonlinear reconnection mechanism in the regime of weak and reversed magnetic shear plasmas, which is relevant for astrophysical and fusion studies.

Flow-Induced Forces for a Group of One Large and Several Small Structures in the Sheared Turbulent Flow

Evaluating the hydrodynamic force fluctuations acting on each structure in a group of subsea objects of different cross-section shapes, sizes and relative positions represents a challenge due to the sensitivity of the vortex shedding process, especially for a variety of sheared flows. The present study uses the numerical 2D computational fluid dynamics model to estimate the flow-induced forces on a group of small circular and D-shaped cylinders in the linear and parabolic sheared flow, which are placed in proximity to a larger structure of the squared cross-section. This allows us to evaluate loads, which are affected by the presence of subsea equipment located on the seabed. The average Reynolds number of the considered linear flow profile is 3900, while the parabolic flow profile has the maximum Reynolds number of 3900. The k-ω SST turbulence model is used for simulations. The work demonstrates the effect of the cross-sectional shape of smaller cylinders on hydrodynamic coefficients, explores the effect from the spacing in between the structures and highlights differences between loads in the linearly sheared and parabolic flow. The results obtained show that the presence of the squared cylinder notably influences the mean drag coefficient on the first cylinder, for both circular and D-shaped cylinders. The parabolic sheared flow profile in this series leads to the highest mean drag and the highest amplitudes of the fluctuating drag and lift coefficients.

VIV response of risers with large aspect ratio and low rigidity using a numerical scheme based on wake oscillator model

The crossflow (CF) response of a flexible riser subjected to vortex-induced vibration (VIV) has been carried out using numerical simulation based on wake oscillator model for different aspect ratio (L/D), flexural rigidity (EI), mass ratio (μ), and the axial tension (Θ). Experiments were conducted on a scale model with a shear flow profile. The numerical model has been validated by comparing it with VIV responses obtained from experiments for shear flow profile. Parametric studies have been performed using the numerical model to obtain the crossflow root-mean-square (RMS) displacement along the length for L/D range of 100 to 3000, the flexural rigidity of 50 to 2870 MPa, mass ratio of 1.955 to 10, and axial tension of 0 to 3000 N for uniform flow profile. The results of the shear flow profile were presented with those obtained from equivalent uniform flow (equivalent mean velocity). The VIV response indicates that the standing wave pattern occurs for L/D < 1500. In contrast, the travelling wave pattern was observed for L/D = 3000 and indicated the wave pattern is mixed for a transition range of L/D = 1500. It was also observed that the response mode is highly dependent on L/D, EI, and shear flow profile during independent on mass ratio. The VIV displacement response of flexible risers with helical wires reduces by 90% compared with riser without helical wire for a riser diameter to wire diameter ratio of 10 and pitch to riser diameter ratio of 8 in uniform flow.

Triadic resonances in internal wave modes with background shear

In this paper, we use asymptotic theory and numerical methods to study resonant triad interactions among discrete internal wave modes at a fixed frequency ( $\omega$ ) in a two-dimensional, uniformly stratified shear flow. Motivated by linear internal wave generation mechanisms in the ocean, we assume the primary wave field as a linear superposition of various horizontally propagating vertical modes at a fixed frequency $\omega$ . The weakly nonlinear solution associated with the primary wave field is shown to comprise superharmonic (frequency $2\omega$ ) and zero frequency wave fields, with the focus of this study being on the former. When two interacting primary modes $m$ and $n$ are in triadic resonance with a superharmonic mode $q$ , it results in the divergence of the corresponding superharmonic secondary wave amplitude. For a given modal interaction $(m, n)$ , the superharmonic wave amplitude is plotted on the plane of primary wave frequency $\omega$ and Richardson number $Ri$ , and the locus of divergence locations shows how the resonance locations are influenced by background shear. In the limit of weak background shear ( $Ri\to \infty$ ), using an asymptotic theory, we show that the horizontal wavenumber condition $k_m + k_n = k_q$ is sufficient for triadic resonance, in contrast to the requirement of an additional vertical mode number condition ( $q = |m-n|$ ) in the case of no shear. As a result, the number of resonances for an arbitrarily weak shear is significantly larger than that for no shear. The new resonances that occur in the presence of shear include the possibilities of resonance due to self-interaction and resonances that occur at the seemingly trivial limit of $\omega \approx 0$ , both of which are not possible in the no shear limit. Our weak shear limit conclusions are relevant for other inhomogeneities such as non-uniformity in stratification as well, thus providing an understanding of several recent studies that have highlighted superharmonic generation in non-uniform stratifications. Extending our study to finite shear (finite $Ri$ ) in an ocean-like exponential shear flow profile, we show that for cograde–cograde interactions, a significant number of divergence curves that start at $Ri\to \infty$ will not extend below a cutoff $Ri$ $\sim O(1)$ . In contrast, for retrograde–retrograde interactions, the divergence curves extend all the way from $Ri\to \infty$ to $Ri = 0.5$ . For mixed interactions, new divergence curves appear at $\omega = 0$ for $Ri\sim O(10)$ and extend to other primary wave frequencies for smaller $Ri$ . Consequently, the total ( $\text {cograde} + \text {retrograde} + \text {mixed}$ ) number of resonant triads is of the same order for small $Ri\approx 0.5$ as in the limit of weak shear ( $Ri\to \infty$ ), although it attains a maximum at $Ri\sim O(10)$ .

Effects of varying shear stress profiles on the regulation of pulmonary artery endothelial cell gene expression: a focus on selected mediators of vascular tone, inflammation and angiogenesis

Abstract Background Pulmonary arterial hypertension (PAH) is a complex pathology characterized by obliterative vascular remodeling that leads to right heart failure and death. Predisposition to PAH is associated with mutations in the BMPR2 gene in approximately 70–80% of familial cases and around 30% for that of sporadic PAH. The study of the pathogenetic basis of PAH is often performed in static endothelial cultures. Such two-dimensional, isolated cell microenvironments fail to consider the heterogeneity in mechanical stress acting on endothelial cells in various regions of the pulmonary vascular tree. In the remodeled pulmonary vasculature, low and oscillatory shear stress is observed in the proximal pulmonary artery with high shear stress in distal pre-capillary pulmonary arterioles. Therefore, the impact of varied shear profiles (including both laminar and oscillatory flow) on pulmonary artery endothelial cell (and that of BMPR2-deplete) gene expression of common vasoactive (EDN1, ENOS), proinflammatory (IL6, IL8) and angiogenic mediators (ANG2, VEGFA), are poorly described. Purpose To evaluate the effects of shear stress magnitude, including unidirectional and oscillatory flow on BMPR2-knockdown human pulmonary artery endothelial cell (HPAEC) gene expression of EDN1, ENOS, IL6, IL8, ANG2 and VEGFA. Methods HPAECs were transfected with siRNA directed against BMPR2 (siB2) or with a non-targeting control (siCon). Cells were exposed to 10 hours of laminar or oscillatory flow (1Hz; 1.5 dyn/cm2, 15 dyn/cm2 or 90 dyn/cm2) using a parallel-plate fluid flow chamber system. Measurement of mRNA expression was performed using qPCR. Results Shear stress intensity and flow type (unidirectional and oscillatory) mediated diverse effects on HPAEC gene expression across the markers studied. Changes in gene expression were calculated relative to that of static siCon-transfected HPAECs and in such a manner are summarized as fold changes in the table below. Asterisks are shown where significant fold differences are reported. *P≤0.05, **P≤0.01, ***P≤0.001, ****P≤0.0001. aP≤0.05, bP≤0.05, cP≤0.05, denote comparisons between groups. Of note, no significant differences in gene expression were observed between static siCon and static siB2. Conclusions For the markers studied, different magnitudes of shear stress and flow profiles (together with BMPR2 loss) exhibit varied patterns of gene expression in the pulmonary vascular endothelium. As such, this illustrates the need for wider study of in vitro endothelial-shear stress interactions in understanding mechanisms of remodeling in PAH. Funding Acknowledgement Type of funding sources: None. Table 1

Phase Structure of Internal Gravity Waves in the Ocean with Shear Flows

Purpose. The description of the internal gravity waves dynamics in the ocean with background fields of shear currents is a very difficult problem even in the linear approximation. The mathematical problem describing wave dynamics is reduced to the analysis of a system of partial differential equations; and while taking into account the vertical and horizontal inhomogeneity, this system of equations does not allow separation of the variables. Application of various approximations makes it possible to construct analytical solutions for the model distributions of buoyancy frequency and background shear ocean currents. The work is aimed at studying dynamics of internal gravity waves in the ocean with the arbitrary and model distributions of density and background shear currents. Methods and Results. The paper represents the numerical and analytical solutions describing the main phase characteristics of the internal gravity wave fields in the stratified ocean of finite depth, both for arbitrary and model distributions of the buoyancy frequency and the background shear currents. The currents are considered to be stationary and horizontally homogeneous on the assumption that the scale of the currents' horizontal and temporal variability is much larger than the characteristic lengths and periods of internal gravity waves. Having been used, the Fourier method permitted to obtain integral representations of the solutions under the Miles – Howard stability condition is fulfilled. To solve the vertical spectral problem, proposed is the algorithm for calculating the main dispersion dependences that determine the phase characteristics of the generated wave fields. The calculations for one real distribution of buoyancy frequency and shear flow profile are represented. Transformation of the dispersion surfaces and phase structures of the internal gravitational waves’ fields is studied depending on the generation parameters. To solve the problem analytically, constant distribution of the buoyancy frequency and linear dependences of the background shear current on depth were used. For the model distribution of the buoyancy and shear flow frequencies, the explicit analytical expressions describing the solutions of the vertical spectral problem were derived. The numerical and asymptotic solutions for the characteristic oceanic parameters were compared. Conclusions. The obtained results show that the asymptotic constructions using the model dependences of the buoyancy frequency and the background shear velocities’ distribution, describe the numerical solutions of the vertical spectral problem to a good degree of accuracy. The model representations, having been applied for hydrological parameters, make it possible to describe qualitatively correctly the main characteristics of internal gravity waves in the ocean with the arbitrary background shear currents.

Fazovyye kharakteristiki poley vnutrennikh gravitatsionnykh voln v okeane so sdvigom skorosti techeniy

Purpose. The description of the internal gravity waves dynamics in the ocean with background fields of shear currents is a very difficult problem even in the linear approximation. The mathematical problem describing wave dynamics is reduced to the analysis of a system of partial differential equations; and while taking into account the vertical and horizontal inhomogeneity, this system of equations does not allow separation of the variables. Application of various approximations makes it possible to construct analytical solutions for the model distributions of buoyancy frequency and background shear ocean currents. The work is aimed at studying dynamics of internal gravity waves in the ocean with the arbitrary and model distributions of density and background shear currents. Methods and Results. The paper represents the numerical and analytical solutions describing the main phase characteristics of the internal gravity wave fields in the stratified ocean of finite depth, both for arbitrary and model distributions of the buoyancy frequency and the background shear currents. The currents are considered to be stationary and horizontally homogeneous on the assumption that the scale of the currents' horizontal and temporal variability is much larger than the characteristic lengths and periods of internal gravity waves. Having been used, the Fourier method permitted to obtain integral representations of the solutions under the Miles – Howard stability condition is fulfilled. To solve the vertical spectral problem, proposed is the algorithm for calculating the main dispersion dependences that determine the phase characteristics of the generated wave fields. The calculations for one real distribution of buoyancy frequency and shear flow profile are represented. Transformation of the dispersion surfaces and phase structures of the internal gravitational waves’ fields is studied depending on the generation parameters. To solve the problem analytically, constant distribution of the buoyancy frequency and linear dependences of the background shear current on depth were used. For the model distribution of the buoyancy and shear flow frequencies, the explicit analytical expressions describing the solutions of the vertical spectral problem were derived. The numerical and asymptotic solutions for the characteristic oceanic parameters were compared. Conclusions. The obtained results show that the asymptotic constructions using the model dependences of the buoyancy frequency and the background shear velocities’ distribution, describe the numerical solutions of the vertical spectral problem to a good degree of accuracy. The model representations, having been applied for hydrological parameters, make it possible to describe qualitatively correctly the main characteristics of internal gravity waves in the ocean with the arbitrary background shear currents.

Modulation Instability of Surface Waves in the Model with the Uniform Wind Profile

The modulation instability of surface capillary-gravity water waves is analysed in a shear flow model with a tangential discontinuity of velocity. It is assumed that air blows along the surface of the water with a uniform profile in the vertical direction. Such a model, despite its simplicity, plays an important role in hydrodynamics as the reference model for investigating basic physical phenomena of wave–current interactions and acquiring insights into a series of complex phenomena. In certain cases where the wavelength of interfacial perturbations is much bigger than the width of the shear flow profile, the model with the tangential discontinuity in the velocity is adequate for describing physical phenomena at least within limited spatial and temporal frameworks. A detailed analysis of the air-flow conditions under which modulation instability sets in is presented. It is also shown that the interfacial waves are subject to dissipative or radiative instability when negative-energy waves appear at the interface.

The Use of a Numerical Weather Prediction Model to Simulate Near-Field Volcanic Plumes

In this paper, a state-of the art numerical weather prediction (NWP) model is used to simulate the near-field plume of a Plinian-type volcanic eruption. The NWP model is run at very high resolution (of the order of 100 m) and includes a representation of physical processes, including turbulence and buoyancy, that are essential components of eruption column dynamics. Results are shown that illustrate buoyant gas plume dynamics in an atmosphere at rest and in an atmosphere with background wind, and we show that these results agree well with those from theoretical models in the quiescent atmosphere. For wind-blown plumes, we show that features observed in experimental and natural settings are reproduced in our model. However, when comparing with predictions from an integral model using existing entrainment closures there are marked differences. We speculate that these are signatures of a difference in turbulent mixing for uniform and shear flow profiles in a stratified atmosphere. A more complex implementation is given to show that the model may also be used to examine the dispersion of heavy volcanic gases such as sulphur dioxide. Starting from the standard version of the weather research and forecasting (WRF) model, we show that minimal modifications are needed in order to model volcanic plumes. This suggests that the modified NWP model can be used in the forecasting of plume evolution during future volcanic events, in addition to providing a virtual laboratory for the testing of hypotheses regarding plume behaviour.

Intrinsic flow and tearing mode rotation in the RFP during improved confinement

We use charge exchange recombination spectroscopy to make the first localized measurements of impurity ion flow velocity profiles in the reversed field pinch. Measurements in improved confinement plasmas reveal an intrinsic flow profile that is peaked on the axis and mostly parallel to the equilibrium magnetic field. The toroidal flow decreases in time at off-axis locations where tearing modes are resonant, giving rise to a highly sheared flow profile near the axis. The tearing mode phase velocity correlates strongly with toroidal flow near the resonant surface and weakly with flow in other locations, providing an opportunity to verify the commonly held assumption that the plasma and mode move together at the resonant surface. Mechanisms for the observed momentum loss during the improved confinement period are evaluated, and it is found that eddy currents in the conducting shell caused by the rotation of the dominant tearing mode dominate over other losses.

Numerical investigation on vortex-induced vibration response characteristics for flexible risers under sheared-oscillatory flows

Surge motion of top-end platform induced by periodic wave makes marine flexible riser encounter equivalent sheared-oscillatory flow, under which the Vortex-induced Vibration (VIV) response will be more complicated than pure sheared flow or oscillatory flow cases. Based on a time domain force-decomposition model, the VIV response characteristics under sheared-oscillatory flows are investigated numerically in this paper. Firstly, the adopted numerical model is validated well against laboratory experiments under sheared flow and oscillatory flow. Then, 20 sheared-oscillatory flow cases with different oscillation periods and top maximum current velocities are designed and simulated. Under long and short oscillation period cases, the structural response presents several similar features owing to the instantaneous sheared flow profile at each moment, but it also has some different patterns because of the differently varying flow field. Finally, the effects and essential mechanism of oscillation period and top maximum current velocity on VIV response are discussed systematically.

The need for prediction in feedback control of a mixing layer

We present the first application of a Smith predictor in the model-based feedback control of a convectively unstable flow. The two-dimensional incompressible mixing layer is chosen as a plant and integrated with a finite-element Navier–Stokes solver. The flow is actuated by a modulation of the inflow mimicking a pulsed jet actuator. The state is monitored by a downstream velocity sensor. The control goal is to command the fluctuation level at the sensor location. As an additional challenge, the incoming shear-flow profile is perturbed by the small noise level. The starting point of this study is a standard low-order control without prediction. A Smith predictor is included to compensate for the convective delay from actuation to sensing. The closed-loop results with a Smith predictor are distinctly better than without it. The design of the linear robust controllers is performed with an open-loop control. We conjecture that predictors may augment feedback control for a large class of convectively unstable flows with significant time-delay from actuation to sensing.

The Spectral Web of stationary plasma equilibria. II. Internal modes

The new method of the Spectral Web to calculate the spectrum of waves and instabilities of plasma equilibria with sizeable flows, developed in the preceding Paper I [Goedbloed, Phys. Plasmas 25, 032109 (2018)], is applied to a collection of classical magnetohydrodynamic instabilities operating in cylindrical plasmas with shear flow or rotation. After a review of the basic concepts of the complementary energy giving the solution path and the conjugate path, which together constitute the Spectral Web, the cylindrical model is presented and the spectral equations are derived. The first example concerns the internal kink instabilities of a cylindrical force-free magnetic field of constant α subjected to a parabolic shear flow profile. The old stability diagram and the associated growth rate calculations for static equilibria are replaced by a new intricate stability diagram and associated complex growth rates for the stationary model. The power of the Spectral Web method is demonstrated by showing that the two associated paths in the complex ω-plane nearly automatically guide to the new class of global Alfvén instabilities of the force-free configuration that would have been very hard to predict by other methods. The second example concerns the Rayleigh–Taylor instability of a rotating theta-pinch. The old literature is revisited and shown to suffer from inconsistencies that are remedied. The most global n = 1 instability and a cluster sequence of more local but much more unstable n=2,3,…∞ modes are located on separate solution paths in the hydrodynamic (HD) version of the instability, whereas they merge in the MHD version. The Spectral Web offers visual demonstration of the central position the HD flow continuum and of the MHD Alfvén and slow magneto-sonic continua in the respective spectra by connecting the discrete modes in the complex plane by physically meaningful curves towards the continua. The third example concerns the magneto-rotational instability (MRI) thought to be operating in accretion disks about black holes. The sequence n=1,2,… of unstable MRIs is located on one continuous solution path, but also on infinitely many separate loops (“pancakes”) of the conjugate path with just one MRI on each of them. For narrow accretion disks, those sequences are connected with the slow magneto-sonic continuum, which is far away though from the marginal stability transition. In this case, the Spectral Web method is the first to effectively incorporate the MRIs into the general MHD spectral theory of equilibria with background flows. Together, the three examples provide compelling evidence of the computational power of the Spectral Web Method.

Compressibility effects on a shear flow in strongly coupled dusty plasma. I. A study using computational fluid dynamics

We study compressibility effects on the two-dimensional strongly coupled dusty plasma by means of computational fluid dynamics (CFD) with the Kolmogorov flow as an initial shear flow profile. Nonlinear compressible vortex flow dynamics and other linear and nonlinear properties of such flow in the presence of variable density, pressure, and electrostatic potential are addressed using a generalised compressible hydrodynamic model. The stabilizing effect of compressibility on the unstable shear flows in the presence of strong correlation (τm&amp;gt;0) is presented. Increasing the Mach number relatively reduces the growth-rate of perturbation. On the other hand, strong correlation makes the medium to be more unstable and increases the growth rate. Using an eigen value solver, various linear properties of compressible Kolmogorov flow have been investigated for a range of variable parameters, for example, Mach number, Reynolds number, and viscoelastic coefficient (τm). Compressible Kolmogorov flow becomes unstable above a critical value of the Reynolds number (Rc), and below Rc, the shear flow is found to be neutrally stable. In this study, it is found that the viscoelasticity reduces the value of Rc. For our choice of parameters, at τm=τmc, the compressible Kolmogorov flow becomes unconditionally unstable and no Rc exists for values of τm higher than τmc. To address the nonlinear properties, for example, mode-mode interaction due to the presence of nonlinearity in the fluid, vortex formation, etc., a massively parallelized Advanced Generalized SPECTral Code (AG-Spect) has been developed. AG-Spect, a newly developed code, is an efficient tool to solve any set of nonlinear fluid dynamic equations. A good agreement in linear growth rates obtained from the eigen value solver and time dependent simulation (AG-Spect) is found. In our CFD study, the suppression of instability, elongated vortex structures, pattern formation, nonlinear saturation, and visco-elastic oscillations in perturbed kinetic energy have been observed for various values of Mach number, Reynolds number and τm.

Study of thermoviscous dissipation on axisymmetric wave propagating in a shear pipeline flow confined by rigid wall. Part I. theoretical formulation

Axisymmetric acoustic wave propagation in a shear pipeline flow confined by a rigid wall is studied in the two-part paper. The effects of viscous friction and thermal conduction on the acoustic wave propagating in the liquid and perfect gas are respectively analyzed under different configurations of acoustic frequency and shear flow profile. In Part 1 of this paper, mathematical models of non-isentropic and isentropic acoustic waves are formulated based on the conservation of mass, momentum and energy for both liquid and perfect gas. Meanwhile, comprehensive solutions based on the Fourier-Bessel theory are provided, which gives a general methodology of iteratively calculating features of the acoustic wave. Numerical comparisons with previous simplified models verify the validity of the proposed models and solutions.