Showing papers on "Dissipation published in 1985"

Artificial Dissipation Models for the Euler Equations

Abstract: Various artificial dissipation models that are used with central difference algorithms for the Euler equations are analyzed for their effect on accuracy, stability, and convergence rates. In particular, linear and nonlinear models are investigated using an implicit approximate factorization code (ARC2D) for transonic airfoils. Fully implicit application of the dissipation models is shown to improve robustness and convergence rates. The treatment of dissipation models at boundaries will be examined. It will be shown that accurate, error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model. I. Introduction T HE solution of the Euler equations using numerical techniques requires the use of either a differencing method with inherent dissipation or the addition of dissipation terms to a nondissipative scheme. This is because the Euler equations do not provide any natural dissipation mechanism (such as viscosity in the Navier-Stokes equations) that would eliminate high frequencies which are caused by nonlinearitie s and especially shocks. A variety of numerical algorithms and computer codes for the Euler equations have been developed. Methods such as MacCormack's1 explicit

Calibration and Verification of a Dissipation Model for Random Breaking Waves

Abstract: A model describing the average rate of energy dissipation in random waves breaking in shallow water, published previously by Battjes and Janssen (1978), has been applied to an extensive set of data for the purposes of calibration and verification. Both laboratory and field data were used, obtained on beaches with a more or less plane slope as well as on barred beaches, and for a wide range of wave conditions. Optimal values have been estimated for an adjustable breaking wave height-coefficient in the model; these appear to vary slightly but systematicaly with the incident wave steepness, in a range that is physically realistic. A parameterization of this dependence allows the use of the model for prediction. Applied to the present data set, the correlation coefficient between measured and predicted rms wave heights is 0.98, with an rms normalized error of 6% and a bias that does not differ significantly from zero.

Small normal-metal loop coupled to an electron reservoir

Abstract: A conceptually simple approach is proposed to introduce dissipation into a normal-metal loop penetrated by a flux. The loop is coupled via a single current lead to an electron reservoir. Scattering processes in the loop are elastic. Inelastic processes occur only in the reservoir and are the source of dissipation. We investigate the effect of this reservoir on the persistent currents in the loop and the adsorption of power in the presence of a sinusoidally modulated flux.

Effect of rotation on isotropic turbulence - Computation and modelling

Abstract: This paper uses numerical simulation to analyse the effects of uniform rotation on homogeneous turbulence. Both large-eddy and full simulations were made. The results indicate that the predominant effect of rotation is to decrease the rate of dissipation of the turbulence and increase the lengthscales, especially those along the axis of rotation. These effects are a consequence of the reduction, due to the generation of inertial waves, of the net energy transfer from large eddies to small ones. Experiments are also influenced by a more complicated interaction between the rotation and the wakes of the turbulence-generating grid which modifies the nominal initial conditions in the experiment. The latter effect is accounted for in simulations by modifying the initial conditions. Finally, a two-equation model is proposed that accounts for the effects of rotation and is able to reproduce the experimental decay of the turbulent kinetic energy.

Application of the E -ε turbulence model to the atmospheric boundary layer

Abstract: In the so called E - e turbulence model, an eddy viscosity is evaluated from turbulent kinetic energy E and energy dissipation e. Although still a first-order closure method in its simpler form, the E- e model yields eddy viscosity for complex turbulent flows without a prior prescription of a length scale needed in so-called mixing-length models. The E - e model has been successfully applied to many flow problems in engineering applications for non-rotating boundary layers. In this paper, the E - e method is extended to the atmospheric boundary layer for which a modification of the dissipation equation is found to be necessary in order to give results comparable with observational data.

A Two-Step Scheme for the Advection Equation with Minimized Dissipation and Dispersion Errors

Abstract: A two-step advection scheme of the Lax-Wendroff type is derived which has accuracy and phase characteristics similar to that of a third-order scheme. The scheme is exactly third-order accurate in time and space for uniform flow. The new scheme is compared with other currently used methods, and is shown to simulate well the advection of localized disturbances with steep gradients. The scheme is derived for constant flow and generalized to two-dimensional nonuniform flow.

On the viscosity of a concentrated suspension of solid spheres

Abstract: Explanations of the very high viscosities of concentrated suspensions of spheres based on the dissipation in squeezing flow between particles pairs are shown to be in error. The dissipation in pair interactions is always of the order of that generated by shearing motions, and this dissipation is of too low an order in concentration for single pair interactions to explain the observed viscosities.

Kinetic Theory of Plasma Waves

Abstract: In this paper, I outline the solution of Vlasov-Maxwell's equations with given initial conditions. When transients have died out, the temporal evolution of each spatial Fourier component is completely determined by a dispersion relation. I derive the electrostatic dispersion relation and discuss the resonant interaction between particles and electrostatic waves. A new derivation of the wave energy density in a plasma with arbitary dissipation is given. The numerical solution of the dispersion relation of waves in a Maxwellian plasma is discussed, and finally I show some examples of numerically evaluated dispersion surfaces.

Diffusion and localization of a particle in a periodic potential coupled to a dissipative environment.

Abstract: The phase diagram of a Hamiltonian which describes a particle moving in a periodic potential and coupled to an external heat bath has been analyzed in detail. By renormalization-group methods, it is proved that this system exhibits an unusual transition between diffusive behavior and a self-trapped phase. The dynamics along the transition line is shown to be integrable and the order parameter, the mobility, is computed exactly.

Quasistatic processes as step equilibrations

Abstract: The proportionality between the square of the distance traversed as measured in thermodynamic length and the minimum associated dissipation of a process is established in a new context independent of dynamical laws. A quasistatic thermodynamic process consisting of K steps, each equilibrating with an appropriate reservoir, is optimized with respect to the position of the steps and the allocation of the total time τ for the process among the steps. It is found that the steps should be of equal thermodynamic length. For large K the bounds based on thermodynamic length are recovered.

Statistics of Mixing Parameters in the Upper Ocean During JASIN Phase 2

Abstract: Turbulence levels obtained during the 1978 Joint Air-Sea Interaction experiment (JASIN) have been examined from measurements of both temperature gradient and velocity shear. These measurements, obtained with the vertical profiler OCTUPROBE 2, have been analyzed to compute viscous dissipation rule, ϵ, and dissipation of temperature variance, χτ. As in a previous study, the dissipation rate increased as the surface energy input parameterized by U103 increased. The JASIN study indicated only one-third of the viscous dissipation rate observed in a similar experiment in a region on the Scotian shelf and this difference is discussed. A mixing parameter, Γ, related the flux Richardson number has been estimated from simultaneous measurements of ϵ and χτ. The mean value of Γ corresponds to a flux Richardson number of 0.21. Heat flux estimates from temperature microstructure measurements were fund to be consistent with other results of the JASIN experiment. The statistical distributions of dissipation, ϵ, ...

Comparison of direct numerical simulation of two-dimensional turbulence with two-point closure: the effects of intermittency

Abstract: We compare results of high-resolution direct numerical simulation with equivalent two-point moment closure (the test-field model) for both randomly forced and spin-down problems. Our results indicate that moment closure is an adequate representation of observed spectra only if the random forcing is sufficiently strong to disrupt the dynamical tendency to form intermittent isolated vortices. For strong white-noise forcing near a lower-wavenumber cut-off, theory and simulation are in good agreement except in the dissipation range, with an enstrophy range less steep than the wavenumber to the minus fourth power. If the forcing is weak in amplitude, red noise, and at large wavenumbers, significant errors are made by the closure, particularly in the inverse-cascade range. For spin-down problems at large Reynolds numbers, the closure considerably overestimates enstrophy transfer to small scales, as well as energy transfer to large scales. We finally discuss the possibility that the closure errors are related to intermittency of various types. Intermittency can occur in either the inverse-cascade range (forced equilibrium) or the intermediate scales (spin-down), with isolated concentrations of vorticity forming the associated coherent structures, or it can occur in the dissipation range owing to the nonlinear amplification of variations in the cascade rate (Kraichnan 1967).

High-energy inverse free-electron-laser accelerator.

Abstract: We study the inverse free-electron-laser (IFEL) accelerator and show that it can accelerate electrons to the few hundred GeV region with average acceleration rates of the order of 200 MeV/m. Several possible accelerating structures are analyzed, and the effect of synchrotron-radiation losses is studied. The longitudinal phase stability of accelerated particles is also analyzed. A Hamiltonian description, which takes into account the dissipative features of the IFEL accelerator, is introduced to study perturbations from the resonant acceleration. Adiabatic invariants are obtained and used to estimate the change of the electron phase-space density during the acceleration process.

Nonequilibrium thermodynamics of pressure solution

Abstract: This paper is concerned with the thermodynamic theory of solution and precipitation processes in wet crustal rocks and with the mechanism of steady pressure-solution slip in ‘contact zones,’ such as grain-to-grain contacts, fracture surfaces, and permeable gouge layers, that are infiltrated by a mobile aqueous solution phase. A local dissipation jump condition at the phase boundary is fundamental to identifying the thermodynamic force driving the solution and precipitation process and is used here in setting up linear phenomenological relations to model near-equilibrium phase transformation kinetics. The local thermodynamic equilibrium of a stressed pure solid in contact with its melt or solution phase is governed by Gibbs's relation, which is rederived here, in a manner emphasizing its independence of constitutive assumptions for the solid while neglecting surface tension and diffusion in the solid. Fluid-infiltrated contact zones, such as those formed by rough surfaces, cannot generally be in thermodynamic equilibrium, especially during an ongoing process of pressure-solution slip, and the existing equilibrium formulations are incorrect in overlooking dissipative processes tending to eliminate fluctuations in superficial free energies due to stress concentrations near asperities, defects, or impurities. Steady pressure-solution slip is likely to exhibit a nonlinear dependence of slip rate on shear stress and effective normal stress, due to a dependence of the contact-zone state on the latter. Given that this dependence is negligible within some range, linear relations for pressure-solution slip can be derived for the limiting cases of diffusion-controlled and interface-reaction-controlled rates. A criterion for rate control by one of these mechanisms is set by the magnitude of the dimensionless quantitykδ/2C pD, wherek is the interfacial transfer coefficient, δ is the mean diffusion path length,C p is the solubility at pressurep, andD is the mass diffusivity.

Theory of resistivity-gradient-driven turbulence

Abstract: A theory of the nonlinear evolution and saturation of resistivity‐driven turbulence, which evolves from linear rippling instabilities, is presented. The nonlinear saturation mechanism is identified both analytically and numerically. Saturation occurs when the turbulent diffusion of the resistivity is large enough so that dissipation caused by parallel electron thermal conduction balances the nonlinearly modified resistivity gradient driving term. The levels of potential, resistivity, and density fluctuations at saturation are calculated. A combination of computational modeling and analytic treatment is used in this investigation.

Resistive decay of Alfven waves in a non-uniform plasma

Abstract: The effect of resistive dissipation on the propagation of an MHD disturbance in a nonuniform plasma is examined. The present analysis, based on a boundary-layer technique, shows the existence of resistive normal modes with complex eigenfrequencies. The real part of the eigenfrequency is associated with an oscillatory behavior and defines the location in space of the layer where resistivity is important. The dissipation mechanism is responsible for the damping of the wave, in contrast with previous works in which the ideal MHD theory was used.

Integrated circuit packaging systems with double surface heat dissipation

Abstract: A mounting arrangement for a semiconductor integrated circuit chip having a first heat sink mounted to the bottom surface of the chip in good heat transfer relation and a second heat sink mounted to a region of the top surface of the chip interior to the bonding pads.

Turbulent stirring in an experimental induction furnace

Abstract: This paper describes an experimental study of the electromagnetic stirring in a mercury induction furnace. The 200 mm-diameter furnace is supplied with a single-phase electric current of frequency 50–4700 Hz. The flow pattern is measured by means of a special two-wire probe, which tracks the thermal wake behind a hot-film probe. The magnitudes of fluctuating velocities are measured by hot-film anemometry. Attention is focused on the influence on the mean and turbulent motion of the electromagnetic-skin depth, which is determined by the supply frequency. The measurements of the mean motion show that, for a fixed magnetic field, stirring is maximum when the value of the skin depth normalized by the pool radius is about 0.2, in agreement with previous theoretical predictions. Two turbulence regimes may be distinguished for different frequency ranges. At low frequency the various properties of the turbulence, such as the mean-square fluctuations, the integral scales and the turbulent dissipation rate, are almost uniform over the whole bath. However, at high frequency the turbulence is non-uniform; there is an increase in the turbulent fluctuations and dissipation rate and a decrease of the integral scale within the electromagnetic-skin depth near the wall.

Breakdown simulation of electronegative gases in non-uniform field

Abstract: Gas breakdown in electronegative gases and short non-uniform field gap is studied with a set of equations taking into account the spatio-temporal changes of the conductivity along the discharge axis and the variation of the neutral species density due to hydrodynamic processes. This simulation from a precise configuration to a general conclusion shows how the spark formation is controlled by electron energy dissipation, and in particularly the fraction of this energy which dissipates as thermal energy and by the attachment process via the field redistribution.

Energy dissipation in clumpy magnetic clouds

Abstract: The dissipation rate of kinetic energy in clumpy, magnetic, molecular clouds is calculated. The analysis includes viscous dissipation by collisions between ions and neutral molecules for slow and rapid accelerations of clump and interclump gas, hydromagnetic shock dissipation in direct collisions between clumps, and shock dissipation in waves that steepen in the interclump medium. The transfer of clump kinetic energy to the external medium along Alfven waves is also discussed. Clumps are modeled by self-gravitating pieces inside self-gravitating clouds, with relative velocities that are either comparable to the virial-theorem velocity in the cloud or given by a velocity-separation relation for turbulence. Alfven wave reflection and transmission at clump-interclump boundaries are included.

Dissipative quantum tunneling at finite temperatures

Abstract: Finite temperatures are incorporated into the calculation of the tunneling rate in the presence of linear dissipation. A theory of finite-temperature tunneling is introduced which is based on the density matrix which provides an approximate description of the metastable state. Semiclassical functional integral methods are used to calculate the density matrix and the Wentzel-Kramers-Brillouin approximation is used to derive the tunnel current from the density matrix. Dissipation appropriate to superconducting quantum-interference devices is introduced into the calculation by the use of the existing model of a heat bath consisting of a prescribed distribution of harmonic oscillators linearly coupled to the tunneling variable. The finite-temperature tunnel escape rate obtained is of the form \ensuremath{\Gamma}=A exp(-S/\ensuremath{\Elzxh}). S is determined from the solution of a nonlinear integro-differential equation. An existing numerical technique was modified to achieve this. The quantity A is approximately evaluated.

Resistive wave dissipation on magnetic inhomogeneities Normal modes and phase mixing

Abstract: Numerical solutions of the linearized, resistive MHD equations indicate the presence of two characteristic forms of wave decay on magnetic inhomogeneities. Solutions for relatively long-wavelength disturbances and large values of the resistivity have the behavior of decaying normal modes. In the opposite limits, phase mixing becomes important, with the eventual build-up of large spatial gradients in which the resistive terms dominate. This composite behavior is shown to be conceptually consistent with analytic results, which predict that the complete solution consists of the sum of collective and noncollective contributions. The numerical simulations go beyond analytic theory by defining where each contribution prevails and computing wave decay when phase mixing is effective. The dispersion relation in the normal-mode regime is also determined analytically, with some approximations, and is in good agreement with the numerical solution. The decay time of the normal modes varies with Lundquist number at S1/6, while the phase-mixed decay time scales as S1/3.

Internal wave dissipation under sea ice

Abstract: The dissipation of internal wave energy in the turbulent boundary layer under pack ice is determined using a time-varying boundary layer model with an eddy coefficient closure scheme. The magnitude of the eddy coefficient is determined by the ice drift velocity, which is assumed greater than the rms water velocity induced by internal waves. The Arctic Ocean internal wave velocity spectrum is represented by a line spectrum with 44 rotary frequency components. The energy at a given frequency is set equal to the energy in a band about the frequency in the continuous spectrum. The dissipation spectrum is found to have an ω−2 shape. For an internal wave energy level representative of Arctic Ocean conditions (energy parameter r equal to 50 m2 cph) the total dissipation is 0.16 mW m−2. This corresponds to a dissipation time scale of 32 days and suggests that underice dissipation is important. The surface boundary layer dissipation process is unique to ice-covered regions, and the predicted amount of dissipation appears to be great enough to explain earlier observations that the internal wave energies in the Arctic Ocean are low compared to internal wave energies measured in ice-free oceans.

Stability of the Rijke thermoacoustic oscillation

Abstract: The stability limit of the Rijke oscillation induced from heated wires in a tube with air current is investigated on the basis of the analysis of heat transfer. By developing a general formulation for the thermoacoustic power generation, it is shown that the in‐phase component of the fluctuating heat release from a heater with the acoustic pressure can generate the acoustic power. The heat transfer response of an isothermal wire to the particle velocity of an acoustic wave is analyzed numerically by treating the flow as incompressible and two dimensional. The amplitude and phase of the fluctuating heat release are computed and displayed in graphs for various values of the air current velocity and the wire radius normalized by the angular frequency and the thermal diffusivity. The acoustic power generation from a heater wire is expressed in terms of an efficiency factor. It is found that the power generation can be maximized if both the normalized velocity of the air current and the normalized radius of the wire become around unity. By equating the acoustic power generation to the power dissipation in the tube, the limiting condition for the onset of oscillation is obtained for the steady heat input. The theoretical prediction to the stability limit is compared with available experimental data and the good agreement demonstrates a substantial verification of the present analysis.

Field distribution in a quantum Hall device

Abstract: The electric field strengths in a long rectangular device carrying a quantised Hall current are calculated. In the ideal system an analytic approximation for the field near the edge is obtained which is in agreement with the numerical results of MacDonald et al. (1983). It is pointed out that even a small departure of the Hall angle from pi /2 leads to a uniform field, and therefore current, across the system. Diamagnetic corrections are shown to be negligible. The fields in the source and drain are calculated, both for a two-dimensional electrode, for which an analytic solution is available, and for a three-dimensional electrode. In the three-dimensional case, most of the energy dissipation occurs within a distance l of two of the corners of the rectangle, where an expression for l is derived.

On the Stability of Soliton-Like Pulses in a Nonlinear Dispersive System with Instability and Dissipation

Abstract: The stability of various equilibrium solutions of a strongly dispersive nonlinear system with instability and dissipation is investigated both numerically and analytically. Periodic trains of soliton-like pulses are found to be stable when the distance between adjacent pulses becomes smaller than a critical value. This critical value is determined by linear stability analysis. A modulational type instability is also observed for a very long string of soliton-like pulses even when the fundamental distance is within the stable regime.

Causes and implications of noise in oceanic dissipation measurements

Abstract: Measurements of the rate of dissipation of turbulent kinetic energy using airfoil probes mounted on Camel profilers show a constant lower limit of about −7 W m −3 . A series of experiments conducted in Jervis Inlet, British Columbia, indicated that this value represents the noise in the measurement and is attributed to vehicular accelerations from hydrodynamically induced forces on the instrument body. Because a large fraction of observations are at the noise level, ambient dissipation rates in the ocean must be −7 W m −3 .

Rotor with permanent magnets for an electrical machine

Abstract: A rotor for an electrical machine with tangentially oriented permanent magnets between which pole pieces are arranged, the rotor featuring radial axes of the arcs of the pole pieces arranged between the radial axes of the pole piece cores and the radial axes of the magnets, the above arcs partially and unilaterally overlapping the magnets. The longitudinal axes of the pole piece arcs alternate in position to form a broken line while the longitudinal axes of the pole piece cores and of the magnets are aligned to form continuous lines. This reduces the magnetic dissipation flux and the unevenness of rotation of the machine.