Symmetric Disturbances Research Articles

Bifurcation and stability of forced convection in curved ducts of square cross-section

A numerical study is made on the fully developed bifurcation structure and stability of the forced convection in a curved duct of square cross-section (Dean problem). In addition to the extension of three known solution branches to the high Dean number region, three new asymmetric solution branches are found from three symmetry-breaking bifurcation points on the isolated symmetric branch. The flows on these new branches are either an asymmetric two-cell state or an asymmetric seven-cell structure. The linear stability of multiple solutions are conclusively determined by solving the eigenvalue system for all eigenvalues. Only two-cell flows on the primary symmetric branch and on the part of isolated symmetric branch are linearly stable. The symmetric six-cell flow is also linearly unstable to asymmetric disturbances although it was ascertained to be stable to symmetric disturbances in the literature. The linear stability is observed to change along some solution branch even without passing any bifurcation or limit points. Furthermore, dynamic responses of the multiple solutions to finite random disturbances are also examined by the direct transient computation. It is found that possible physically realizable fully developed flows evolve, as the Dean number increases, from a stable steady two-cell state at lower Dean number to a temporal periodic oscillation state, another stable steady two-cell state, a temporal intermittent oscillation, and a chaotic temporal oscillation. Among them, three temporal oscillation states have not been reported in the literature. A temporal periodic oscillation between symmetric/asymmetric two-cell flows and symmetric/asymmetric four-cell flows are found in the range where there are no stable steady fully developed solutions. The symmetry-breaking point on the primary solution branch is determined to be a sub-critical Hopf point by the transient computation.

On the stability of a compressible axisymmetric rotating flow in a pipe

The linear stability of a compressible inviscid axisymmetric and rotating columnar flow of a prefect gas in a finite-length straight circular pipe is investigated. This work extends a previous analysis to include the influence of Mach number on the flow dynamics. A well-posed model of the unsteady motion of a swirling flow, with inlet and outlet conditions that may reflect the physical situation, is formulated. The linearized equations of motion for the evolution of infinitesimal axially symmetric disturbances are derived. A general mode of disturbance, that is not limited to the axial-Fourier mode, is introduced and an eigenvalue problem is developed. It is found that a neutral mode of disturbance exists at ‘the critical swirl ratio for a compressible vortex flow’. The flow changes its stability characteristics as the swirl ratio increases across this critical level. When the swirl ratio is below the critical level (supercritical flow), an asymptotically stable mode is found and, when it is above the critical level (subcritical flow), an unstable mode of disturbance develops. This result cannot be predicted by any of the previous stability criteria. When the characteristic Mach number of the base flow tends to zero, the results are the same as found for incompressible swirling flows in pipes. The growth rate ratio is positive for all Mach numbers, but decreases as Mach number is increased. This ratio vanishes at the limit Mach number at which the critical swirl tends to infinity. The present results also demonstrate that the axisymmetric breakdown of high-Reynolds-number compressible vortex flows may be delayed to higher swirl ratios with the increase of the incoming flow Mach number.

Stability analyses of long liquid bridges in the presence of gravity and flow

The stability of liquid bridges under terrestrial conditions can be enhanced when a recirculating flow is introduced inside the bridge. The Plateau–Rayleigh (PR) limit sets the stability limit of a liquid bridge in the absence of gravity and flow. The PR limit corresponds to a cylindrical bridge of length L equal to its circumference, L = 2π R . At lengths exceeding this first onset point, antisymmetric disturbances grow and result in disconnection. In recent experiments involving flow in the bridge, stable lengths greater than the PR limit were obtained by suppressing the antisymmetric disturbances. The observed lengths are close to the second bifurcation or onset point, where centro–symmetric disturbances become unstable. The second onset point occurs at L ≈ 8.987 R . In this paper, the problem is modelled using the lubrication approximation and a rectilinear flow within the bridge with zero flow rate across the cross–section is assumed. The bifurcation analysis indicates that while gravity or flow acting alone is destabilizing, a combination of the two can increase the region of stability. Local bifurcation analysis using the Liapunov–Schmidt approach is complemented by global computations of the nonlinear model equations using pseudoarclength continuation with the AUTO software. Symmetries affect the stability of the bridge solutions in a key way. Singularity theory provides a framework for the unfolding of the two bifurcations (antisymmetric and centro–symmetric branches). A detailed analysis of the governing equation obtains the coefficients in the unfolding. A surprising result is that there is a maximal influence that flow can have on the centro–symmetric disturbances. That is, as flow is increased, imperfection increases up to a certain value, beyond which the imperfection diminishes with increasing flow rate. Singularity theory provides a framework for understanding this and other reports of stabilization of the PR instability.

On problem of nonlinear symmetric instability in zonal shear flow

This paper is focused on the problem of nonlinear symmetric instability in a baroclinic basic flow. The limited amplitude characteristics of unsteady wave were investigated with the aid of equations of adiabatic, inviscid, nonlinear symmetric disturbance and a multi-scale singular perturbation technique. Evidence suggests that the limited amplitude of unsteady wave exhibits an oscillatory trend of its intensity; the amplitude of the symmetric disturbance displays periodical variation both in super- and sub-critical shear case, and the duration of the periods is related not only to the stability parameters of the basic field and wave properties but to the amplitude of initial disturbance and its time-varying change rate as well.

Income and Price Insurance Aspects of Monetary Union

Regional monetary union offers important income and price-level insurance to its members. The welfare gains available through the completion of financial markets from income and consumption insurance alone are especially large. They are much greater than those available from access to noncontingent international borrowing among members that may be promoted by monetary union. While insurance tackles asymmetric, and hence diversifiable, risks, the single monetary policy seeks to cushion symmetric disturbances that have a net effect on the union as a whole. Thus increased correlations among residual country disturbances are not necessary for the ex post justification of a monetary union although they remain likely because of other effects. Monetary union also ensures low inflation and low inflation dispersion among members. Some factors making for national inflation differentials, such as entering into monetary union at an undervalued exchange rate, have only transitory effects. Other dispersion effects, such as technology catch-up of some members with others, are more persistent but correspondingly mild. Monetary union further contributes to the efficiency of international pricing by both reducing and equalizing discriminatory degrees of pricing-to-market. Beneficial effects are expected from a better balance of power between major internally integrated markets such as those of the euro area and the United States. Keywords: monetary union, insurance, stabilization, inflation

Changes in convective properties over the solar cycle: effect on p-mode damping rates

Measurements of both solar irradiance and p-mode oscillation frequencies indicate that the structure of the Sun changes with the solar cycle. Balmforth, Gough & Merryfield investigated the effect of symmetrical thermal disturbances on the solar structure and the resulting pulsation frequency changes. They concluded that thermal perturbations alone cannot account for the variations in both irradiance and p-mode frequencies, and that the presence of a magnetic field affecting acoustical propagation is the most likely explanation of the frequency change, in the manner suggested earlier by Gough & Thompson and by Goldreich et al. Numerical simulations of Boussinesq convection in a magnetic field have shown that at high Rayleigh number the magnetic field can modify the preferred horizontal length scale of the convective flow. Here, we investigate the effect of changing the horizontal length scale of convective eddies on the linewidths of the acoustic resonant mode peaks observed in helioseismic power spectra. The turbulent fluxes in these model computations are obtained from a time-dependent, non-local generalization of the mixing-length formalism. The modelled variations are compared with p-mode linewidth changes revealed by the analysis of helioseismic data collected by the Birmingham Solar-Oscillations Network (BiSON); these low-degree (low-l) observations cover the complete falling phase of solar activity cycle 22. The results are also discussed in the light of observations of solar-cycle variations of the horizontal size of granules and with results from 2D simulations by Steffen of convective granules.

Unifying the relationships of species richness to productivity and disturbance.

Although species richness has been hypothesized to be highest at 'intermediate' levels of disturbance, empirical studies have demonstrated that the disturbance-diversity relationship can be either negative or positive depending on productivity On the other hand, hypothesized productivity diversity relationships can be positive, negative or unimodal, as confirmed by empirical studies. However, it has remained unclear under what conditions each pattern is realized, and there is little agreement about the mechanisms that generate these diverse patterns. In this study, I present a model that synthesizes these separately developed hypotheses and shows that the interactive effects of disturbance and productivity on the competitive outcome of multispecies dynamics can result in these diverse relationships of species richness to disturbance and productivity The predicted productivity diversity relationship is unimodal but the productivity level that maximizes species richness increases with increasing disturbance. Similarly, the predicted disturbance diversity relationship is unimodal but the peak moves to higher disturbance levels with increasing productivity Further, these patterns are well explained by the opposite effects of productivity and disturbance on competitive outcome that are suggested by the change in community composition along these two environmental gradients: higher productivity favours superior competitors while higher disturbance levels favour inferior competitors.

Characteristic impedance extraction using calibration comparison

A robust line impedance identification method is presented in this paper. It determines the characteristic impedance of on-wafer thru-line-reflect (TLR) standards measured after an initial off-wafer line-reflect-match or TLR calibration. The only assumption made is that the obtained trans-wafer error boxes are a cascade of a symmetric probe-related disturbance and a change in reference impedance. The proposed method yields an unbiased estimate of the complex characteristic impedance. Results from coplanar lines on a medium resistivity silicon substrate support the made assumption.

Stability of a spherical flame ball in a porous medium

Gaseous flame balls and their stability to symmetric disturbances are studied numerically and asymptotically, for large activation temperature, within a porous medium that serves only to exchange heat with the gas. Heat losses to a distant ambient environment, affecting only the gas, are taken to be radiative in nature and are represented using two alternative models. One of these treats the heat loss as being constant in the burnt gases and linearizes the radiative law in the unburnt gas (as has been studied elsewhere without the presence of a solid). The other does not distinguish between burnt and unburnt gas and is a continuous dimensionless form of Stefan's law, having a linear part that dominates close to ambient temperatures and a fourth power that dominates at higher temperatures.Numerical results are found to require unusually large activation temperatures in order to approach the asymptotic results. The latter involve two branches of solution, a smaller and a larger flame ball, provided heat losses are not too high. The two radiative heat loss models give completely analogous steady asymptotic solutions, to leading order, that are also unaffected by the presence of the solid which therefore only influences their stability. For moderate values of the dimensionless heat-transfer time between the solid and gas all flame balls are unstable for Lewis numbers greater than unity. At Lewis numbers less than unity, part of the branch of larger flame balls becomes stable, solutions with the continuous radiative law being stable over a narrower range of parameters. In both cases, for moderate heat-transfer times, the stable region is increased by the heat capacity of the solid in a way that amounts, simply, to decreasing an effective Lewis number for determining stability, just as if the heat-transfer time was zero.

Energy and pseudomomentum of propagating disturbances on the beta-plane

The far-field amplitude of the waves generated by a steadily propagating radially symmetric disturbance on the beta-plane is calculated using Lighthill's method. From this can be obtained the fluxes of quantities such as wave energy which are radiated away from the disturbance. The radiated wave power is computed for a variety of forms of the disturbance. The rate of change of pseudomomentum in the system is also calculated: the component parallel to the motion of the disturbance is the radiated wave power divided by velocity. Results are compared to previous work and some physical issues are discussed.

Monte Carlo inference in econometric models with symmetric stable disturbances

The paper develops Markov Chain Monte Carlo methods to perform exact posterior analysis in models with symmetric stable Paretian disturbances. It is shown how posterior moments and marginal densities of functions of parameters can be computed methodically by combining a Gibbs sampler with Metropolis independence chains. The new method is shown to perform satisfactorily in constructed examples. The method is also applied to a set of monthly real exchange rates and the question of difference versus trend stationarity is taken up jointly with the problem of inference about the parameter of the stable distribution.

Integrated Direct Methods for Transient Stability Analysis

In this paper, three direct methods (i.e., Controlling Unstable Equilibrium Point (CUEP) method, Potential Energy Boundary Surface (PEBS) method, and Extended Equal Area Criterion (EEAC) method) for power system transient stability analysis have been reviewed and compared. Their analysis accuracy and their error sources are investigated. Then, an integrated direct method with much higher accuracy and reliability is proposed. The proposed method has been applied to two Chinese power systems for transient stability analysis of more than two thousand cases under large disturbances of symmetrical and unsymmetrical faults and autoreclosure operating sequence disturbances. Statistical results clearly illustrate the effectiveness of the proposed method.

Nonlocal Nonlinear Schrödinger Equations as Models of Superfluidity

Condensate models for superfluid helium II with nonlocal potentials are considered. The potentials are chosen so that the models give a good fit to the Landau dispersion curve; i.e., the plot of quasi-particle energy E versus momentum p has the correct slope at the origin (giving the correct sound velocity) and the roton minimum is close to that experimentally observed. It is shown that for any such potential the condensate model has non-physical features, specifically the development of catastrophic singularities and unphysical mass concentrations. Two numerical examples are considered: the evolution of a radially symmetric mass disturbance and the flow around a solid sphere moving with constant velocity, both using the nonlocal Ginsburg–Pitaevskii model. During the evolution of the solution in time, mass concentrations develop at the origin in the radially symmetric case and along the axis of symmetry for the motion of the sphere.

Properties and diffraction of vector Bessel–Gauss beams

We examine a family of Bessel–Gauss beam solutions to the vector wave equation that allow a combination of azimuthal and radial polarization in the transverse electric field. Recently reported linear and azimuthal Bessel–Gauss beams may be identified as members of this set. Several free parameters determine the form and behavior of each beam; varying these parameters can produce distinctly different intensity patterns and beam behavior. We find a general diffraction integral for circularly symmetric disturbances and investigate two special cases, a thin lens and a circular aperture.

Linear analysis of the instability of two-dimensional non-Newtonian liquid sheets

The instability of two-dimensional non-Newtonian liquid sheets moving in an inviscid gaseous environment is investigated. A linearized stability analysis shows that non-Newtonian liquid sheets have a higher growth rate than Newtonian liquid sheets for both symmetric and antisymmetric disturbances, indicating that non-Newtonian liquid sheets are more unstable than Newtonian liquid sheets. It is found that the surface tension effects always resist, whereas the aerodynamic effects promote, the occurrence and development of instability of non-Newtonian liquid sheets. Similar results were obtained for inviscid and Newtonian liquid sheets by many other authors before. It is observed that in non-Newtonian liquid sheets the liquid viscosity tends to damp the instability, whereas the liquid elasticity results in an enhancement of instability. It is seen that both the growth rate and the instability range of non-Newtonian liquid sheets increase greatly with the gas Weber number, the Reynolds number, and the ratio of gas to liquid density for symmetric and antisymmetric disturbances, indicating that non-Newtonian liquid sheets destabilize more easily at high values of these three parameters. When the liquid viscosity is increased, the growth rate of symmetric and antisymmetric disturbances on Newtonian and non-Newtonian liquid sheets decreases, but the cutoff wave number remains unchanged. At low liquid viscosity, the growth rate of non-Newtonian liquid sheets is close to that of Newtonian ones. The growth rates of symmetric and antisymmetric disturbances decrease with the ratio of deformation retardation to stress relaxation time but increase with the liquid elasticity, whereas the instability range does not change with these two parameters. Moreover, increasing the gas Weber number, the Reynolds number, and the ratio of gas to liquid density substantially, enhances the maximum growth rate and the dominant wave number of non-Newtonian liquid sheets for symmetric and antisymmetric types of disturbances. However, the effects of the ratio of deformation retardation to stress relaxation time, the Ohnesorge number, and the Elasticity number on both the maximum growth rate and the dominant wave number are relatively weak. It is discovered that the maximum growth rate of antisymmetric disturbances is always larger than that of symmetric disturbances, while the dominant wave number of antisymmetric disturbances is always smaller than that of symmetric disturbances. This indicates that antisymmetric disturbances always prevail over symmetric disturbances for non-Newtonian liquid sheets.

Cylindrical solitary waves and their interaction in Bénard-Marangoni layers

We consider a motionless Newtonian and incompressible shallow liquid layer bounded below by a bottom plate where temperature is held fixed and above with a free deformable surface whose tension is linearly temperature dependent and on which the heat flux is fixed. When the dimensionless surface tension gradient, measured by a Marangoni number, slightly exceeds its critical value, radially symmetric, long-wavelength excitations obey a dissipative cylindrical Korteweg--de Vries (DCKdV) equation. A dissipative cylindrical Kadomtsev-Petviashvili (DCKP) equation is also derived for nearly radially symmetric disturbances. Exact solitary wave solutions of the DCKP equation are found and the solitary wave solutions of the DCKdV equation are also discussed. Finally the head-on collision between two concentric cylindrical solitary waves is considered and its solitonic character is displayed.

Instability of a liquid sheet of parabolic velocity profile

A power series mathematical solution is advanced for the problem of instability of an inviscid liquid sheet of parabolic velocity profile emanated from a nozzle into an inviscid gas. A comparison of the instability of a sheet of parabolic velocity profile with one of a uniform velocity profile is performed in order to deduce the effects of velocity profile relaxation on instability. The results show that for both antisymmetrical and symmetrical disturbances departure from uniformity of the velocity profile causes the instability to be reduced. The physical interpretation and practical implications of the present findings are discussed.

Stochastic models and variable returns to scales in data envelopment analysis

Stochastic Data Envelopment Analysis (DEA) models were developed by taking random disturbances into account for the possibility of variations in input-output data structure. The stochastic efficiency measure of a Decision Making Unit (DMU) is defined via joint probabilistic comparisons of inputs and outputs with other DMUs, and can be characterized by solving a chance constrained programming problem. Deterministic equivalents are derived for both situations of multivariate symmetric random disturbances and a single random factor in the production relationships. An analysis of stochastic variable returns to scale is developed.

Transient behaviour of optimum‐designed three‐phase squirrel‐cage induction motors

AbstractThis paper describes the transient behaviour of optimum‐designed three‐phase squirrel‐cage induction motors. These motors have been designed based upon three different objective functions. They are cost, efficiency and combination of efficiency‐cost functions. Transient performance of these optimum designs and an industrial motor are compared and a suitable design for a particular fault is then introduced. A symmetrical voltage disturbance, startup and a symmetrical three‐phase short circuit are three cases considered in this investigation.

EFFECTS OF COMPRESSIBILITY ON THE INSTABILITY OF LIQUID SHEETS

The effect of compressibility of fluids on the instability of a liquid sheet issued from a nozzle into an ambient gas is investigated by use of linear stability analysis. It is found that increasing the gas Mach number from subsonic to transonic causes the maximum growth rate, dominant wave number, and cut-off wave number of disturbances to increase. Liquid compressibility has a minimal effect on instability. At a constant wave number, the growth rate of disturbances increases as the gas Mach number tends to 1 and then begins to decline with further increase in the gas Mach number. Hence, liquid sheet breakup is due to surface disintegration not gross fracturing in agreement with experimental observations. At small values of wave number, antisymmetrical disturbances grow faster than symmetrical ones while the growth rate of both types of disturbances approach each other at large wave numbers. At small Weber number, antisymmetrical disturbances exhibit a higher maximum growth rate and a lower dominant wave number than symmetrical disturbances. However, the maximum growth rate and dominant wave number of the two types of disturbances are almost identical when Weber number becomes large. An increase in the gas-to-liquid density ratio enhances the instability. Surface tension always opposes the development of instability.