Showing papers on "Dissipation published in 1975"

Global dynamics and climate - a system of minimum entropy exchange

Abstract: It is found that the mean meridional distribution of temperature, cloud cover and meridional energy flux can be predicted with extraordinary accuracy by application of a simple minimum principle to a multi-box model of the globe which contains no direct specification of the system dynamics. The minimized quantity is related to the global net rate of production of entropy. It is the sum over all latitude zones of the ratio of net radiant energy input to the effective emission temperature of the zone. The result suggests that global dynamics is something of a passive variable which alters so as to satisfy a condition akin to minimum energy dissipation.

High-beta turbulence in two-dimensional magnetohydrodynamics

Abstract: Incompressible turbulent flows were investigated in the framework of ideal magnetohydrodynamics. Equilibrium canonical distributions are determined in a phase whose coordinates are the real and imaginary parts of the Fourier coefficients for the field variables. The magnetic field and fluid velocity have variable x and y components, and all field quantities are independent of z. Three constants of the motion are found which survive the truncation in Fourier space and permit the construction of canonical distributions with three independent temperatures. Spectral densities are calculated. One of the more novel physical effects is the appearance of macroscopic structures involving long wavelength, self-generated, magnetic fields ("magnetic islands"). In the presence of finite dissipation, energy cascades to higher wave numbers can be accompanied by vector potential cascades to lower wave numbers, in much the same way that in the fluid dynamic case, energy cascades to lower wave numbers accompany entropy cascades to higher wave numbers.

The Vertical Transports of Kinetic Energy by Turbulence and Pressure in the Boundary Layer

Abstract: The transport of energy by turbulence and pressure is examined for a turbulent surface layer over a dry prairie grassland. Both terms are found to be significant in the budget of turbulent kinetic energy. The values of the divergences are deduced by considering the variations of the non-dimensionalized terms with respect to z/L. It was found that the divergence of the turbulent kinetic energy flux was about equal to minus the buoyancy production. The main contribution was due to the divergence of the vertical transfer of the vertical component of kinetic energy. The divergence of pressure transfer was found to be of opposite sign and of about equal magnitude to the divergence of turbulent energy flux. The dissipation of turbulent kinetic energy about equalled the local production. The spectral components of the energy budget are briefly examined. It was found that the non-dimensional frequency range with no appreciable production nor dissipation was only about a decade wide whereas the spectral f...

The effect of local non-uniformities on thermal switching and high field behaviour of structures with chalcogenide glasses

Abstract: A refinement of the theory of thermal switching is presented which takes into account local defects (pre-existing or built-in during the forming process). The contribution of these local defects in reducing the filament temperature is calculated. When high-field non-ohmic effects are also included in the theory, some switching phenomena can be explained, which were not considered as thermal, and in which the average dissipation is no longer a significant factor. It is also shown that the presence of local defects may have significantly altered the available information concerning very steep high field behaviours in chalcogenide glasses.

Frictional properties of dilute polymer solutions. I. Rotational friction coefficient

Abstract: The theory of Debye and Bueche for the frictional properties of dilute polymer solutions is placed on a microscopic basis. It is shown that the microscopic foundations for the theories of Debye−Bueche and Kirkwood−Riseman are identical, but that the theories differ in their statistical analysis. The Debye−Bueche equations are applied to the rotational friction coefficient of a spherically symmetric polymer with arbitrary radial density distribution. An exact result is derived for a Gaussian distribution of low density. A variational principle of minimum energy dissipation is formulated which is suitable for numerical work.

On the dynamics of internal waves in the deep ocean

Abstract: The dynamical processes affecting the evolution of a random internal wave field are considered. If the statistical properties of the internal wave field vary slowly with space and time, these dynamical processes can be treated as small perturbations about the local steady state of the free linear field. The time evolution of the wave field is then governed by a radiative transfer equation describing changes in the action density spectrum of the wave field along wave group trajectories. The source function describing these changes is determined by the superposition of all processes governing the generation, transfer, and dissipation of wave energy. Some terms of the source function, those corresponding to expansible processes, can be derived rigorously by using weak interaction concepts. Other terms, corresponding to nonexpansible processes which are governed locally by strongly nonlinear dynamics, cannot be determined completely. For the case where the internal wave field can adequately be described in the WKBJ approximation, a rather complete list of source terms is presented. The evaluation of these source terms is difficult partly because of their complicated functional structure and partly because the geophysical fields involved are not sufficiently known. Those source terms which have been evaluated in detail are briefly reviewed, and their implications on the energy balance of the internal wave field are discussed.

Numerical computations of the flow in curved ducts.

Abstract: The paper describes the application of a recently developed numerical scheme to the computation of the flow in a curved duct. The flow situation is partially-parabolic in nature as there are significant elliptic effects, which are transmitted through the pressure field. The turbulence model used comprises two differential equations, one for the kinetic energy of turbulence and the other for its dissipation rate. It has been observed that the predictions using the new procedure agree very satisfactorily with the experimental data. Comparisons are also made with the predictions of a fully-parabolic calculation procedure.

Experimental and theoretical study of energy dissipation profiles of keV electrons in polymethylmethacrylate

Abstract: Energy dissipation profiles of keV electron beams in polymethylmethacrylate (PMM) were investigated both in theory and experiment. The results measured using a scanning electron microscope as a source of the electron beam were followed by the Monte Carlo calculations which were performed for the same conditions as the experiment. Good agreement was obtained not only for equidissipation profiles but also for absolute values of the energy dissipation between the experiment and the calculation. This encourages us to apply the Monte Carlo calculations to problems of electron resist exposure important for microelectronics.

Generalised elements for t.l.m. method of numerical analysis

Abstract: The paper shows how the conduction term in Maxwell's equations can be introduced into the t.l.m. method of numerical analysis. The use of series nodes is also examined, thus laying the foundations for the development of the general 3-dimensional t.l.m. method.

Energy dissipation in a thin polymer film by electron beam scattering: Experiment

Abstract: A series of experiments of scanning electron beam exposure of PMMA films on silicon, copper, and gold substrates is described, and compared with the calculations of Monte Carlo and analytic models of energy dissipation per unit volume. Film thickness was varied from 1000 to 10 000 A, accelerating voltage from 10 to 20 kV, and linear charge density from 1×10−9 to 1×10−5 C/cm. Good agreement was obtained in the comparison with the predictions of Monte Carlo calculations, whereas some discrepancies were observed in the comparison with the analytic models. The assumption inherent in the theoretical approaches that PMMA acts like a linear recording medium, in the sense that exposure is additive, is experimentally evaluated by means of an Abel inversion. The assumption that developed profiles represent surfaces of equal energy dissipation was examined by means of a computer simulation of the development process.

Mode-Mode Coupling Theory of the Heat Convection Threshold

Abstract: The fluctuations of a horizontal fluid layer heated from below are analyzed, based on the hydrodynamic equations in the Boussinesq approximation including thermodynamic fluctuating forces. By means of a formalism, recently developed by Martin, Rose, and Siggia, a system of coupled nonlinear integral equations is derived for a set of correlation functions, response functions, and appropriate ’’self−energies.’’ The equations are solved approximately in several steps of simplification. In addition to results of an earlier linear theory, our results cover a narrow region near the convection threshold, where mode−mode coupling provides the only mechanism of energy dissipation. The fluctuation intensities, and the correlation times and correlation lengths, are calculated in that region. These quantities diverge at the convection threshold in the linearized theory, but remain finite, if mode−mode coupling is taken into account.

Energy spectrum of ultra high energy cosmic rays

Abstract: AT energies above ∼ 1017 eV it becomes increasingly difficult to maintain the observed near isotropy of ultra high energy cosmic rays if they are of Galactic origin, unless there is an extensive halo magnetic field, and the primaries are heavy nuclei1; instead, extragalactic origin is often assumed. The models proposed can be divided into three main groups: (1) ‘universal’, in which there is a class of galaxies in the Universe (of which our own is not a member) which are roughly uniformly distributed, and which generate the ultra high energy particles; (2) ‘universal plus supercluster enhancement’2, in which the existence of a supercluster is assumed—the enhanced density of galaxies in the SC allows a larger fraction, than is its share by volume, to have come from this region; and (3) ‘Supercluster trapping’3, where energetic phenomena in the SC generate the particles which are then trapped for periods of perhaps 109–1010 yr.

Statistics of Surface Layer Turbulence over the Tropical Ocean

Abstract: Atmospheric surface layer turbulent statistics measured during the Barbados Oceanographic and Meteorological Experiment 8 and 30 m above mean sea level are presented. The budget equations of turbulent kinetic energy, humility variance and temperature variance are examined. Within discussed limitations it is concluded that production equals dissipation in the case of turbulent kinetic energy and humidity variance. The analysis of the temperature variance budget revealed large differences between productions and dissipations computed assuming standard similarity functions derived from other data sets. Initial computation of fluxes revealed large systematic decreases with height in the shear stress and heat flux. Comparison with other results suggested corrections which would eliminate these differences. Comparison between profile fluxes and direct measurements suggests strong similarity of momentum and water vapor transfer.

A theoretical and experimental study of turbulent diffusion flames in cylindrical furnaces

Abstract: Turbulent diffusion flames in a small, axisymmetrical cylindrical furnace are studied, using town gas. Results are reported, of the measurements made by an ionization probe of the probability of reaction at many locations inside the furnace. Predictions are also obtained for the experimental, conditions by numerical solution of a set of six simultaneous, elliptic, partial differential equations. The time-mean hydrodynamic characteristics are described by the four variables: stream function, vorticity, turbulence kinetic energy and the rate, of dissipation of turbulence energy; the reaction is described by the time-mean mixture fraction, f , and the mean-squared fluctuations of the mixture fraction, g . Instantaneous values of the mass fractions and the temperature are evaluated from the assumption that the variation with time of the instantaneous values of f is described by a random wave form which has a suitably clipped Gaussian distribution of the probability density. Effects on the time-mean density of the concentration and temperature fluctuations are accounted for. A method is suggested for calculating the probability of chemical reaction at points in the flow field. Computed results agree fairly well with measurements.

Mechanics of peeling of rubbery materials. I. Peel strength and energy dissipation

Abstract: The peel strength found in the trousers-type peeling process is treated for the case in which the adherends, assumed to be flexible but inextensible are bonded by rubbery viscoelastic adhesives. Taking into consideration energy dissipation during deformation of the adhesive, Griffith's criterion is extended to the peeling of viscoelastic materials. For the peeling force per unit width f it is deduced that 2f = Γ + u′h, where T is twice the surface energy, u' is the energy dissipation per unit volume of adhesive, and h is the thickness of the adhesive layer. Values of u' obtained from peeling tests for various thicknesses are compared with those from the tensile tests and found to agree with the above relation. The deduction that the peel strength is independent of the thickness for adhesives with no energy dissipation is also verified experimentally.

Studies on the Flow of Cross-Flow Impellers : 2nd Report, Analytical Study

Abstract: Using an actuator model, velocity and pressure distributions of a flow around a cross-flow impeller are derived, which are in good agreement with experimental results on impellers with radial blades. Under the assumption that the stability of an eccentric vortex in the radial direction inside an impeller is achieved when an input furnished to the flow by impeller-bladings balances with energy dissipation by fluid viscosity, the stability conditions are discussed. Critical Reynolds number of stability for an axisymmetric vortical flow is given as a function of eccentricity of vortex. Performance of a fan with a simple casing around an impeller is obtained by numerical computation and influences of several parameters on it are clarified. It is found that only one circumferential location of stability of a vortex to make input maximum exists for a given eccentricity.

Analysis of rotor fragment impact on ballistic fabric engine burst containment shields

Abstract: As a step toward a better understanding of engine burst containment and ascertaining practical shield requirements, a large deflection shell computer program has been modified to model fragment impact, simultaneously calculate the motion of the fragment and shield and predict perforation. Recent test data indicates that substantial savings in engine burst containment shield weight may be possible by the use of ballistic fabrics. In metal shields the dissipation of fragment kinetic energy is due to compressive and shear deformation in the impact region followed by extensive bending and stretching deformation due to structural excitation. In contrast, a fabric shield dissipates the energy almost wholly by tensile deformation. The mechanical energy is distributed relatively rapidly throughout the shield as a result of the fabric's high wave speed and membrane response. Encouraging results were found in analytical comparisons with experimental data.

Form of the turbulence dissipation equation as applied to curved and rotating turbulent flows

Abstract: An exact turbulence dissipation equation in the generalized relative system is presented. Simplified forms of the equation are obtained for computational purposes in the high Reynolds number approximation. Modeling of the rotation term is proposed. Modeling of the other higher‐order terms is also presented in a generalized system using the tensor invariance technique. An estimate of the angular velocity is provided for the rotation term to be included in the turbulence dissipation equation. The associated significant curvature terms for turbomachinery flows are also identified.

Theory of energy dissipation in heavy-ion reactions

Abstract: A formalism for the description of energy dissipation in heavy-ion reactions within the two-centre shell model is proposed. Here dissipation is considered as due to the coupling of relative motion to intrinsic degrees of freedom. First, the formulation is carried out quantum mechanically. The problem reduces to the solution of coupled integrodifferential equations for energy distribution functionsfn(β) and\(\bar f_\varepsilon \)(β), where |\(\bar f_\varepsilon \)(β)|2 de is the probability of finding the intrinsic energy within the intervale andɛ+dɛ. By introducing suitable boundary conditions with incoming and outgoing waves the equations can be solved by iterative methods. The second method is based on the semi-classical approximation and is formulated in the time-dependent picture. Finally, a relationship between the friction coefficient and the distribution functions is given.

Adiabaticity limits to radio-frequency-augmented magnetic-mirror confinement

Abstract: The effect of adiabaticity and superadiabaticity limitations on the use of radio-frequency-augmented magnetic-mirror confinement is examined. It is shown that the scaling of the region over which the r. f. fields are applied to maintain a given level of adiabaticity is such that, although the fields decrease as resonance is approached, the total r. f. energy stored in the resonance region remains constant. Assuming that the dissipation is proportional to the energy stored, we conclude that the external energy supplied is not reduced from the energy requirements of non-resonant r. f. containment. In fact, the weak additional scaling required to maintain containment by superadiabaticity implies that resonant r. f. containment requires more applied power. The stochastic heating, resulting from the small-phase uncorrelated energy changes occurring on each pass through resonance, when superadiabaticity is not satisfied, is such that only a small improvement in the field strength required for containment can be made by operating in this mode.

Prediction of turbulent flow in curved pipes

Abstract: A finite-difference procedure is employed to predict the development of turbulent flow in curved pipes. The turbulence model used involves the solution of two differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate. The predicted total-velocity contours for the developing flow in a 180° bend are compared with the experimental data. Predictions of fully developed velocity profiles for long helically wound pipes are also presented and compared with experimental measurements.

A virtual dissipation principle and Lagrangian equations in non-linear irreversible thermodynamics

Abstract: . — A principle of virtual dissipation is derived which genera¬ lizes d'Alembert's principle to non-linear irreversible thermodynamics, leading to a corresponding Hamiltonian form and Lagrangian equations. It constitutes the fundamental mathematical tool for the analysis of general non-linear dissipative physical systems by methods similar to those of classical mechanics. The principle provides a derivation of the differential field equations or the Lagrangian equations which govern any particular dissipative thermodynamic system and is not based on a priori knowledge of the field equations. Results are essentially an ultimate development of the author's earlier work originated in 1954 which was presented in a more restricted context.

Balance of kinetic energy in the tropical circulation over the Western Pacific

Abstract: The balance of kinetic energy in the large-scale disturbances and general flow of the tropical circulation was investigated with special Marshall Islands upper-air network data during 1958. The cross-isobaric generation of eddy kinetic energy has two maxima: in the lower boundary and in the upper troposphere. However, the intensity of generation is about one to two orders of magnitude smaller than that in synoptic disturbances in the middle latitudes. A major portion of the generated eddy kinetic energy is exported outside the area. The space eddies are shown to derive a significant amount of kinetic energy from the kinetic energy reservoir of the basic flow in the area. The eddy kinetic energy is mainly dissipated in the lower boundary. There is a small amount of eddy dissipation in the upper troposphere. However, as a whole the free atmosphere provides very little damping to the disturbances through eddy dissipation. The kinetic energy balance in the general flow is determined mainly by the cross-isobaric generation of kinetic energy and the dissipation term. The vertical distribution of the cross-isobaric generation shows there is a large internal source of kinetic energy in the tropospheric easterlies and the kinetic energy is destroyed adiabatically in the upper-level westerlies and easterlies. The vertical profile of the dissipation closely follows that of the generation. Examination of the dissipation term obtained as the residual term of the kinetic energy equation suggests that processes of different scales of motion are significantly involved in the kinetic energy balance of the observed scale.