Showing papers on "Dissipation published in 2003"

Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box

Abstract: High-resolution direct numerical simulations (DNSs) of incompressible homogeneous turbulence in a periodic box with up to 40963 grid points were performed on the Earth Simulator computing system. DNS databases, including the present results, suggest that the normalized mean energy dissipation rate per unit mass tends to a constant, independent of the fluid kinematic viscosity ν as ν→0. The DNS results also suggest that the energy spectrum in the inertial subrange almost follows the Kolmogorov k−5/3 scaling law, where k is the wavenumber, but the exponent is steeper than −5/3 by about 0.1.

Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems

Abstract: We study the entropy stability of difference approximations to nonlinear hyperbolic conservation laws, and related time-dependent problems governed by additional dissipative and dispersive forcing terms. We employ a comparison principle as the main tool for entropy stability analysis, comparing the entropy production of a given scheme against properly chosen entropy-conservative schemes.To this end, we introduce general families of entropy-conservative schemes, interesting in their own right. The present treatment of such schemes extends our earlier recipe for construction of entropy-conservative schemes, introduced in Tadmor (1987b). The new families of entropy-conservative schemes offer two main advantages, namely, (i) their numerical fluxes admit an explicit, closed-form expression, and (ii) by a proper choice of their path of integration in phase space, we can distinguish between different families of waves within the same computational cell; in particular, entropy stability can be enforced on rarefactions while keeping the sharp resolution of shock discontinuities.A comparison with the numerical viscosities associated with entropy-conservative schemes provides a useful framework for the construction and analysis of entropy-stable schemes. We employ this framework for a detailed study of entropy stability for a host of first- and second-order accurate schemes. The comparison approach yields a precise characterization of the entropy stability of semi-discrete schemes for both scalar problems and systems of equations.We extend these results to fully discrete schemes. Here, spatial entropy dissipation is balanced by the entropy production due to time discretization with a suffciently small time-step, satisfying a suitable CFL condition. Finally, we revisit the question of entropy stability for fully discrete schemes using a different approach based on homotopy arguments. We prove entropy stability under optimal CFL conditions.

Angular Momentum Transport by MHD Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability

Abstract: The saturation level of the magnetorotational instability (MRI) is investigated using three-dimensional MHD simulations. The shearing box approximation is adopted and the vertical component of gravity is ignored, so that the evolution of the MRI is followed in a small local part of the disk. We focus on the dependence of the saturation level of the stress on the gas pressure, which is a key assumption in the standard alpha disk model. From our numerical experiments it is found that there is a weak power-law relation between the saturation level of the Maxwell stress and the gas pressure in the nonlinear regime; the higher the gas pressure, the larger the stress. Although the power-law index depends slightly on the initial field geometry, the relationship between stress and gas pressure is independent of the initial field strength, and is unaffected by Ohmic dissipation if the magnetic Reynolds number is at least 10. The relationship is the same in adiabatic calculations, where pressure increases over time, and nearly-isothermal calculations, where pressure varies little with time. Our numerical results are qualitatively consistent with an idea that the saturation level of the MRI is determined by a balance between the growth of the MRI and the dissipation of the field through reconnection. The quantitative interpretation of the pressure-stress relation, however, may require advances in the theoretical understanding of non-steady magnetic reconnection.

Nonlinear internal waves in the South China Sea: Observation of the conversion of depression internal waves to elevation internal waves

Abstract: [1] The conversion of depression nonlinear internal solitons to elevation internal waves has been observed twice at the South China Sea continental shelf break. Shipboard X-band radar, tow-yo CTD, ADCP and high frequency acoustic flow visualization of the process are presented. The data focuses on up slope propagation of depression internal solitons from a water depth of ∼264 m to a water depth of ∼110 m. Dissipation by large amplitude shear instabilities was observed. The kinetic energy density was found to be a decreasing monotonic function of range with an energy dissipation rate coefficient of 0.063 km−1. The rate of energy dissipation over the ∼16.5 km soliton propagation path was 0.17 W/m/m. Simple numerical models of the waveform evolution are qualitatively compared to the observations. The observations, extracted scale parameters and dissipation rates should be useful for testing a variety of evolution equation representations of internal soliton propagation.

Alfvenic turbulence in the extended solar corona: kinetic effects and proton heating

Abstract: We present a model of magnetohydrodynamic (MHD) turbulence in the extended solar corona that contains the effects of collisionless dissipation and anisotropic particle heating. Recent observations have shown that preferential heating and acceleration of positive ions occur in the first few solar radii of the high-speed solar wind. Measurements made by the Ultraviolet Coronagraph Spectrometer aboard SOHO have revived interest in the idea that ions are energized by the dissipation of ion cyclotron resonant waves, but such high-frequency (i.e., small-wavelength) fluctuations have not been observed. A turbulent cascade is one possible way of generating small-scale fluctuations from a preexisting population of low-frequency MHD waves. We model this cascade as a combination of advection and diffusion in wavenumber space. The dominant spectral transfer occurs in the direction perpendicular to the background magnetic field. As expected from earlier models, this leads to a highly anisotropic fluctuation spectrum with a rapidly decaying tail in the parallel wavenumber direction. The wave power that decays to high enough frequencies to become ion cyclotron resonant depends on the relative strengths of advection and diffusion in the cascade. For the most realistic values of these parameters, however, there is insufficient power to heat protons and heavy ions. The dominant oblique fluctuations (with dispersion properties of kinetic Alfven waves) undergo Landau damping, which implies strong parallel electron heating. We discuss the probable nonlinear evolution of the electron velocity distributions into parallel beams and discrete phase-space holes (similar to those seen in the terrestrial magnetosphere), which can possibly heat protons via stochastic interactions.

Energy dissipation mechanisms in carbon nanotube oscillators.

Abstract: Multiwalled carbon nanotubes (MWNTs) have been proposed as candidates for nanoscale molecular bearings, springs, and oscillators [1‐3]. Zheng and Jiang have estimated that these nano-oscillators can have frequencies far beyond 1 GHz, pointing to a path for creating nanomachines operating in the gigahertz range [3], which has been viewed as one of the milestones on the road map of molecular manufacturing [4,5]. Despite unlimited prospects of applications for low-friction nanobearings, nanosprings, and nano-oscillators, performance, wear and load-bearing properties of fundamental components of nanomachines are largely not understood. We investigate in this Letter possible scenarios for realizing nearly frictionless and superefficient nano-oscillators. Our aim is to provide an understanding of nanoscale motioninduced heating mechanisms and to propose means for reducing frictional effects that hinder oscillator performance and efficiency. The friction phenomenon, or the energy dissipation between two contacting parties which slide with respect to each other, is in general taken to denote the conversion of orderly translational energies into disorderly vibrational energies. In this Letter, using molecular dynamics (MD), double-walled carbon nanotube (DWNT) oscillators of various lengths and constructions are compared for their oscillation resilience under motion-induced selfheating. We show that friction in these oscillators is primarily associated with an off-axial rocking motion of the inner nanotube and a wavy deformation of the outer nanotube, which may or may not occur, depending upon both configurations of individual oscillators and initial system energies, and that oscillation is nearly frictionless in the absence of the rocking motion and the wavy deformation. Our model DWNT has an inner tube and an outer tube of chiralities (5; 0) and (8; 8), respectively, and an intertube spacing � 3:4 � A, which is also the spacing between adjacent sheets in graphite. Both ends of the outer wall are open and those of the inner wall are closed. Structure optimization and simulation of the two-tube oscillators are carried out using the CHARMM force field [6]. A time step of 1 fs is used for all simulations. A precise description of interactions between graphene sheets may include interlayer electronic delocalization [7], although the van der Waals forces are dominant for our purpose here. To check the accuracy of the force field, the radial breathing mode frequency of an (8; 8) carbon nanotube is calculated to be 232 cm � 1 in good agreement with that from observed Raman lines, 211 cm � 1 [8]. We define the relative kinetic energy of two tubes

Measuring intense rotation and dissipation in turbulent flows

Abstract: Turbulent flows are highly intermittent--for example, they exhibit intense bursts of vorticity and strain. Kolmogorov theory describes such behaviour in the form of energy cascades from large to small spatial and temporal scales, where energy is dissipated as heat. But the causes of high intermittency in turbulence, which show non-gaussian statistics, are not well understood. Such intermittency can be important, for example, for enhancing the mixing of chemicals, by producing sharp drops in local pressure that can induce cavitation (damaging mechanical components and biological organisms), and by causing intense vortices in atmospheric flows. Here we present observations of the three components of velocity and all nine velocity gradients within a small volume, which allow us to determine simultaneously the dissipation (a measure of strain) and enstrophy (a measure of rotational energy) of a turbulent flow. Combining the statistics of all measurements and the evolution of individual bursts, we find that a typical sequence for intense events begins with rapid strain growth, followed by rising vorticity and a final sudden decline in stretching. We suggest two mechanisms which can produce these characteristics, depending whether they are due to the advection of coherent structures through our observed volume or caused locally.

Systems and methods for modifying an ice-to-object interface

Abstract: Systems and methods for thermally modifying an ice-to-object interface. One system includes a power supply configured to generate a magnitude of power. The magnitude of the power is sufficient to melt an interfacial layer of ice at the interface; typically the interfacial layer has a thickness in a range one micron to one millimeter. A controller may be used to limit the duration in which power supply generates the magnitude of the power, to limit unneeded heat energy dissipation into the environment. Modulating the pulsed heating energy to the interface modifies a coefficient of friction between the object and the ice.

The dynamics of breaking progressive interfacial waves

Abstract: Two- and three-dimensional numerical simulations are performed to study interfacial waves in a periodic domain by imposing a source term in the horizontal momentum equation. Removing the source term before breaking generates a stable interfacial wave. Continued forcing results in a two-dimensional shear instability for waves with thinner interfaces, and a convective instability for waves with thick interfaces. The subsequent three-dimensional dynamics and mixing is dominated by secondary cross-stream convective rolls which account for roughly half of the total dissipation of wave energy. Dissipation and mixing are maximized when the interface thickness is roughly the same size as the amplitude of the wave, while the mixing efficiency is a weak function of the interface thickness. The maximum instantaneous mixing efficiency is found to be 0.36 ± 0.02.

Rheology of suspensions with high particle inertia and moderate fluid inertia

Abstract: We consider the averaged flow properties of a suspension in which the Reynolds number based on the particle diameter is finite so that the inertia of the fluid phase is important. When the inertia of the particles is sufficiently large, their trajectories, between successive particle collisions, are only weakly affected by the interstitial fluid. If the particle collisions are nearly elastic the particle velocity distribution is close to an isotropic Maxwellian. The rheological properties of the suspension can then be determined using kinetic theory, provided that one knows the granular temperature (energy contained in the particle velocity fluctuations). This energy results from a balance of the shear work with the loss due to the viscous dissipation in the interstitial fluid and the dissipation due to inelastic collisions. We use lattice-Boltzmann simulations to calculate the viscous dissipation as a function of particle volume fraction and Reynolds number (based on the particle diameter and granular temperature). The Reynolds stress induced in the interstitial fluid by the random motion of the particles is also determined. We also consider the case where the interstitial fluid is moving relative to the particles, as would occur if the particles experienced an external body force. Owing to the nonlinearity of the equations of motion for the interstitial fluid, there is a coupling between the viscous dissipation caused by the fluctuating motion of the particles and the drag associated with a mean relative motion of the two phases, and this coupling is explored by computing the dissipation and mean drag for a range of values of the Reynolds numbers based on the mean relative velocity and the granular temperature.

Performance of a Saturation-Based Dissipation-Rate Source Term in Modeling the Fetch-Limited Evolution of Wind Waves

Abstract: A new formulation of the spectral dissipation source term Sds for wind-wave modeling applications is investigated. This new form of Sds is based on a threshold behavior of deep-water wave-breaking onset associated with nonlinear wave-group modulation. It is expressed in terms of the azimuth-integrated spectral saturation, resulting in a nonlinear dependence of dissipation rates on the local wave spectrum. Validation of the saturation-based Sds is made against wave field parameters derived from observations of fetch-limited wind-wave evolution. Simulations of fetch-limited growth are made with a numerical model featuring an exact nonlinear form of the wave–wave-interactions source term Snl. For reference, the performance of this saturation-based Sds is compared with the performance of the wave-dissipation source-term parameterization prescribed for the Wave Modeling Project (WAM) wind-wave model. Calculations of integral spectral parameters using the saturation-based model for Sds agree closely wi...

Swell Transformation across the Continental Shelf. Part I: Attenuation and Directional Broadening

Abstract: Extensive wave measurements were collected on the North Carolina–Virginia continental shelf in the autumn of 1999. Comparisons of observations and spectral refraction computations reveal strong cross-shelf decay of energetic remotely generated swell with, for one particular event, a maximum reduction in wave energy of 93% near the Virginia coastline, where the shelf is widest. These dramatic energy losses were observed in light-wind conditions when dissipation in the surface boundary layer caused by wave breaking (whitecaps) was weak and wave propagation directions were onshore with little directional spreading. These observations suggest that strong dissipation of wave energy takes place in the bottom boundary layer. The inferred dissipation is weaker for smaller-amplitude swells. For the three swell events described here, observations are reproduced well by numerical model hindcasts using a parameterization of wave friction over a movable sandy bed. Directional spectra that are narrow off the s...

Effects of wave‐current interaction on rip currents

Abstract: [1] The time evolution of rip currents in the nearshore is studied by numerical experiments. The generation of rip currents is due to waves propagating and breaking over alongshore variable topography. Our main focus is to examine the significance of wave-current interaction as it affects the subsequent development of the currents, in particular when the currents are weak compared to the wave speed. We describe the dynamics of currents using the shallow water equations with linear bottom friction and wave forcing parameterized utilizing the radiation stress concept. The slow variations of the wave field, in terms of local wave number, frequency, and energy (wave amplitude), are described using the ray theory with the inclusion of energy dissipation due to breaking. The results show that the offshore directed rip currents interact with the incident waves to produce a negative feedback on the wave forcing, hence to reduce the strength and offshore extent of the currents. In particular, this feedback effect supersedes the bottom friction such that the circulation patterns become less sensitive to a change of the bottom friction parameterization. The two physical processes arising from refraction by currents, bending of wave rays and changes of wave energy, are both found to be important. The onset of instabilities of circulations occurs at the nearshore region where rips are “fed,” rather than offshore at rip heads as predicted with no wave-current interaction. The unsteady flows are characterized by vortex shedding, pairing, and offshore migration. Instabilities are sensitive to the angle of wave incidence and the spacing of rip channels.

Attitude Stability Criteria for Dual Spin Spacecraft

Abstract: Attitude stability eriteria are developed for "dual spin" spacecraft, which consist of two primary bodies capable of unlimited relative rotation about a common axis. Such vehieles, typified in existing hardware by the Orbiting Solar Observatory (OSO) satellites, have applicability to missions for which the simplicity, reliability, and longevity of spin stabilization combine with a requirement for unidirectional pointing of a component, such as an antenna or a solar panel. The utility of dual spin systems is substantially increased by the results of attitude stability analysis, which reveals the possibility of obtaining passive stable spin-axis attitude by spinning a vehicle about its axis of greatest or least inertia, providing only that an effective energy dissipation device is attaced to a counter-rotating platform which has greatly reduced "spin." This result is coutrary to common interpretation of the familiar "major axis spin" requirement for stability, according to which energy dissipation in a vchicle rotating about its axis of least inertia must produce instability. Stability eriteria are developed first by Routhian analysis of a system with energy dissipation capability in only one of the two primary bodies, and subsequently in more general (but less rigorous) terms for a fully dissipative vehiele. Numerical integration and model studies provide corroboration.

The structure of fine-scale scalar mixing in gas-phase planar turbulent jets

Abstract: Fine-scale scalar mixing in gas-phase planar turbulent jets is studied using measurements of three-component scalar gradient and scalar energy dissipation rate fields. Simultaneous planar Rayleigh scattering and planar laser-induced fluorescence, applied in parallel planes, yield the three-dimensional scalar field measurements. The spatial resolution is sufficient to permit differentiation in all three spatial directions. The data span a range of outer-scale Reynolds numbers from 3290 to 8330. Direct measurement of the thicknesses of scalar dissipation structures (layers) shows that the thicknesses scale with outer-scale Reynolds number as ) plays a significant role in the scalar dissipation process. The present data resolve a range of length scales from the dissipation scales up to nearly the jet full width, and thus can be used in a priori testing of subgrid models for scalar mixing in large-eddy simulations (LES). Comparison of two models for subgrid scalar variance, a scale-similarity model and a gradient-based model, indicates that the scale-similarity model is more accurate at larger LES filter sizes.

A Novel Semi-Active Multi-Modal Vibration Control Law for a Piezoceramic Actuator

Abstract: In this paper, a novel semi-active energy rate multi-modal vibration control technique is developed for a piezoceramic actuator coupled to a switching resistor/inductor shunt. The technique works by briefly connecting a resistor/inductor shunt to a piezoceramic actuator in order to apply the necessary signed charge to allow energy dissipation. The switch timing is determined by a control scheme that observes the rate of energy change in controlled modes. The control scheme is developed in the paper, and is simplified to enable practical implementation. This new multi-modal control law is applied to both a simple numerical and an experimental test structure. The results from the numerical and experimental tests show that the energy rate multi-mode control law is able to dissipate energy from one, two and three modes of the flexible structures using a single actuator.

Kelvin-wave cascade on a vortex in superfluid 4He at a very low temperature.

Abstract: A study by computer simulation is reported of the behavior of a quantized vortex line at a very low temperature when there is continuous excitation of low-frequency Kelvin waves. There is no dissipation except by phonon radiation at a very high frequency. It is shown that nonlinear coupling leads to a net flow of energy to higher wave numbers and to the development of a simple spectrum of Kelvin waves that is insensitive to the strength and frequency of the exciting drive. The results are likely to be relevant to the decay of turbulence in superfluid 4 He at very low temperatures.

Binary droplet collisions in a vacuum environment: an experimental investigation of the role of viscosity

Abstract: An experimental investigation of viscous binary droplet collisions in a vacuum environment is conducted. The fundamental ramifications of conducting such experiments in a vacuum environment are twofold. The first, which is the motivating factor of this work, assures that the collision products are unimpeded by aerodynamic effects which tend to disrupt the collision process at a much earlier stage in the processes than if they were absent, and second, the phenomenon of encapsulation of the host medium between the colliding droplets is not present in this study; a fact that limits the scope of direct application of this study to a number of (but not all) applications. Droplets are generated from capillary stream breakup with the imposition of an amplitude-modulated disturbance which results in the generation of highly uniform pre-collision drops at separations far extending those which are possible from a standard (monochromatic) sinusoidal disturbance. Hence, the collision products are able to deform unimpeded by interactions with neighboring collision products. Measurements over a broad range of Weber number, We, indicate that the value of the critical Weber number, We c, is more than 100 times greater for the 30-cSt fluid than the corresponding value for similarly sized water drops in a standard ambient environment. Measurements of the oblate and prolate half-cycle oscillation periods resulting from the binary collision reveal a distinct behavior that is observed and documented here for the first time. Additionally, measurements of the radial extent of the deformed mass at the instant of maximum deformation have been conducted and allow quantification of the energy dissipation. These measurements show that the energy dissipation increases with increasing fluid viscosity, which contradicts the results published by others.

Single drop impaction on a solid surface

Abstract: An experimental and theoretical study is presented on spreading and retracting of a single drop impacting on a smooth surface at room temperature. The experimental study showed the influence of kinetic energy, liquid-solid interaction, and energy dissipation on the impact process. The results are reported for Reynolds number from 180 to 5,513, Weber number from 0.2 to 176, four different liquids (distilled water, n-Octane, n-Tetradecane, and n-Hexadecane), and four different surfaces (slide glass, uncoated silicon wafer, HMDS coated silicon wafer, and Teflon film). A theoretical model based on an energy balance was developed to predict the maximum spreading ratio at low impact velocity. The key novel feature of this model is that the shape of the drop is assumed to be a spherical cap during the spreading process. When compared to models in the literature, the present model not only gives better predictions for low drop impact velocities, but also in most cases gives predictions that are within 10% of the experimental data at high impact velocities.

A Rate-Independent Model for Inelastic Behavior of Shape-Memory Alloys

Abstract: We formulate a model describing rate-independent hysteretic response of shape-memory alloys under slow external forcing. Under natural assumptions we prove that this model has a solution. The microstructure is treated on a "mesoscopic" level, described by volume fractions of particular phases in terms of Young measures. The whole formulation is based on energetic functionals for energy storage and energy dissipation. The latter is built into the model by a dissipation distance between different values of these volume fractions.

Creeping friction dynamics and molecular dissipation mechanisms in glassy polymers.

Abstract: The dissipation mechanism of nanoscale kinetic friction between an atomic force microscopy tip and a surface of amorphous glassy polystyrene has been studied as a function of two parameters: the scanning velocity and the temperature. Superposition of the friction results using the method of reduced variables revealed the dissipative behavior as an activated relaxation process with a potential barrier height of 7.0 kcal/mol, corresponding to the hindered rotation of phenyl groups around the C-C bond with the backbone. The velocity relationship with friction F(v) was found to satisfy simple fluctuation surface potential models with F proportional to const-ln(v) and F proportional to const-ln(v)2/3.

Analytic calculation of the parallel mean free path of heliospheric cosmic rays. II. Dynamical magnetic slab turbulence and random sweeping slab turbulence with finite wave power at small wavenumbers

Abstract: The parallel mean free path of cosmic ray particles in partially turbulent electromagnetic fields is calculated for two particular turbulence models: slab-like dynamical and random sweeping turbulence. Using the general results for the pitch-angle Fokker-Planck coefficient from Teufel & Schlickeiser (2002) the rigidity dependence and the absolute value of the mean free path for these specific turbulence models are calculated for a turbulence power spectrum with finite wave amplitude at very small wavenumbers. We demonstrate that this modification affects especially the mean free path at very large rigidities. We also derive approximations for the mean free path for realistic Kolmogorov-type turbulence power spectra which include the steepening at high wavenumbers due to turbulence dispersion and/or dissipation.

Semiconductor integrated circuits with power reduction mechanism

Abstract: Power dissipation of a semiconductor integrated circuit chip is reduced when it is operated at an operating voltage of 2.5 V or below. A switching element is provided in each circuit block within the chip. Constants of the switching element are set so that leakage current in each switching element in their off-state is smaller than the subthreshold current of MOS transistors within the corresponding circuit block. Active current is supplied to active circuit blocks, while switching elements of non-active circuit blocks are turned off. Thus, dissipation currents of non-active circuit blocks are limited to leakage current value of corresponding switching elements. Thus, the sum of dissipation currents of non-active circuit blocks is made smaller than the active current in the active circuit blocks. As a result, power dissipation in the semiconductor integrated circuit chip can be reduced even in the active state.