Showing papers on "Dissipation published in 1999"

The Energy Dissipation Rate of Supersonic, Magnetohydrodynamic Turbulence in Molecular Clouds

Abstract: Molecular clouds have broad line widths, which suggests turbulent supersonic motions in the clouds. These motions are usually invoked to explain why molecular clouds take much longer than a free-fall time to form stars. Classically, it was thought that supersonic hydrodynamical turbulence would dissipate its energy quickly but that the introduction of strong magnetic fields could maintain these motions. A previous paper has shown, however, that isothermal, compressible MHD and hydrodynamical turbulence decay at virtually the same rate, requiring that constant driving occur to maintain the observed turbulence. In this paper, direct numerical computations of uniform, randomly driven turbulence with the ZEUS astrophysical MHD code are used to derive the value of the energy-dissipation coefficient, which is found to be with ηv = 0.21/π, where vrms is the root-mean-square (rms) velocity in the region, Ekin is the total kinetic energy in the region, m is the mass of the region, and is the driving wavenumber. The ratio τ of the formal decay time Ekin/kin of turbulence to the free-fall time of the gas can then be shown to be where Mrms is the rms Mach number, and κ is the ratio of the driving wavelength to the Jeans wavelength. It is likely that κ < 1 is required for turbulence to support gas against gravitational collapse, so the decay time will probably always be far less than the free-fall time in molecular clouds, again showing that turbulence there must be constantly and strongly driven. Finally, the typical decay time constant of the turbulence can be shown to be where is the driving wavelength.

Dissipation range dynamics: Kinetic Alfvén waves and the importance of β e

Abstract: In a previous paper we argued that the damping of obliquely propagating kinetic Alfven waves, chiefly by resonant mechanisms, was a likely explanation for the formation of the dissipation range for interplanetary magnetic field fluctuations. This suggestion was based largely on observations of the dissipation range at 1 AU as recorded by the Wind spacecraft. We pursue this suggestion here with both a general examination of the damping of obliquely propagating kinetic Alfven waves and an additional examination of the observations. We explore the damping rates of kinetic Alfven waves under a wide range of interplanetary conditions using numerical solutions of the linearized Maxwell-Vlasov equations and demonstrate that these waves display the nearly isotropic dissipation properties inferred from the previous paper. Using these solutions, we present a simple model to predict the onset of the dissipation range and compare these predictions to the observations. In the process we demonstrate that electron Landau damping plays a significant role in the damping of interplanetary magnetic field fluctuations which leads to significant heating of the thermal electrons.

Energy‐conserving and decaying Algorithms in non‐linear structural dynamics

Abstract: A generalized formulation of the Energy-Momentum Methodwill be developed within the framework of the GeneralizedMethodwhich allows at the same time guaranteed conservation or decay of total energy and controllable numerical dissipation of unwanted high frequency response. Furthermore, the latter algorithm will be extended by the consistently integrated constraints of energy and momentum conservation originally derived for the Constraint Energy-Momentum Algorithm. The goal of this general approach of implicit energyconserving and decaying time integration schemes is, to compare these algorithms on the basis of an equivalent notation by the means of an overall algorithmic design and hence to investigate their numerical properties. Numerical stability and controllable numerical dissipation of high frequencies will be studied in application to non-linear structural dynamics. Among the methods considered will be the Newmark Method, the classical -methods, the Energy-Momentum Methodwith and without numerical dissipation, the Constraint EnergyMomentum Algorithm and the Constraint Energy Method. Copyright ? 1999 John Wiley & Sons, Ltd.

A Macroscopic Turbulence Model for Flow in a Porous Medium

Abstract: A complete set of macroscopic two-equation turbulence model equations has been established for analyzing turbulent flow and heat transfer within porous media. The volume-averaged transport equations for the mass, momentum, energy, turbulence kinetic energy and its dissipation rate were derived by spatially averaging the Reynolds-averaged set of the governing equations. The additional terms representing production and dissipation of turbulence kinetic energy are modeled introducing two unknown model constants, which are determined from a numerical experiment using a spatially periodic array. In order to investigate the validity of the present macroscopic turbulence model, a macroscopically unidirectional turbulent flow through an infinite array of square rods is considered from both micro- and macroscopic-views

Droplet Spreading: Partial Wetting Regime Revisited

Abstract: We study the time evolution of a sessile liquid droplet, which is initially put onto a solid surface in a nonequilibrium configuration and then evolves towards its equilibrium shape. We adapt here the standard approach to the dynamics of mechanical dissipative systems, in which the driving force, i.e., the gradient of the system's Lagrangian function, is balanced against the rate of the dissipation function. In our case, the driving force is the loss of the droplet's free energy due to the increase of its base radius, whereas the dissipation occurs because of viscous flows in the core of the droplet and frictional processes in the vicinity of the advancing contact line, associated with attachment of fluid particles to solid. Within this approach, we derive closed-form equations for the evolution of the droplet's base radius and specify regimes at which different dissipation channels dominate. Our analytical predictions compare very well with experimental data.

Energy transduction of isothermal ratchets: generic aspects and specific examples close to and far from equilibrium.

Abstract: We study the energetics of isothermal ratchets which are driven by a chemical reaction between two states, and operate in contact with a single heat bath of constant temperature. We discuss generic aspects of energy transduction such as Onsager relations in the linear response regime as well as the efficiency and dissipation close to and far from equilibrium. In the linear response regime where the system operates reversibly, the efficiency is in general nonzero. Studying the properties for specific examples of energy landscapes and transitions, we observe in the linear response regime that the efficiency can have a maximum as a function of temperature. Far from equilibrium in the fully irreversible regime, we find a maximum of the efficiency with values larger than in the linear regime for an optimal choice of the chemical driving force. We show that the corresponding efficiencies can be of the order of 50%. A simple analytic argument allows us to estimate the efficiency in this irreversible regime for small external forces.

Two-dimensional navier-stokes simulation of breaking waves

Abstract: Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier–Stokes equation. The numerical modeling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Capillary effects are taken into account such as a nonisotropic stress tensor concentrated near the interface. Results concerning the time evolution of liquid–gas interface and velocity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles. Breaking processes including overturning, splash-up and gas entrainment, and breaking induced vortex-like motion beneath the surface and energy dissipation, are presented and discussed. It is found that strong vorticities are generated during the breaking process, and that more than 80% of the total pre-breaking wave energy is dissipated within three wave periods. The numerical results are compared with some laboratory measurements, and a favorable agreement is found.

A generalized Korteweg-de Vries model of internal tide transformation in the coastal zone

Abstract: A nonlinear model is developed, based on the rotated-modified extended Korteweg-de Vries (reKdV) equation, of the evolution of an initially sinusoidal long wave in the coastal zone, representing an internal tide, into nonlinear waves including internal solitary waves. The coefficients of the basic equation are calculated using observed conditions for the north west shelf (NWS) of Australia. The roles of both quadratic and cubic nonlinearity, the Earth's rotation, and frictional dissipation are discussed. The combined action of nonlinearity and rotation leads to a number of intersting features in the wave form including solitons of both polarities, “thick” solitons, and sharp waves with steep fronts. It is shown that rotation is important for modelling the evolution of the internal tide, even for the relatively low latitude on the NWS of 20°S. Rotation increases the phase speed of the long internal tide, reduces the number of internal solitary waves that form from a long wave, and changes the form of the waves. The effects of nonlinearity on the vertical modal structure of the internal waves are also discussed. Results of numerical simulations are compared with current and temperature observations of the internal wave field on the NWS which show many of the features produced by the generalized KdV model.

Electron magnetohydrodynamic turbulence

Abstract: Electron magnetohydrodynamic (EMHD) turbulence is studied in two- and three-dimensional (2D and 3D) systems. Results in 2D are particularly noteworthy. Energy dissipation rates are found to be independent of the diffusion coefficients. The energy spectrum follows a k−5/3 law for kde>1 and k−7/3 for kde<1, which is consistent with a local spectral energy transfer independent of the linear wave properties, contrary to magnetohydrodynamic (MHD) turbulence, where the Alfven effect dominates the transfer dynamics. In 3D spectral properties are similar to those in 2D.

Coupled sea surface-atmosphere model: 1. Wind over waves coupling

Abstract: A wind over waves coupling scheme to be used in a coupled wind waves-atmosphere model is described. The approach is based on the conservation of momentum in the marine atmospheric surface boundary layer and allows to relate the sea drag to the properties of the sea surface and the properties of the momentum exchange at the sea surface. Assumptions concerning the local balance of the turbulent kinetic energy production due to the mean and the wave-induced motions, and its dissipation, as well as the local balance between production and dissipation of the mean wave-induced energy allow to reduce the problem to two integral equations: the resistance law above waves and the coupling parameter, which are effectively solved by iterations. To calculate the wave-induced flux, the relation of Plant [1982] for the growth rate parameter is used. However, it is shown by numerical simulations that the local friction velocity rather than the total friction velocity has to be used in this relation, which makes the growth rate parameter dependent on the coupling parameter. It is shown that for light to moderate wind a significant part of the surface stress is supported by viscous drag. This is in good agreement with direct measurements under laboratory conditions. The short gravity and capillary-gravity waves play a significant role in extracting momentum and are strongly coupled with the atmosphere. This fact dictates the use of the coupled short waves-atmosphere model in the description of the energy balance of those waves.

Bent- beam electro- thermal a ctua tors for high force applications

Abstract: This paper describes in-plane microactuators fabricated by standard microsensor materials and processes that can generate forces upto about a milli-newton. They operate by leveraging the deformations produce by localized thermal stresses. Analytical and finite element models of device performance are presented along with measured results of fabricated devices using electroplated Ni, LPCVD polysilicon, and p++ Si as structural materials. A maskless process extension for incorporating thermal and electrical isolation is outlined. Test results show that static displacements of =lo pm can be achieved with power dissipation of =lo0 mW, and output forces >300 pN can be achieved with input power <250 mW. It is also shown that cascaded devices offer a 4X improvement in displacement. The displacements are rectilinear, and the output forces generated are lox-1OOX higher than those available from other comparable options. This performance is achieved at much lower drive voltages than necessary for electrostatic actuation, indicating that bentbeam thermal actuators are suitable for integration in a variety of microsystems.

External control of dissipation in a nanometer-scale radiofrequency mechanical resonator

Abstract: We demonstrate a technique by which the quality factor of a magnetically-actuated mechanical resonator is controlled by an external electrical circuit. Modulation of this parameter is achieved by local variation of the electrical impedance presented to the resonator at its resonance frequency. We describe a theory that explains this result as arising from eddy currents in the external electrical circuit, which are driven by electromotive forces generated through motion of the resonator in the applied magnetic field. The theory is in good agreement with the induced variation in quality factor that we observe.

Dissipation Effects on the Superconductor-Insulator Transition in 2D Superconductors

Abstract: Results on the superconductor to insulator transition in two-dimensional films are analyzed in terms of a coupling of the system to a dissipative bath. Upon lowering the temperature the parameter that controls this coupling becomes relevant and a wide range of metallic phase is recovered.

Spontaneous hole–clump pair creation

Abstract: Numerical simulations and quantitative theoretical explanations are presented for the spontaneous formation of a hole–clump pair in phase space. The equilibrium is close to the linear threshold for instability and the destabilizing resonant kinetic drive is nearly balanced by either extrinsic dissipation or a second stabilizing resonant kinetic component. The hole and clump, each support a nonlinear wave where the trapping frequency of the particles is comparable to the kinetic linear growth rate from the destabilizing species alone. The power dissipated is balanced by energy extracted by trapped particles locked to the changing wave-phase velocities. With extrinsic dissipation, phase space structures always form just above the linear instability threshold. With a stabilizing kinetic component, an electrostatic interaction is considered with varying mass ratios of the stabilizing and destabilizing species together with collisional effects. With these input parameters, various nonlinear responses arise, only some of which sweep in frequency.

On the thermomechanics of shape memory wires

Abstract: The thermomechanical behavior of a shape memory wire is modeled based on a theory that takes cognizance of the fact that the body can possess multiple natural configurations [1]. The constitutive equations are developed by first constructing the form of the Helmholtz potential (based on different modes of energy storage), and dissipation mechanisms. The internal energy includes contributions from the strain energy, the latent energy, the interfacial energy and thermal energy. The entropy of the system includes the"entropy jump" associated with the phase transition.¶The role of the rate of mechanical dissipation as a mechanism for entropy generation and its importance in describing the hysteretic behavior is brought out by considering the difference between hysteretic and non-hysteretic (dissipation-less) behavior.¶Finally, simple linear or quadratic forms are assumed for the various constitutive functions and the full shape memory response is modeled. A procedure for the determination of the constants is also indicated and the constants for two systems (CuZnAl and NiTi) are calculated from published experimental data (see [2, 3]). The predictions of the theory show remarkable agreement with the experimental data. However, some of the results predicted by the theory are different from the experimental results reported in Huo and Muller [2] We discuss some of the issues regarding this discrepancy and show that there appears to be some internal inconsistency between the experimental data reported in Figure 6 and Figure 9 of Huo and Muller [2] (provided they represent the same sample).

Heating and cooling of protons by turbulence-driven ion cyclotron waves in the fast solar wind

Abstract: The effects of parallel propagating nondispersive ion cyclotron waves on the solar wind plasma are investigated in an attempt to reproduce the observed proton temperature anisotropy, namely, Tp⊥ ≫ Tp‖ in the inner corona and Tp⊥ < Tp‖ at 1 AU. Low-frequency Alfven waves are assumed to carry most of the energy needed to accelerate and heat the fast solar wind. The model calculations presented here assume that nonlinear cascade processes, at the Kolmogorov and Kraichnan dissipation rates, transport energy from low-frequency Alfven waves to the ion cyclotron resonant range. The energy is then picked up by the plasma through the resonant cyclotrou interaction. While the resonant interaction determines how the heat is distributed between the parallel and perpendicular degrees of freedom, the level of turbulence determines the net dissipation. Ion cyclotron waves are found to produce a significant temperature anisotropy starting in the inner corona, and to limit the growth of the temperature anisotropy in interplanetary space. In addition, this mechanism heats or cools protons in the direction parallel to the magnetic field. While cooling in the parallel direction is dominant, heating in the parallel direction occurs when Tp⊥ ≫ Tp‖. The waves provide the mechanism for the extraction of energy from the parallel direction to feed into the perpendicular direction. In our models, both Kolmogorov and Kraichnan dissipation rates yield Tp⊥ ≫ Tp‖ in the corona, in agreement with inferences from recent ultraviolet coronal measurements, and predict temperatures at 1 AU which match in situ observations. The models also reproduce the inferred rapid acceleration of the fast solar wind in the inner corona and flow speeds and particle fluxes measured at 1 AU. Since this mechanism does not provide direct energy to the electrons, and the electron-proton coupling is not sufficient to heat the electrons to temperatures at or above 106 K, this model yields electron temperatures which are much cooler than those currently inferred from observations.

Dissipative dynamics of the Jaynes-Cummings model in the dispersive approximation: Analytical results

Abstract: We present the time evolution of a two-level atom interacting dispersively with an electromagnetic field in a dissipative cavity. We investigate the influence of dissipation on the entanglement of the two subsystems $(\mathrm{atom}+\mathrm{field}).$ Simple but realistic, the model displays several nontrivial quantum features, which emerge when an environment is taken into account: the cavity is shown to have practically no influence in the coherence properties of the field from the qualitative point of view. On the other hand, although the atom is not directly coupled to the cavity modes, its coherent properties are strongly influenced by dissipation both qualitatively as well as quantitatively.

Near critical reflection of internal waves

Abstract: Using a matched asymptotic expansion we analyse the two-dimensional, near-critical reflection of a weakly nonlinear internal gravity wave from a sloping boundary in a uniformly stratified fluid. Taking a distinguished limit in which the amplitude of the incident wave, the dissipation, and the departure from criticality are all small, we obtain a reduced description of the dynamics. This simplification shows how either dissipation or transience heals the singularity which is presented by the solution of Phillips (1966) in the precisely critical case. In the inviscid critical case, an explicit solution of the initial value problem shows that the buoyancy perturbation and the alongslope velocity both grow linearly with time, while the scale of the reflected disturbance is reduced as 1/t. During the course of this scale reduction, the stratification is 'overturned' and the Miles-Howard condition for stratified shear flow stability is violated. However, for all slope angles, the 'overturning' occurs before the Miles-Howard stability condition is violated and so we argue that the first instability is convective. Solutions of the simplified dynamics resemble certain experimental visualizations of the reflection process. In particular, the buoyancy field computed from the analytic solution is in good agreement with visualizations reported by Thorpe & Haines (1987). One curious aspect of the weakly nonlinear theory is that the final reduced description is a linear equation (at the solvability order in the expansion all of the apparently resonant nonlinear contributions cancel amongst themselves). However, the reconstructed fields do contain nonlinearly driven second harmonics which are responsible for an important symmetry breaking in which alternate vortices differ in strength and size from their immediate neighbours.

Planar measurements of the full three-dimensional scalar dissipation rate in gas-phase turbulent flows

Abstract: A simultaneous planar Rayleigh scattering and planar laser-induced fluorescence (PLIF) technique is described which allows planar measurement of the full three-dimensional scalar gradient, ∇C (x, t), and scalar energy dissipation rate, χ≡D ∇C·∇C, in gas-phase turbulent flows. The conserved scalar used is the jet fluid concentration, where the jet consists of propane and seeded acetone. The propane serves as the primary Rayleigh scattering medium, while the acetone is used for fluorescence. For a given amount of available laser energy, this planar Rayleigh scattering/PLIF technique yields much higher signals levels than would, for example, a two-plane Rayleigh scattering technique. By applying the current technique to a single spatial plane, the errors incurred in measuring a spatial derivative across distinct planes are quantified. The errors are found to be well described by a random distribution, and the magnitude of these errors is found to be smaller than the magnitude of significant events in the true scalar gradient fields. Sample results for the fields of the three-dimensional scalar gradient and scalar energy dissipation in a planar turbulent jet, with outer scale Reynolds numbers between 3200 and 8400, are shown, demonstrating the applicability of these measurements to analyses of the fine scale mixing in turbulent flows. The application of these measurements to determination of the scaling properties of the dissipation rate is also discussed.

Fluctuation-dissipation model for synthesis of superheavy elements

Abstract: Fusion-fission dynamics in superheavy elements is investigated by an approximate fluctuation-dissipation model, i.e., a diffusion model in the deformation space, assuming that the kinetic energy of the incident ion dissipates immediately after the contact. The probability accumulated inside the fission barrier is calculated by the one-dimensional Smoluchowski equation taking account of the temperature dependence of the shell correction energy. A new mechanism for an optimum condition is found as a compromise of two conflicting requirements: higher incident energy for larger fusion probability and lower excitation energy of compound nuclei for larger survival probability. Enhancements of the residue cross sections at the optimum condition are obtained for the cases in which the cooling is quick to restore the shell correction energy, combined with slow fissioning motion due to the strong friction. With symmetric combinations of incident ions, the (HI, $3\ensuremath{-}4n)$ channels show the enhancement.

Evolution and modelling of subgrid scales during rapid straining of turbulence

Abstract: The response, evolution, and modelling of subgrid-scale (SGS) stresses during rapid straining of turbulence is studied experimentally. Nearly isotropic turbulence with low mean velocity and Rλ˜290 is generated in a water tank by means of spinning grids. Rapid straining (axisymmetric expansion) is achieved with two disks pushed towards each other at rates that for a while generate a constant strain rate. Time-resolved, two-dimensional velocity measurements are performed using cinematic PIV. The SGS stress is subdivided to a stress due to the mean distortion, a cross-term (the interaction between the mean and turbulence), and the turbulent SGS stress τ(T)ij. Analysis of the time evolution of τ(T)ij at various filter scales shows that all scales are more isotropic than the prediction of rapid distortion theory, with increasing isotropy as scales decrease. A priori tests show that rapid straining does not affect the high correlation and low square-error exhibited by the similarity model. Analysis of the evolution of total SGS energy dissipation reveals, surprisingly, that the Smagorinsky model with a constant coefficient (determined from isotropic turbulence data) underpredicts the dissipation during rapid straining. While the partial dissipation −〈τ(T)ij S˜ij〉 (due only to the turbulent part of the stress) is overpredicted by the Smagorinsky model, addition of the cross-terms reverses the trend. The similarity model with a constant coefficient appropriate for isotropic turbulence, on the other hand, overpredicts SGS dissipation. Owing to these opposite trends a linear combination of both models (mixed model) provides better prediction of SGS dissipation during rapid straining. However, the mixed model with coefficients determined from dissipation balance underpredicts the SGS stress.

Statistics of shear-induced rearrangements in a two-dimensional model foam.

Abstract: Under steady shear, a foam relaxes stress through intermittent rearrangements of bubbles accompanied by sudden drops in the stored elastic energy. We use a simple model of foam that incorporates both elasticity and dissipation to study the statistics of bubble rearrangements in terms of energy drops, the number of nearest neighbor changes, and the rate of neighbor-switching $(T1)$ events. We do this for a two-dimensional system as a function of system size, shear rate, dissipation mechanism, and gas area fraction. We find that for dry foams, there is a well-defined quasistatic limit at low shear rates where localized rearrangements occur at a constant rate per unit strain, independent of both system size and dissipation mechanism. These results are in good qualitative agreement with experiments on two-dimensional and three-dimensional foams. In contrast, we find for progessively wetter foams that the event size distribution broadens into a power law that is cut off only by system size. This is consistent with criticality at the melting transition.