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Criteria of stability different in different sets of coordinates. Report discusses dependence of criteria of hydrodynamic instability upon frame of reference used to analyze motion of fluid.
Abstract Magnetic reconnection in 3D fusion devices is investigated. With the use of Boozer co-ordinates, we reduce the non-linear resistive magnetohydrodynamic equations in the limit of large aspect ratio and finite pressure fluctuations, to obtain a set of non-linear equations suitable for magnetic reconnection studies in stellarators. Magnetic flux unfreezing due to a finite electron mass is also considered. Equations that govern the linear regime and some of their general properties are given. We emphasise the role of magnetic geometry and identify how some aspects of stellarator optimisation could have an impact on reconnecting instabilities, in particular by exacerbating those enabled by electron inertia. The effect of 3D coupling on the linear reconnection rates and the mode structure is quantitatively addressed in the case in which the equilibrium rotational transform has one specific resonant location for which one mode can reconnect while coupled to an arbitrary number of non-resonant harmonics. The full problem is rigorously reduced to an equivalent cylindrical one, by introducing some geometrically modified plasma inertial and dissipative scales. The 3D scalings for the growth rates of reconnection instabilities and their destabilisation criteria are given.
An experimental investigation of the hydrodynamic characteristics of two-phase R-113 flow has been carried out. Straight tube pressure drop data, as a function of mass flow rate (mass flux) and flow quality has been obtained using the Two-Phase Flow Test Facility located in the Advanced Thermal Laboratories of the Crew and Thermal Systems Division at the Lyndon B. Johnson Space Center. Additionally, after successfully obtaining the straight tube pressure drop data, the test facility was modified in order to obtain pressure drop data for the flow of two-phase R-113 through 180 deg piping bends. Inherent instabilities of the test facility prevented the successful acquisition of pressure drop data through the piping bends. The experimental straight tube data will be presented and compared with existing predictive correlations in an attempt to gain insight into the utility of such correlations as the basis for developing design criteria. A discussion of the instabilities which rendered successful acquisition of the piping bend data will be presented and suggestions will be made for eliminating these system tendencies. Finally, recommendations for future investigations, based on successful reconfiguration of the test facility, will be made.
Analytical study of the longitudinal dynamic stability of a nonrolling, lifting vehicle gliding at hypersonic speeds. The analysis applies to shuttle vehicles designed for operating up to the rim of a planetary atmosphere. A general nondimensional time transformation is introduced to derive a unified second-order linear differential equation for the angle of attack, valid for all types of reentry of a general type of vehicle. The stability of motion is discussed for two fundamental regimes of flight that are based on widely different assumptions. For near ballistic entry along a straight line trajectory, the equation reduces to a confluent hypergeometric equation, the solution of which can be expressed in terms of Whittaker's function. Using a theorem in the theory of stability of differential equations, criteria for damped oscillations are derived. It is shown that the aerodynamic criteria for stability are the same as for the case of ballistic entry. In addition, for each vehicle configuration, and specified planetary atmosphere, there exists an altitude range where the angle of attack frequency is nearly equal to the orbital frequency causing instability in pitch. This resonance instability is due to the ellipticity of the orbit. Criteria for eccentricity instability are derived.
ABSTRACT Collisional self-interactions occurring in protostellar jets give rise to strong shocks, the structure of which can be affected by radiative cooling within the flow. To study such colliding flows, we use the AstroBEAR AMR code to conduct hydrodynamic simulations in both one and three dimensions with a power-law cooling function. The characteristic length and time-scales for cooling are temperature dependent and thus may vary as shocked gas cools. When the cooling length decreases sufficiently and rapidly, the system becomes unstable to the radiative shock instability, which produces oscillations in the position of the shock front; these oscillations can be seen in both the one- and three-dimensional cases. Our simulations show no evidence of the density clumping characteristic of a thermal instability, even when the cooling function meets the expected criteria. In the three-dimensional case, the nonlinear thin shell instability (NTSI) is found to dominate when the cooling length is sufficiently small. When the flows are subjected to the radiative shock instability, oscillations in the size of the cooling region allow NTSI to occur at larger cooling lengths, though larger cooling lengths delay the onset of NTSI by increasing the oscillation period.
Abstract Experimental data on electromagnetic fluctuations in DIII-D, made available by the Faraday-effect radial interferometer-polarimeter (RIP) diagnostic Chen (2016 Rev. Sci. Instrum. 87 11E108), is examined in comparison with detailed gyrokinetic simulations using gyrokinetic electromagnetic numerical experiment (GENE). The diagnostic has the unique capability of making internal measurements of fluctuating magnetic fields ∫ n e δ B r d R ∫ n e d R . Local linear simulations identify microtearing modes (MTMs) over a substantial range of toroidal mode numbers (peaking at n = 15) with frequencies in good agreement with the experimental data. Local nonlinear simulations reinforce this result by producing a magnetic frequency spectrum in good agreement with that diagnosed by RIP. Simulated heat fluxes are in the range of experimental expectations. However, magnetic fluctuation amplitudes are substantially lower than the experimental expectations. Possible sources of this discrepancy are discussed, notably the fact that the diagnostics are localized at the mid-plane—the poloidal location where the simulations predict the fluctuation amplitudes to be smallest. Despite some discrepancies, several connections between simulations and experiments, combined with general criteria discriminating between potential pedestal instabilities, strongly point to MTMs as the source of the observed magnetic fluctuations.
A linearized stability analysis has been applied to a fluid flowing in a gravity field between horizontal planes in Couette flow under conditions such that the temperature of the bottom plane exceeds that of the top. It is shown that, under conditions likely to be encountered with polymer solutions, oscillatory instabilities will not be controlling. Criteria are offered for ascertaining when an analysis based upon a second-order fluid model may be expected to yield physically meaningful results. It is also shown that, for the fluid model considered, critical conditions for stability are not changed when disturbances which vary in the flow direction are substituted for those which are a function of the coordinate transverse to the flow.
In this work, we discuss the response of both moving and trapped solitary wave solutions of a two-component nonlinear Schrödinger system in 1 + 1 dimensions to an odd-$\mathcal{PT}$ external periodic complex potential. The dynamical behavior of perturbed solitary waves is explored by conducting numerical simulations of the nonlinear system and using a collective coordinate variational approximation. We present case examples corresponding to choices of parameter values and initial conditions involved therein. The results of the collective coordinate approximation are compared against numerical simulations where we observe qualitatively good agreement between the two. Unlike the case for a single-component solitary wave in a complex periodic $\mathcal{PT}$-symmetric potential, the collective coordinate equations do not have a small oscillation regime, and initially the height of the two components changes in opposite directions often causing instability. We find that the dynamic stability criteria we have used in the one-component case are a good indicator for the onset of dynamic instabilities in the present setup.
Detailed proton spectral and pitch angle distribution observations were obtained from two proton detectors and a fluxgate magnetometer flown on Small Scientific Satellite A (Explorer 45). The data of interest are from orbit 99 in-bound occurring on 17 December 1971, some 8 hours prior to the sudden commencement of a magnetic storm. The data are consistent with the initiation of ion cyclotron instability when certain requirements are met. These criteria are met initially at the altitude at which the sudden intensity decrease occurs. However, after the initiation of the instability, the linear theory is unable to explain the further evolution of intensities, pitch angle distributions, and energy spectra of the ring current particles.
Oxidative instability of the liquid electrolyte at or near battery cathode oxide surfaces has significant detrimental effects on batteries. Organic solvent molecules are often the fuel and precursors of such degradation processes, releasing electrons and protons that react with cathode oxides and electrolyte anions. These reactions contribute to cathode–electrolyte interphase (CEI) film formation, transition-metal ion dissolution, and phase transformation of the surface regions of the cathode. Here we apply density functional theory calculations to examine four criteria of oxidative stability (oxidation potential, hydrogen removal energies, and initial reactivity on two types of oxide facets) using four different solvent/additive molecules (ethylene carbonate, fluoroethylene carbonate, 1,3-dioxolane, and dimethyl ether). The ranking of molecular stability differs with each criterion. Surprisingly, the all-oxygen-terminated basal planes of layered oxides exhibit lower reaction barriers than spinel surface facets with exposed transition-metal cations, especially for ether solvents; the calculations also suggest basal planes contribute to the dissolution of transition-metal ions. Further, the structure–degradation relation complexity underscores the challenge of understanding the function of the CEI but also offers a guide to future degradation-mitigation strategies including facet engineering. Our predictions and models help establish a framework for future studies relevant to high-voltage conditions.
Fluid interface instability suppression via feedback, noting stability criteria and parameters
The problem of time-steady accretion of gas irradiated by a self-consistently generated quasar-like continuum is investigated. A controversy in the literature is resolved by a careful distinction between the existence of solutions and their stability. Specific criteria are found for when thermal instabilities may disrupt single-phase steady flow. As a function of initial temperature (1,000,000-100,000,000 K), the boundaries of stable flow in the luminosity are determined relative to the Eddington (L/LE)-efficiency plane. The thermal and dynamical history of these steady flows is analyzed. The observational data that define quasars and type I Seyfert galaxies are matched to find values of efficiency and L/LE required for consistent spherically symmetric steady-flow models. The efficiency is constrained to be less than 1/100, and L/LE resides between several times 1/1000-1/100.
Design features and concepts that have primary influence on the stable operating flow range of propellant-feed centrifugal turbopumps in a rocket engine are discussed. One of the throttling limitations of a pump-fed rocket engine is the stable operating range of the pump. Several varieties of pump hydraulic instabilities are mentioned. Some pump design criteria are summarized and a qualitative correlation of key parameters to pump stall and surge are referenced. Some of the design criteria were taken from the literature on high pressure ratio centrifugal compressors. Therefore, these have yet to be validated for extending the stable operating flow range of high-head pumps. Casing treatment devices, dynamic fluid-damping plenums, backflow-stabilizing vanes and flow-reinjection techniques are summarized. A planned program was undertaken at LeRC to validate these concepts. Technologies developed by this program will be available for the design of turbopumps for advanced space rocket engines for use by NASA in future space missions where throttling is essential.
After reviewing the role of Compton scattering in accretion disks around black holes, it is discussed whether Lightman-Eardley (LE) secular instabilities can trigger and maintain Pringle-Rees (PR) thermal instabilities. The radiative-transfer-equation and equation-of-state criteria for LE stability in alpha-viscosity-law disk models and dynamic viscosity criteria for more general situations is derived. On the basis of these considerations the LE instability is insufficient for inducing PR instabilities and hot thick inner regions important in accretion-disk models of compact hard X-ray sources. The density thinning due to radial velocity gradients in the accretion flow is suggested as a more likely and satisfactory mechanism.
The effects of a given nonthermal low-frequency density-fluctuation spectrum on the amplification of Langmuir waves by a 'bump-on-tail' beam of electrons are studied. The density-fluctuation spectrum is assumed to contain a uniform distribution of wavelengths ranging from much shorter than the beam mode wavelength to of the same order. This permits multiple large-angle (back) scattering to occur. One-dimensional numerical solutions of the kinetic equations are found which yield criteria for linear saturation of the beam instability of a cascade of backscattering to high wavenumber. The relevant time scales and spectral shapes are also determined in both the stable and unstable regions. Linear damping and Cerenkov emission by a possible nonthermal tail of electrons is taken into account. An application is made to the beam modes observed simultaneously with density fluctuations off the Jovian bow shock. It is shown that the observed level of density fluctuations is sufficient to saturate the unstable Langmuir waves, although nonthermal Landau damping may prevent a cascade to very high wavenumbers.
Quantum materials that are found on the verge of structural, magnetic, and electronic instabilities are deep reservoirs for exotic phenomena. Our criteria to study the reported Ln 5 Ru 6 Sn 18 (Ln = Gd, Tb) are guided by the tolerance factor for Remeika phases─a class of intermetallic compounds with the general formula A 3 M 4 X 13 (where A = rare-earth element, M = transition metal, and X = tetrel), which can be viewed as structural analogues of pseudoperovskites (4 × ABX 3 ), with one of the tetrel atoms occupying the A-site. We have grown single crystals, up to 0.5 cm on the largest facet, of Gd 5 Ru 6 Sn 18 (a = 13.8052(12) Å) and Tb 5 Ru 6 Sn 18 (a = 13.7825(9) Å), which we expect to be on the verge of a formation instability. Bulk magnetic, heat capacity, and electrical transport measurements reveal unusual behavior that originates from the trivalent Gd and Tb ions, with deviations from typical metallic behavior and magnetic ordering that is short-range or disrupted in some other way. Furthermore, to better understand these phenomena, single-crystal neutron diffraction is investigated, which reveals short-range correlations among the partially occupied Tb and Sn sublattices, with 3D-ΔPDF analysis supporting direction-dependent local order. Taken together, these measurements show the utility of using tolerance factors in identifying materials that are likely to exhibit complex phenomena and uncover environments where a formation instability may strongly impact emergent bulk magnetic and electronic phenomena.
The wrinkling phenomenon in elasticity is mathematically defined and described as a special type of instability associated with the loss of hyperbolicity of the governing equations when some of the characteristic speeds of elastic wave propagation become imaginary. The developed criteria of wrinkling are applied to such structural elements as membranes, strings, soft shells, soft rods, and laminated material. The cause of wrinkling in these elements is due to compression in longitudinal directions that exceeds the through-the-thickness shear modulus. For elements with internal fluid flow the critical compression is reduced due to the destabilizing effect of the flow. The most effective mathematical analysis technique is a combination of tensor analysis and index notations.
Second breakdown and other thermal instabilities analyzed by heat flow equation, obtaining stability criteria predicting reduced power dissipation for transistor at low currents