Large-scale Instability Research Articles

The Large Scale Instability in Rotating Fluid with Small Scale Force

In this paper, we find a new large scale instability in rotating flow forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain the nonlinear stage of the instability and the generation vortex kinks.

Nonlinear Vortex Structures in Obliquely Rotating Fluid

In this paper, we find a new large scale instability which appears in obliquely rotating flow with the small scale turbulence, generated by external force with small Reynolds number. The external force has no helicity. The theory is based on the rigorous method of multi-scale asymptotic expansion. Nonlinear equations for instability are obtained in the third order of the perturbation theory. In this article, we explain in detail the nonlinear stage of the instability and we find the nonlinear periodic vortices and the vortex kinks of Beltrami type.

Exploring the full parameter space for an interacting dark energy model with recent observations including redshift-space distortions: Application of the parametrized post-Friedmann approach

Dark energy can modify the dynamics of dark matter if there exists a direct interaction between them. Thus a measurement of the structure growth, e.g., redshift-space distortions (RSD), can provide a powerful tool to constrain the interacting dark energy (IDE) models. For the widely studied $Q=3\beta H\rho_{de}$ model, previous works showed that only a very small coupling ($\beta\sim\mathcal{O}(10^{-3})$) can survive in current RSD data. However, all these analyses had to assume $w>-1$ and $\beta>0$ due to the existence of the large-scale instability in the IDE scenario. In our recent work [Phys. Rev. D 90, 063005 (2014)], we successfully solved this large-scale instability problem by establishing a parametrized post-Friedmann (PPF) framework for the IDE scenario. So we, for the first time, have the ability to explore the full parameter space of the IDE models. In this work, we reexamine the observational constraints on the $Q=3\beta H\rho_{de}$ model within the PPF framework. By using the Planck data, the baryon acoustic oscillation data, the JLA sample of supernovae, and the Hubble constant measurement, we get $\beta=-0.010^{+0.037}_{-0.033}$ ($1\sigma$). The fit result becomes $\beta=-0.0148^{+0.0100}_{-0.0089}$ ($1\sigma$) once we further incorporate the RSD data in the analysis. The error of $\beta$ is substantially reduced with the help of the RSD data. Compared with the previous results, our results show that a negative $\beta$ is favored by current observations, and a relatively larger interaction rate is permitted by current RSD data.

Non-linear Simulations of MHD Instabilities in Tokamaks Including Eddy Current Effects and Perspectives for the Extension to Halo Currents

The dynamics of large scale plasma instabilities can be strongly influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important.The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities.Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK [1, 2] has been coupled [3] with the resistive wall code STARWALL [4], which allows us to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations.This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described.

Dynamics of large-scale instabilities in conductors electrically exploded in strong magnetic fields

The growth of large-scale instabilities during the propagation of a nonlinear magnetic diffusion wave through a conductor was studied experimentally. The experiment was carried out using the MIG terawatt pulsed power generator at a peak current up to 2.5 MA with 100 ns rise time. It was observed that instabilities with a wavelength of 150 μm developed on the surface of the conductor hollow part within 160 ns after the onset of current flow, whereas the surface of the solid rod remained almost unperturbed. A system of equations describing the propagation of a nonlinear diffusion wave through a conductor and the growth of thermal instabilities has been solved numerically. It has been revealed that the development of large- scale instabilities is obviously related to the propagation of a nonlinear magnetic diffusion wave.

Parametrized post-Friedmann framework for interacting dark energy

Dark energy might directly interact with cold dark matter. However, in such a scenario, an early-time large-scale instability occurs occasionally, which may be due to the incorrect treatment for the pressure perturbation of dark energy as a nonadiabatic fluid. To avoid this nonphysical instability, we establish a new framework to correctly calculate the cosmological perturbations in the interacting dark energy models. Inspired by the well-known parametrized post-Friedmann approach, the condition of the dark energy pressure perturbation is replaced with the relationship between the momentum density of dark energy and that of other components on large scales. By reconciling the perturbation evolutions on the large and small scales, one can complete the perturbation equations system. The large-scale instability can be successfully avoided and the well-behaved density and metric perturbations are obtained within this framework. Our test results show that this new framework works very well and is applicable to all the interacting dark energy models.

Effects of cumulus parameterizations on predictions of summer flood in the Central United States

This study comprehensively evaluates the effects of twelve cumulus parameterization (CUP) schemes on simulations of 1993 and 2008 Central US summer floods using the regional climate-weather research and forecasting model. The CUP schemes have distinct skills in predicting the summer mean pattern, daily rainfall frequency and precipitation diurnal cycle. Most CUP schemes largely underestimate the magnitude of Central US floods, but three schemes including the ensemble cumulus parameterization (ECP), the Grell-3 ensemble cumulus parameterization (G3) and Zhang-McFarlane-Liang cumulus parameterization (ZML) show clear advantages over others in reproducing both floods location and amount. In particular, the ECP scheme with the moisture convergence closure over land and cloud-base vertical velocity closure over oceans not only reduces the wet biases in the G3 and ZML schemes along the US coastal oceans, but also accurately reproduces the Central US daily precipitation variation and frequency distribution. The Grell (GR) scheme shows superiority in reproducing the Central US nocturnal rainfall maxima, but others generally fail. This advantage of GR scheme is primarily due to its closure assumption in which the convection is determined by the tendency of large-scale instability. Future study will attempt to incorporate the large-scale tendency assumption as a trigger function in the ECP scheme to improve its prediction of Central US rainfall diurnal cycle.

Magnetic flux concentrations from dynamo-generated fields

The mean-field theory of magnetized stellar convection gives rise to the two possibility of distinct instabilities: the large-scale dynamo instability, operating in the bulk of the convection zone, and a negative effective magnetic pressure instability (NEMPI) operating in the strongly stratified surface layers. The latter might be important in connection with magnetic spot formation, but the growth rate of NEMPI is suppressed with increasing rotation rates, although recent direct numerical simulations (DNS) have shown a subsequent increase in the growth rate. We examine quantitatively whether this increase in the growth rate of NEMPI can be explained by an alpha squared mean-field dynamo, and whether both NEMPI and the dynamo instability can operate at the same time. We use both DNS and mean-field simulations (MFS) to solve the underlying equations numerically either with or without an imposed horizontal field. We use the test-field method to compute relevant dynamo coefficients. DNS show that magnetic flux concentrations are still possible up to rotation rates above which the large-scale dynamo effect produces mean magnetic fields. The resulting DNS growth rates are quantitatively well reproduced with MFS. As expected, for weak or vanishing rotation, the growth rate of NEMPI increases with increasing gravity, but there is a correction term for strong gravity and large turbulent magnetic diffusivity. Magnetic flux concentrations are still possible for rotation rates above which dynamo action takes over. For the solar rotation rate, the corresponding turbulent turnover time is about 5 hours, with dynamo action commencing in the layers beneath.

Supernova explosion mechanism taking into account large-scale convection and neutrino transport

Two types of supernovae are considered: thermonuclear supernovae, whose explosions are due to thermonuclear energy, and core-collapse supernovae, whose explosions are due to the gravitational energy of collapsing stars released in the form of neutrinos. Numerical models of supernovae are discussed. Themain problem in devising supernova explosion mechanisms is producing the energy required to disperse the envelope. In theoretical models, it is necessary to solve multi-dimensional problems involving complex physics (3D gas dynamics, neutrino transport, large-scale convective instability, and other important physical processes). In recent years, the development of large-scale convection during supernova explosions has been reconsidered. Self-consistent problems problems in three-dimensional, gas-dynamical instability have been considered. Two-dimensional gas-dynamical calculations taking into account neutrino absorption in the envelope have been performed. The spherically symmetric collapse and neutrino transport were calculated including all reactions, leading to a new understanding of possible paths for the development of supernova theory. The main emphasis is placed on the neutrino transport and the basis for promising multidimensional models taking into account large-scale convective instability.

MEASUREMENT OF CONTINUOUS PHASE VELOCITIES IN A CONFINED SOLID-LIQUID JET USING LDV

A two-component LDV was used to investigate how flow structures in a liquid jet are influenced by the presence of solid particles. Solid glass spheres with a density of 2.5 kg/dm3 and three different sizes (0.5 mm, 1 mm, and 2 mm) at different solids loading (0–6.2 vol.%) were used as particles, while water served as continuous phase. No significant influence of the solid particles on the rate of decrease in the centerline liquid velocity or the jet expansion ratio could be observed. Two flow regimes were identified: a stable jet characterized by a symmetric shear layer close to the nozzle, and a flow dominated by large-scale instabilities farther from the nozzle. The spreading of particles was dominated by interparticle collisions in the region close to the nozzle and by jet instability in the region farther from the nozzle. With increased solids loading increased liquid RMS values in the region close to the nozzle could be found. The effect on RMS values was larger with larger particles. For the 1 mm particles the RMS increased in this region, but decreased in the region farther from the nozzle. The presence of 2 mm particles acted to stabilize the jet, and the instability moved farther downstream. Suspensions with smaller particles had no effect on the instability, strength, or location.

The ballistic transport instability in Saturn's rings - III. Numerical simulations

Saturn's inner B-ring and its C-ring support wavetrains of contrasting amplitudes but with similar length scales, 100-1000 km. In addition, the inner B-ring is punctuated by two intriguing `flat' regions between radii 93,000 km and 98,000 km in which the waves die out, whereas the C-ring waves coexist with a forest of plateaus, narrow ringlets, and gaps. In both regions the waves are probably generated by a large-scale linear instability whose origin lies in the meteoritic bombardment of the rings: the ballistic transport instability. In this paper, the third in a series, we numerically simulate the long-term nonlinear evolution of this instability in a convenient local model. Our C-ring simulations confirm that the unstable system forms low-amplitude wavetrains possessing a preferred band of wavelengths. B-ring simulations, on the other hand, exhibit localised nonlinear wave `packets' separated by linearly stable flat zones. Wave packets travel slowly while spreading in time, a result that suggests the observed flat regions in Saturn's B-ring are shrinking. Finally, we present exploratory runs of the inner B-ring edge which reproduce earlier numerical results: ballistic transport can maintain the sharpness of a spreading edge while building a `ramp' structure at its base. Moreover, the ballistic transport instability can afflict the ramp region, but only in low-viscosity runs.

Proper orthogonal decomposition-based spectral higher-order stochastic estimation

A unique routine, capable of identifying both linear and higher-order coherence in multiple-input/output systems, is presented. The technique combines two well-established methods: Proper Orthogonal Decomposition (POD) and Higher-Order Spectra Analysis. The latter of these is based on known methods for characterizing nonlinear systems by way of Volterra series. In that, both linear and higher-order kernels are formed to quantify the spectral (nonlinear) transfer of energy between the system's input and output. This reduces essentially to spectral Linear Stochastic Estimation when only first-order terms are considered, and is therefore presented in the context of stochastic estimation as spectral Higher-Order Stochastic Estimation (HOSE). The trade-off to seeking higher-order transfer kernels is that the increased complexity restricts the analysis to single-input/output systems. Low-dimensional (POD-based) analysis techniques are inserted to alleviate this void as POD coefficients represent the dynamics of the spatial structures (modes) of a multi-degree-of-freedom system. The mathematical framework behind this POD-based HOSE method is first described. The method is then tested in the context of jet aeroacoustics by modeling acoustically efficient large-scale instabilities as combinations of wave packets. The growth, saturation, and decay of these spatially convecting wave packets are shown to couple both linearly and nonlinearly in the near-field to produce waveforms that propagate acoustically to the far-field for different frequency combinations.

Large-scale stable interacting dark energy model: Cosmological perturbations and observational constraints

Dark energy might interact with cold dark matter in a direct, nongravitational way. However, the usual interacting dark energy models (with constant $w$) suffer from some catastrophic difficulties. For example, the $Q\ensuremath{\propto}{\ensuremath{\rho}}_{\mathrm{c}}$ model leads to an early-time large-scale instability, and the $Q\ensuremath{\propto}{\ensuremath{\rho}}_{\text{de}}$ model gives rise to the future unphysical result for cold dark matter density (in the case of a positive coupling). In order to overcome these fatal flaws, we propose in this paper an interacting dark energy model (with constant $w$) in which the interaction term is carefully designed to realize that $Q\ensuremath{\propto}{\ensuremath{\rho}}_{\text{de}}$ at the early times and $Q\ensuremath{\propto}{\ensuremath{\rho}}_{\mathrm{c}}$ in the future, simultaneously solving the early-time superhorizon instability and future unphysical ${\ensuremath{\rho}}_{\mathrm{c}}$ problems. The concrete form of the interaction term in this model is $Q=3\ensuremath{\beta}H\frac{{\ensuremath{\rho}}_{\mathrm{de}}{\ensuremath{\rho}}_{\mathrm{c}}}{{\ensuremath{\rho}}_{\mathrm{de}}+{\ensuremath{\rho}}_{\mathrm{c}}}$, where $\ensuremath{\beta}$ is the dimensionless coupling constant. We show that this model is actually equivalent to the decomposed new generalized Chaplygin gas (NGCG) model, with the relation $\ensuremath{\beta}=\ensuremath{-}\ensuremath{\alpha}w$. We calculate the cosmological perturbations in this model in a gauge-invariant way and show that the cosmological perturbations are stable during the whole expansion history provided that $\ensuremath{\beta}>0$. Furthermore, we use the Planck data in conjunction with other astrophysical data to place stringent constraints on this model (with eight parameters), and we find that indeed $\ensuremath{\beta}>0$ is supported by the joint constraint at more than $1\ensuremath{\sigma}$ level. The excellent theoretical features and the support from observations all indicate that the decomposed NGCG model deserves more attention and further investigation.

A novel approach to generate random surface thermal loads in piping

Abstract There is a need to perform three-dimensional mechanical analyses of pipes, subjected to complex thermo-mechanical loadings such as the ones evolving from turbulent fluid mixing in a T-junction. A novel approach is proposed in this paper for fast and reliable generation of random thermal loads at the pipe surface. The resultant continuous and time-dependent temperature fields simulate the fluid mixing thermal loads at the fluid–wall interface. The approach is based on reproducing discrete fluid temperature statistics, from experimental readings or computational fluid dynamic simulation's results, at interface locations through plane-wave decomposition of temperature fluctuations. The obtained random thermal fields contain large scale instabilities such as cold and hot spots traveling at flow velocities. These low frequency instabilities are believed to be among the major causes of the thermal fatigue in T-junction configurations. The case study found in the literature has been used to demonstrate the generation of random surface thermal loads. The thermal fields generated with the proposed approach are statistically equivalent (within the first two moments) to those from CFD simulations results of similar characteristics. The fields maintain the input data at field locations for a large set of parameters used to generate the thermal loads. This feature will be of great advantage in future sensitivity fatigue analyses of three-dimensional pipe structures.

A regular Strouhal number for large-scale instability in the far wake of a rotor

AbstractThe flow behind a model of a wind turbine rotor is investigated experimentally in a water flume using particle image velocimetry (PIV) and laser Doppler anemometry (LDA). The study performed involves a three-bladed wind turbine rotor designed using the optimization technique of Glauert (Aerodynamic Theory, vol. IV, 1935, pp. 169–360). The wake properties are studied for different tip speed ratios and free stream speeds. The data for the various rotor regimes show the existence of a regular Strouhal number associated with the development of an instability in the far wake of the rotor. From visualizations and a reconstruction of the flow field using LDA and PIV measurements it is found that the wake dynamics is associated with a precession (rotation) of the helical vortex core.

Recurrent bursts via linear processes in turbulent environments.

Large-scale instabilities occurring in the presence of small-scale turbulent fluctuations are frequently observed in geophysical or astrophysical contexts but are difficult to reproduce in the laboratory. Using extensive numerical simulations, we report here on intense recurrent bursts of turbulence in plane Poiseuille flow rotating about a spanwise axis. A simple model based on the linear instability of the mean flow can predict the structure and time scale of the nearly periodic and self-sustained burst cycles. Poiseuille flow is suggested as a prototype for future studies of low-dimensional dynamics embedded in strongly turbulent environments.

Gasdynamic instabilities during decay of the submicrosecond spark discharge channel

This work is devoted to studying the dynamics of breakdowns of submicrosecond high-voltage electric discharge and discharge-accompanying hydrodynamic phenomena and to analyzing the possibility of its application for acceleration of the component mixing in solving high-speed combustion problem. This work presents the results of experimental and numerical studies of the development of gasdynamic disturbances during the afterspark channel decay. The main parameters of the discharge are as follows: the typical length is 50–60 mm, the breakdown voltage is up to 120 kV, the duration time is 80–100 ns, the energy is up to 2 J, and the order of magnitude of the instantaneous power is 100 MW. For the first time, jet-type instabilities have been studied in detail and described. It is shown that the development of large-scale instabilities is tightly related to the discharge channel geometry. The mechanism of the breakdown development and the related possibility of controlling the discharge channel shape are discussed.

Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field

Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding the growth rate of this large-scale instability, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached. This results in magnetic spots that are reminiscent of sunspots. Here we want to find out under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. We use a combination of MFS, DNS, and implicit large-eddy simulations to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. We confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using turbulence simulations, we find that magnetic flux concentrations occur for different values of the Mach number between 0.1 and 0.7. DNS and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. The resulting vertical magnetic flux tubes are being confined by downflows along the tubes and corresponding inflow from the sides, which keep the field concentrated.

Characterization, Modeling and Mapping of the landslide affecting the centre-town of Azazga (Algeria)

The morphology of the North Algerian basins characterized by precarious stability constitutes an important issue for the development and the economy of many cities in the region. The landslide affecting the city of Azazga represents one of the most active and dramatic land movements experienced by the region in recent years. The city affected by the movement is situated at about 20 Kms in the East of the Wilaya of Tizi - Ouzou (in northern Algeria); the instability is located in a slope, composed of flysch (Azazga flysch are compounds of two terms of marly clay with small sandstone beds), with an inclination of about 13 °. Several factors have acted to activate this instability. Furthermore, water factor and geological conditions of this region are the main parameters of the susceptibility of the site to landslides.The Geographic Information Systems (GIS) are an effective alternative for the analysis of large-scale instabilities (such as Azazga landslides). GIS made for the site of Azazga allowed better management and interpretation of spatial data as well as good understanding of deformation mechanisms and the extent of this landslide. Geological profile has been defined for this slope using the results of spatial data analysis. Numerical modeling of this slope was then carried out, using the finite element software PLAXIS 2D , with taking in consideration the effect of the water level. Those studies show the important influence of the position of water table on the activity of the landslide and the safety factor.

On three-dimensional global linear instability analysis of flows with standard aerodynamics codes

The development of a general Jacobian-free approach for the solution of large-scale global linear instability analysis eigenvalue problems by coupling a time-stepping algorithm with industry-standard second-order accurate aerodynamic codes is presented. The three-dimensional lid-driven cavity, a challenging flow in the context of required computational resources and physical complexity, has been chosen for validation. Results in excellent agreement with the literature have been obtained by using the proposed theoretical methodology coupled with the incompressible solver of the open-source toolbox OpenFOAM. The moderate computational resources required for the solution of the TriGlobal eigenvalue problem using this method opens up a new avenue for the performance of instability analysis of flows of engineering relevance.