Showing papers on "Dissipation published in 1989"

A consistent characteristic length for smeared cracking models

Abstract: A numerical scheme for crack modelling by means of continuous displacement fields is presented. In two-dimensional problems a crack is modelled as a limiting case of two singular lines (with continuous displacements, but discontinuous displacement gradients across them) which tend to coincide with each other. An analysis of the energy dissipated inside the band bounded by both lines allows one to obtain an expression for the characteristic length as the ratio between the energy dissipated per unit surface area (fracture energy) and the energy dissipated per unit volume (specific energy) at a point. The application of these mathematical expressions to the finite element discretized medium allow one to obtain a general spatial and directional expression for the characteristic length which guarantees the objectivity of the results with respect to the size of the finite element mesh. The numerical results presented show the reliability of the proposed expressions.

Quantification of sand bar morphology: A video technique based on wave dissipation

Abstract: A technique is presented to remotely measure the scales and morphology of natural sand bars based on the preferential dissipation of wind waves and swell over the crests of the bar. Photographic or video images are recorded and statistical uncertainties associated with incident wave height modulations removed by averaging (time exposures). Ground truth testing of the technique was carried out as part of the SUPERDUCK experiment in October 1986. The time exposures generally provided a good mapping of underlying morphology, allowing detection of the bar and determination of cross-shore and longshore length scales. However, during high waves, persistent surface foam obscures the relationship of image intensity to local dissipation (modeled theoretically by dissipation of a random wave field), and an enhancement technique of image differencing must be done to remove the bias. Errors in the estimate of bar crest distance from the shoreline are generally less than 35%, but this value depends on the geometry of the particular bar. Logistic simplicity and quantitative capabilities make this technique very attractive.

Evaluation of turbulent transport and dissipation closures in second-order modeling

Abstract: We show that the turbulence statistics from our (96)3 large-eddy-simulation (LES) studies of a convective boundary layer are in excellent agreement with those from the Deardorff–Willis laboratory convection tank. Using these LES data, we evaluate contemporary parameterizations for turbulent transport and dissipation in second-order closure models of the convective boundary layer. The gradient-diffusion parameterization for turbulent transport fares poorly, due in large part to the direct influence of buoyancy. This leads to poor predictions of the vertical profiles of some turbulence statistics. We also find that the characteristic length scales for the mechanical and thermal dissipation rates typically used in second-order closure models are a factor of 2–3 too small; this leads to underpredictions of turbulence kinetic energy levels. Finally, we find that the flux and variance budgets for conservative scalars are substantially different in top-down and bottom-up diffusion. In order to reproduce...

Dynamics of Decaying Two-Dimensional Magnetohydrodynamic Turbulence

Abstract: High‐resolution numerical studies of decaying two‐dimensional magnetohydrodynamic turbulence were performed with up to 10242 collocation points in general periodic systems using various initial states, but restricting consideration to weak velocity‐magnetic field correlation ρ. The global evolution is self‐similar with constant kinetic to magnetic energy ratio EV/EM, macro‐ and microscale Reynolds numbers, and correlation ρ, while the total energy decays as E(t)∝(t+t0)−1. As in three dimensions, dissipative small‐scale turbulence adjusts in such a way as to make the energy dissipation rate e independent of the collisional dissipation coefficients. Normalized energy spectra are also invariant. The spectral index in the inertial range is, in general, close to 3/2 in agreement with Kraichnan’s Alfven wave argument Ek =DB1/2e1/2k−3/2, B=(EM)1/2, D≂1.8±0.2, but may be close to 5/3 in transient states, in which turbulence is concentrated in regions of weak magnetic field. In the dissipation range, intermittency...

Further experiments on the evolution of turbulent stresses and scales in uniformly sheared turbulence

Abstract: Measurements of the Reynolds stresses, integral lengthscales and Taylor microscales are reported for several cases of uniformly sheared turbulent flows with shear values in a range substantially wider than those of previous measurements. It is shown that such flows demonstrate a self-preserving structure, in which the dimensionless Reynolds stress ratios and the dissipation over production ratio, e/ P , remain essentially constant. Flows with sufficiently large $k_{\rm s} = (1/\overline{U_{\rm c}}){\rm d}\overline{U_1}dx_2$ have exponentially growing stresses and e/ P ≈ 0.68; a linear relationship between the coefficient in the exponentiallaw and k s is shown to be compatible with measurements having k s > 3. The possibility of a self-preserving structure with asymptotically constant stresses and e/ P ≈ 1.0 is also compatible with measurements, corresponding to flows with small values of k s . The integral lengthscales appear to grow according to a power law with an exponent of about 0.8, independent of the mean shear, while the Taylor microscales, in general, approach constant values. Various attempts to scale the stresses and to predict their evolution are discussed and the applicability of Hasen's theory is scrutinized. Finally, an ‘exact’ expression for the pressure-strain rate covariance is derived and compared to some popular models.

A Theory of Enhanced Saturation of the Gravity Wave Spectrum Due to Increases in Atmospheric Stability

Abstract: In this paper we consider a vertical wavenumber spectrum of vertically propagating gravity waves impinging on a rapid increase in atmospheric stability. If the high-wavenumber range is saturated below the increase, as is usually observed, then the compression of vertical scales as the waves enter a region of higher stability results in that range becoming supersaturated, that is, the spectral amplitude becomes larger than the saturation limit. The supersaturated wave energy must then dissipate in a vertical distance of the order of a wavelength, resulting in an enhanced turbulent energy dissipation rate. If the wave spectrum is azimuthally anisotropic, the dissipation also results in an enhanced vertical divergence of the vertical flux of horizontal momentum and enhanced wave drag in the same region. Estimates of the enhanced dissipation rates and radar reflectivities appear to be consistent with the enhancements observed near the high-latitude summer mesopause. Estimates of the enhanced mean flow acceleration appear to be consistent with the wave drag that is needed near the tropopause and the high-latitude summer mesopause in large-scale models of the atmosphere. Thus, this process may play a significant role in determining the global effects of gravity waves on the large-scale circulation.

Creation of Current Filaments in the Solar Corona

Abstract: It has been suggested that the solar corona is heated by the dissipation of electric currents. The low value of the resistivity requires the magnetic field to have structure at very small length scales if this mechanism is to work. In this paper it is demonstrated that the coronal magnetic field acquires small-scale structure through the braiding produced by smooth, randomly phased, photospheric flows. The current density develops a filamentary structure and grows exponentially in time. Nonlinear processes in the ideal magnetohydrodynamic equations produce a cascade effect, in which the structure introduced by the flow at large length scales is transferred to smaller scales. If this process continues down to the resistive dissipation length scale, it would provide an effective mechanism for coronal heating.

Inelastic deformation of porous materials

Abstract: This paper examines the structure of material constitutive laws for time-independent plastic and creeping porous bodies through the determination of bounds to the flow and strain-rate potentials. The results are a logical extension of conventional plasticity and creep formalisms for incompressible materials. It is demonstrated that the shape of the yield surface for a time-independent plastic material and the surface of constant energy dissipation rate for a creeping solid are a function of stress and void volume fraction only, and independent of material parameters apart from a weak dependence on the creep exponent, n. This condition is not satisfied by the model proposed by G urson (J. Engng Mater. Tech. Trans. ASME, 99, 2, 1977) and modifications are suggested to his model and its extension to material hardening. The predictions obtained for a creeping solid are in broad agreement with results of other studies.

Linearized dynamics of spherical bubble clouds

Abstract: The present work investigates the dynamics of the one-dimensional, steady flow of a spherical bubble cloud subject to harmonic far-field pressure excitation. Bubble dynamics effects and energy dissipation due to viscosity, heat transfer, liquid compressibility and relative motion of the two phases are included. The equations of motion for the average flow and the bubble radius are linearized and a closed-form solution is obtained. The results are then generalized by means of Fourier synthesis to the case of arbitrary far-field pressure excitation. The flow displays various regimes (sub-resonant, trans-resonant and super-resonant) with different properties depending on the value of the relevant flow parameters. Examples are discussed in order to show the effects of the inclusion of the various energy dissipation mechanisms. Finally the results for the case of Gaussian-shaped far-field pressure change are presented and the most important limitations of the theory are briefly discussed. The simple linearized dynamical analysis developed so far clearly deminstrates the importance of the complex phenomena connected to the interaction of the dynamics of the bubbles with the flow and provides an introduction to the more realistic study of the same flows with nonlinear bubble dynamics.

Numerical simulation of coronal heating by resonant absorption of Alfvén waves

Abstract: The heating of coronal loops by resonant absorption of Alfven waves is studied in compressible, resistive magnetohydrodynamics. The loops are approximated by straight cylindrical, axisymmetric plasma columns and the incident waves which excite the coronal loops are modelled by a periodic external driver. The stationary state of this system is determined with a numerical code based on the finite element method. Since the power spectrum of the incident waves is not well known, the intrinsic dissipation is computed. The intrinsic dissipation spectrum is independent of the external driver and reflects the intrinsic ability of the coronal loops to extract energy from incident waves by the mechanism of resonant absorption. The numerical results show that resonant absorption is very efficient for typical parameter values occurring in the loops of the solar corona. A considerable part of the energy supplied by the external driver, is actually dissipated Ohmically and converted into heat. The heating of the plasma is localized in a narrow resonant layer with a width proportional to η 1/3. The energy dissipation rate is almost independent of the resistivity for the relevant values of this parameter. The efficiency of the heating mechanism and the localization of the heating strongly depend on the frequency of the external driver. Resonant absorption is extremely efficient when the plasma is excited with a frequency near the frequency of a so-called ‘collective mode’.

Statistical properties of decaying geostrophic turbulence

Abstract: High-resolution, high-Reynolds-number numerical solutions of fully three-dimensional, decaying, geostrophic turbulence are examined. The results include the demonstration of a substantial degree of similarity between geostrophic and two-dimensional turbulence: transfer of energy to larger scales; transfer of potential enstrophy to smaller scales; vanishing energy dissipation as the Reynolds number increases; the emergence and growth to dominance of isolated, coherent vortices; and a competition between the vortices and Rossby waves, with an associated horizontal anisotropy when the latter are dominant. Properties that are distinct to geostrophic turbulence include the following: approximate three-dimensional wavenumber isotropy, with significant departures on large scales due to boundedness of the domain and on smaller scales due to anisotropic spectrum transfer rates; insensitivity of solution properties to anisotropy or vertical inhomogeneity in the dissipation; persistence of vertical inhomogeneity; development of inhomogeneity due to solid vertical boundaries; and the processes of alignment, attachment, and vertical straining associated with the finite vertical extent of the coherent vortices.

Large‐eddy simulation of passive scalar diffusion in isotropic turbulence

Abstract: A spectral large‐eddy simulation of the velocity and passive temperature fields in three‐dimensional isotropic turbulence is developed at high Reynolds numbers and a Prandtl number of the order of 1. The temperature spectrum in the large scales is shown to develop a range of the form ET(k)≈0.1η[〈u2〉/e]k−1, where e and η are the kinetic energy and temperature variance dissipation rates, respectively. This range, which is a result of shearing by large scale velocity gradients, is followed by a k−5/3 inertial‐convective range at higher wavenumbers. The temperature variance decays much faster in time than the kinetic energy. Finally, the spectral eddy conductivity rises logarithmically with k toward small wavenumbers, contrary to the eddy viscosity that displays a plateau.

Vortex creep and the internal temperature of neutron stars - Linear and nonlinear response to a glitch

Abstract: The dynamics of pinned superfluid in neutron stars is determined by the thermal 'creep' of vortices. Vortex creep can respond to changes in the rotation rate of the neutron star crust and provide the observed types of dynamical relaxation following pulsar glitches. It also gives rise to energy dissipation, which determines the thermal evolution of pulsars once the initial heat content has been radiated away. The different possible regimes of vortex creep are explored, and it is shown that the nature of the dynamical response of the pinned superfluid evolves with a pulsar's age. Younger pulsars display a linear regime, where the response is linear in the initial perturbation and is a simple exponential relaxation as a function of time. A nonliner response, with a characteristic nonlinear dependence on the initial perturbation, is responsible for energy dissipation and becomes the predominant mode of response as the pulsar ages. The transition from the linear to the nonlinear regime depends sensitively on the temperature of the neutron star interior. A preliminary review of existing postglitch observations is given within this general evolutionary framework.

Energy dissipation of Alfven wave packets deformed by irregular magnetic fields in solar-coronal arches

Abstract: The importance of field line geometry for shear Alfven wave dissipation in coronal arches is demonstrated. An eikonal formulation makes it possible to account for the complicated magnetic geometry typical in coronal loops. An interpretation of Alfven wave resonance is given in terms of gradient steepening, and dissipation efficiencies are studied for two configurations: the well-known slab model with a straight magnetic field, and a new model with stochastic field lines. It is shown that a large fraction of the Alfven wave energy flux can be effectively dissipated in the corona.

Velocity profiles, the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer

Abstract: The logarithmic + polynomial approximation is suggested for vertical profiles of velocity components in a planetary boundary layer (PBL) at neutral and stable stratification. The resistance law functions A and B are determined on the basis of this approximation, using integral relations derived from the momentum equations, the Monin-Obukhov asymptotic formula for the wind profile in a stably stratified near-surface layer and the known expressions for the PBL depth. This result gives a realistic and convenient method for calculating the surface friction velocity and direction and the total dissipation rate of mean flow kinetic energy in terms of geostrophic velocity, buoyancy flux at the surface, the roughness parameter and the Coriolis parameter. In the course of these derivations a review is given of current views on the main problems of the neutral and stable PBL.

Ultrasonic welding of thermoplastics in the far‐field

Abstract: Ultrasonic welding is one of the most popular techniques for joining thermoplastics because it is fast, economical, and easily automated. In near-field ultrasonic welding, the distance between the horn and the joint interface is 6 mm or less. This study investigated the near-field ultrasonic welding of amorphous (acrylonitrile-butadiene-styrene and polystyrene) and semicrystalline (polyethylene and polypropylene) polymers. High frequency ultrasonic wave propagation and attenuation measurements were made in order to estimate the dynamic mechanical moduli of the polymers. The estimated moduli were entered into a lumped parameter model in order to predict heating rates and energy dissipation. Experimental results showed that variations in the welding pressure had little effect on energy dissipation or joint strength; Increasing the amplitude of vibration increased the energy dissipation and the weld strength. For the semicrystalline polymers, increasing the weld time improved strength up to weld times greater than 1.5 s, where strength leveled off. For the amorphous polymers, the weld strength increased with Increasing weld time up to times of 0.8 s; for longer weld times, the power required was too high, causing overloading of the welder. Monitoring of the energy dissipation and static displacement or collapse provided valuable information on weld quality.

Influence of dissipation on the Landau-Zener transition.

Abstract: The quantum dynamics of the Landau-Zener transition in a dissipative environment is studied and analytical results for the transition probability are given in terms of temperature, coupling strength, and the Landau-Zener time. For short Landau-Zener time there is no effect of dissipation. In the oppotise limit we distinguish various temperature regimes: The adiabatic limit is shown to be restricted to low temperatures and no effect of dissipation is present at zero temperature. At intermediate temperatures thermal transitions dominate for weak coupling and high temperatures correspond to the strong-coupling limit.

An Entropy-Based Approach to Nonlinear Stability

Abstract: Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.

Numerical modeling of the nocturnal urban boundary layer

Abstract: A numerical case study with a second-order turbulence closure model is proposed to study the role of urban canopy layer (UCL) for the formation of the nocturnal urban boundary layer (UBL). The turbulent diffusion coefficient was determined from an algebraic stress model. The concept of urban building surface area density is proposed to represent the UCL. Calculated results were also compared with field observation data. The height of the elevated inversion above an urban center was simulated and found to be approximately twice the average building height. The turbulent kinetic energy k, energy dissipation rate e, and turbulence intensities 〈u2〉 and 〈w2〉 increase rapidly at the upwind edge of the urban area. The Reynolds stress 〈uw〉 displayed a nearly uniform profile inside the UBL, and the vertical sensible heat flux 〈wθ〉 had a negative value at the inversion base height. This indicates that the downward transport of sensible heat from the inversion base may play an important role in the formation of the nocturnal UBL.

Nonlinear interactions among solar acoustic modes

Abstract: We evaluate the rates at which nonlinear interactions transfer energy among the normal modes of a plane-parallel, stratified atmosphere. The atmosphere resembles the outer part of the Sun including the convection zone and the optically thin region above the photosphere up to the temperature minimum. The acoustic modes are assigned energies such that their photospheric velocities match those of the Sun's p-modes. The nonlinearity parameter is the acoustic Mach number, M, the ratio of the total acoustic velocity due to all of the modes to the sound speed. For M^2 ≪ 1 the leading nonlinear interactions are those which couple three-modes. We show that every p-mode in the 5 minute band is involved in many near-resonant triplets. As a consequence, the energy transfer rates are independent of the mode line widths. Because M increases with height, the dominant contributions to the three-mode coupling coefficients occur in the upper part of the convection zone and in the optically thin isothermal layer. Moreover, the coupling coefficients tend to increase with ω and k_h. Nonlinear interactions which couple two trapped modes and one propagating mode drain energy from the trapped modes. They are far more effective than interactions among three trapped modes which drive the modes toward equipartition of energy. Thus, every trapped mode suffers a net loss of energy due to its nonlinear interactions. Estimates of the nonlinear energy transfer rates are plagued by two uncertainties. Some of the coefficients which couple two trapped modes to a propagating mode formally diverge as the thickness of the isothermal layer is increased to infinity; physically, this reflects the exponential growth of the acoustic Mach number with height in the isothermal layer. Also, the energy transfer rates are sensitive to the unknown energies of the high-degree trapped modes. Plausible assumptions lead to energy transfer rates which are somewhat smaller than the products of the mode energies and line widths. Thus, nonlinear mode coupling is probably not the dominant damping process for the solar p-modes, at least for those with small l. However, this cannot be regarded as a secure conclusion. The observational signature of damping due to nonlinear mode coupling would be a decrease in the energy per mode with increasing l at fixed ω. In addition, it might be responsible, at least in part, for the steep decline in the energy per mode at frequencies above 3 mHz which is usually attributed to radiative damping. Our investigation indirectly bears on the question of the stability of the p-modes. We find that nonlinear mode couplings cannot limit the growth of overstable p-modes. This favors the hypothesis that the Sun's p-modes are stochastically excited by turbulent convection.

Wave transmission over submerged breakwaters

Abstract: Monochromatic wave reflection and transmission over a submerged impermeable breakwater is predicted numerically by slightly modifying the numerical model developed previously for predicting wave reflection and run‐up on rough or smooth impermeable slopes. The slight modification is related to the landward boundary condition required for the transmitted wave propagating landward. In addition to the conservation equations of mass and momentum used to compute the flow field, an equation of energy is derived to estimate the rate of energy dissipation due to wave breaking. The computed reflection and transmission coefficients are shown to be in agreement with available small‐scale test data. The numerical model also predicts the spatial variation of the energy dissipation, the mean water level difference, and the time‐averaged volume flux per unit width, although available measurements are not sufficient for evaluating the capabilities and limitations of the numerical model for predicting these quantities.

Dissipation of quantum fields from particle creation.

Abstract: We discuss the nature and origin of the dissipation of quantum fields due to the back reaction of particle creation. We derive the effective action of a scalar $g{\ensuremath{\varphi}}^{3}$ theory in the closed-time-path-integral formalism. From the real and causal equation of motion for the background field we deduce a dissipative function for this process and for the cosmological anisotropy damping problem studied earlier. This model illustrates that the appearance of dissipative behavior from the back reaction of particle creation in quantum fields is a general feature. It also suggests that the role of gravity in the display of dissipative behavior in semiclassical processes is not unique.

Seismic Behavior of Concentrically Braced Frame

Abstract: Seismic tests on a full‐scale six‐story steel building have been conducted as part of the U.S.‐Japan Joint Research Program. The first phase of this research includes extensive tests on a concentrically braced frame, and detailed results of these tests are described. The concentrically braced frame is tested for elastic, moderate, and final tests. The elastic test simulates a small, frequent earthquake, and the structure remains elastic throughout the test. The moderate test simulates an intermediate‐size earthquake. Limited yielding and brace buckling and an unusual three‐piece tear in the web of the beam at the second floor brace beam splice are noted. This unusual failure is analyzed and is compared to U.S. design practice. The final test simulates a major earthquake, and extensive brace buckling and yielding are noted. The distribution of energy dissipation within the structure is analyzed for both the moderate and final tests. The effect of brace buckling and composite action of the floor system on t...

A critical comparison of turbulence models for homogeneous shear flows in a rotating frame

Abstract: A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of their predictions.

Observing Groups of Solitary Internal Waves and Turbulence with BATFISH and Echo-Sounder

Abstract: Acoustic backscatter from a 200 kHz echo-sounder and temperature fine-structure from a towed CTD (BAT-FISH) am compared prior to and during the passage of a group of large-amplitude internal waves on the continental shelf off Nova Scotia. The results indicate that a significant increase in acoustic backscatter and temperature gradient variance is observed in well-defined layers of approximately 5–15 m thickness and that these layers are generated by the passage of the group of internal waves. Consideration of the nature of the internal waves shows that the layers occur where shear instability is expected to be large and the local Richardson number is smaller than the critical value required for the generation of turbulence. Estimates of energy levels and rates of dissipation of energy in the internal waves provide a way, using standard turbulence theory, to calculate the expected acoustic scattering cross-sections. The measured and the calculated cross-sections are consistent. It is concluded tha...

An accurate simulation technique for short-circuit power dissipation based on current component isolation

Abstract: A circuit simulation technique is presented which permits the measurement of the average short-circuit power dissipation component in integrated circuits. This technique is most appropriate for low-power circuit design and can be applied effectively to any complementary circuit structure, such as CMOS, that does not permit current flow (other than leakage current) during steady-state operation. Short-circuit power dissipation expressions are derived, and SPICE simulation results for a differently ratioed W/sub p//W/sub n/ circuit are shown. >