Showing papers on "Dissipation published in 1976"

One-dimensional nuclear dynamics in the time-dependent Hartree-Fock approximation

Abstract: The time-dependent Hartree-Fock theory is applied to the large amplitude dynamics of slabs of spin and isospin symmetric nuclear matter. The slabs are translationally invariant in two transverse dimensions, and with the simplified effective interaction used in this work, the problem is reduced to a set of coupled nonlinear equations for time-dependent functions of a single spatial variable. By specification of appropriate initial conditions, large amplitude oscillations of a single slab, the scattering of a slab from an external potential barrier, and collisions of two slabs have been investigated. The results evidence a wide variety of dynamic phenomena, including fusion, compound nucleus formation, dissipation, strongly damped collisions, shock wave propagation, and fragmentation. The microscopic aspects of the dynamics, the relation to fluid mechanics, and the practical and conceptual problems arising from the theory are discussed in detail.

The Energetics of Entrainment Across a Density Interface

Abstract: A theory of the fluid entrainment rate into a turbulent, mixed layer across a horizontal density interfaceis presented. By integrating the turbulent kinetic energy equation over the depth of the mixed layer and assuming that turbulence dissipation rates are proportional to production rates, an equation is derived relatingthe potential energy change and entrainment rate to four major terms: 1) buoyant production of energy dueto heating at the earths surface; 2) mechanical production due to wind shear at the earths surface; 3) mechanical production due to wind shear and dynamic instabilities such as Kelvin-Helmholtz waves at theversion interface; and 4) energy losses due to internal gravity waves. It is shown that most previously published theories are just special cases of this more general energetics theory.

The Noninteraction of Waves with the Zonally Averaged Flow on a Spherical Earth and the Interrelationships on Eddy Fluxes of Energy, Heat and Momentum

Abstract: For linearized hydrostatic waves on a spherical earth with a zonal mean wind which is a function of latitude and pressure I derive, without further approximations, expressions for the vertical and meridional energy fluxes in terms of the meridional heat flux and the vertical and meridional fluxes of zonal momentum. Using these expressions, I prove that in the absence of critical surfaces, dissipation, thermal heating and nonharmonic time dependence, that the waves and mean flow do not interact: the wave Reynold's stresses are exactly balanced by a mean meridional circulation whose streamfunction is simply the meridional beat flux divided by the static stability. In the presence of dissipation, thermal heating or transience, 1 am able to express the net forcing of the mean blow by the waves as expressions which are explicitly proportional to the coefficients of dissipation and heating and to the imaginary part of the phase speed. My work significantly extends earlier theorems on the noninteraction...

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 calculation of near-wake flows

Abstract: Calculated flow properties are compared with measurements obtained in twodimensional isothermal wakes with and without recirculation. The equations of continuity and momentum were solved numerically together with equations which formed a turbulence model. Calculations were made using three turbulence models : the first comprised transport equations for turbulence kinetic energy and the rate of turbulence dissipation; the second and third comprised equations for the rate of turbulence dissipation and two forms of Reynolds-stress equations characterized by different redistribution terms. The results show that, for wakes without recirculation, the particular turbulence model is less important than the boundary condition assumed in the plane of the trailing edge of the body; though the Reynolds-stress models do, of course, provide a better representation of the individual normal stresses. In the case of wakes with recirculation, both the length of the recirculation region and the rate of spread of the downstream wake are underestimated. The second discrepancy is particularly evident and appears to stem from the form of the dissipation equation. A suggestion for improving the modelling of this equation is provided together with necessary justification.

Nonlinear energy transfer and the energy balance of the internal wave field in the deep ocean

Abstract: The source function describing the energy transfer between the components of the internal wave spectrum due to nonlinear interactions is derived from the Lagrangian of the fluid motion and evaluated numerically for the spectral models of Garrett & Munk (1972a, 1975). The characteristic time scales of the transfer are found to be typically of the order of some days, so that nonlinear interactions will play an important role in the energy balance of the wave field. Thus implications of the nonlinear transfer within the spectrum for generation and dissipation processes are considered.

Planetary Waves in Horizontal and Vertical Shear: Asymptotic Theory for Equatorial Waves in Weak Shear

Abstract: A simple multiple-scale expansion procedure is given for calculating corrections to the structure of equatorial planetary waves in the presence of weak shear and dissipation. For upward-propapting Rossby-gravity (Yanai-Maruyama) and Kelvin (Wallace-Kousky) waves, explicit results are obtained for the case of Newtonian cooling and Rayleigh friction, correct to the first two orders in the ratio μ of wave to mean-flow height scales. The results are used in a direct calculation of the horizontal Reynolds stress u′v′¯ and demonstrate the strong dependence of u&primev′¯ on the ratio of friction to cooling coefficients. In certain parameter regimes of interest in the tropical stratosphere, a slight north-south asymmetry in the y profile of ū can cause changes in the wave structure such that the mean zonal acceleration ∂ū/∂t tends to have the same asymmetry. That is, there may be a tendency for asymmetries in ū(y) to amplify in the presence of dissipating waves.

Dissipation and fluctuations in nonequilibrium thermodynamics

Abstract: A relationship between dissipation and fluctuations is described which leads to a unified theory of irreversible processes far from equilibrium. The development is based on the principle that dissipation and fluctuations are caused by elementary molecular processes. This permits the formulation of a canonical form for the rate of dissipation of the extensive variables. The canonical form depends on the thermodymanic quantities which are conjugate to the extensive variables, and it is shown that the canonical form leads to the customary transport equations for a variety of linear and nonlinear relaxation processes. Because fluctuations are also caused by molecular events, this formulation of dissipation can be used to examine deviations from the average. The theory associates a nonstationary, Markov stochastic process with fluctuations away from the conditionally averaged extensive variables. This description of nonequilibrium thermodynamics does not require the entropy to be introduced, and for rate proce...

Wave Action and Bottom Movements in Fine Sediments

Abstract: Mudbanks have been observed to have an extraordinary calming effect on the sea surface. In certain cases this effect is due primarily to the transfer of energy through the sea/mud interface and its frictional dissipation within the bottom sediments. This paper describes an experiment that measured wave characteristics and the resulting sea floor oscillations in an area where the bottom is composed of fine-grained sediments. The energy lost by the waves at the position of the experimental setup is calculated and compared with a direct measurement of the net energy lost by the waves in going from the point of the experiment to a station 3.35 km inshore. Results show that bottom motions in the range of wave-induced bottom pressures from near zero to 2.39 x 10-3 Pascal have the appearance of forced waves on an elastic half space. The apparent effect of internal viscosity is seen in a phase shift between the crest of the pressure wave and the trough of the mud wave. Measurements show this angle to be 22° (ill") for the peak spectral component (T = 7.75 seconds). The energy lost to the bottom by the waves at the field site was found to be at least an order of magnitude greater than that resulting from the processes of percolation or that caused by normal frictional effects. This newly observed mechanism for the dissipation of wave energy is particularly important for waves in intermediate-depth water and could be a prime factor in determining design wave heights in muddy coastal areas.

Compact electronic control and power unit structure

Abstract: To reduce the overall size of the housing of an electronic control unit having power stages of substantial power, and hence high heat dissipation, in combination with its associated control stage having but little power and hence low heat dissipation, a printed circuit board is located in the structure having essentially rectangular cross section by placing the printed circuit board diagonally therein, holding it in fixed position at one end but loose at the other to permit relative movement with respect to the housing, and thermal dimensional changes, the printed circuit board dividing the chamber into one permitting high heat dissipation and one of low heat dissipation. The structure is particularly applicable for automotive electrical control systems such as, for example, ignition systems for placing in cramped locations.

Energy dissipation and nucleon transfer in heavy-ion reactions

Abstract: We report a correlation between the kinetic energy loss and nucleon diffusion for Kr- and Xe-induced reactions on heavy targets. Although this correlation suggests that these two phenomena occur on the same general time scale, the rate of kinetic energy loss decreases with interaction time. Evidence is presented to show that the initial energy dissipation rate is consistent with a frictional force which is proportional to the relative velocity. (AIP)

Vibrations of an infinite plate with a frequency independent Q

Abstract: The dissipation in an elastic medium is represented by a dissipation mechanism which is similar to one used in an earlier paper [M. Caputo, Geophys. J. R. Astron. Soc. 13, 529–539 (1967)], but is simpler and has a frequency‐independent Q−1. The vibrations of a plate are studied by obtaining the eigenfrequencies, the amplitude of the displacement, the dispersion relation, the Q−1, the hysteresis cycle, and the yield stress.Subject Classification: [43]40.24.

Doppler Radar Measurements of Turbulent Kinetic Energy Dissipation Rates in a Northeastern Colorado Convective Storm

Abstract: In this paper we report the results of measurements of turbulent kinetic energy dissipation rates within a convective storm. The measurements were obtained with two Doppler radars, one scanning the storm from a distance at low elevation angles and the other pointing vertically with the storm passing overhead. With the scanning radar we measured the wind shear in the radial velocity field and the turbulent kinetic energy dissipation rates within the storm. These dissipation rates showed good agreement with those measured by the zenith-pointing radar data; dissipation rates ranged from 30 cm2 s−3 to greater than 3500 cm2 s−3 in the region between the updraft and downdraft.

The dissipative mechanism in flowing polymers: theory and experiments

Abstract: The application of modern non-linear continuum thermodynamics to the analysis of energy dissipation in both isothermal and non-isothermal flow of polymers is discussed. A fundamental simplification of the field equation for the balance of energy arises if the assumption is made that the flowing polymer is a material with entropic elasticity. This assumption is partly justified by structural arguments, and its validity can be checked experimentally. The results of the experiments performed support the validity of the assumption.

Microscopic calculation of nuclear dissipation

Abstract: By use of a time-dependent wave function of the BCS form, we compute microscopically the energy dissipated for a system with a monopole pairing force moving under the influence of a time-dependent single-particle potential. Quasiparticle generation and coupling of the two-quasiparticle modes of the system are included automatically and provide contact with the Landau-Zener formula. The single-particle potential is related to nuclear shapes generated by viscous hydrodynamical calculations of a fissioning 236U nucleus. We attempt to determine the energy dissipated between the saddle point and scission point by requiring that at the scission point the energy dissipated in the microscopic calculations equal that dissipated in the macroscopic hydrodynamical calculations. This procedure leads to 34 MeV of dissipated energy, which is almost twice the value of 18 MeV obtained from macroscopic hydrodynamical calculations that reproduce experimental fission-fragment kinetic energies. The corresponding value of the nuclear viscosity coefficient determined from the microscopic calculations is 0.04 TP, compared to 0.015 ± 0.005 TP obtained from the macroscopic hydrodynamical calculations. The viscosity coefficient determined from the microscopic calculations is even larger if the dissipated energies are compared at a finite scission neck radius. As a possible resolution of this discrepancy, we propose that level splittings arising from axially asymmetric and reflection-asymmetric deformations during the descent from the saddle point to scission reduce the energy dissipation and make the nuclei only moderately viscous.

A Kinetic Energy Budget over North America During a Period of Short Synoptic wave Development

Abstract: A kinetic energy budget over North America is computed using standard rawinsonde data during 11–24 April 1970, a period of repeated short synoptic wave development. A comparative analysis with energy transformation documented for periods of intermediate synoptic wave influence is presented. In both the abort and intermediate wave periods, horizontal flux convergence is an important energy source. However, the two periods differ in both their kinetic energy generation and dissipation. In contrast to the intermediate wave case, the short wave period is dominated by negative generation of kinetic energy. In addition, the vertically-integrated dissipation, determined as the residual term in the kinetic energy budget, is substantially smaller for the short wave case. This latter result, which occurs primarily because the residual quantity is positive in the upper troposphere, is hypothesized to be associated with subgrid-to-grid-scale kinetic energy exchange. Of particular interest is a secondary wave...

Entropy per particle in the early Bianchi type-I Universe

Abstract: We consider the behaviour of the radiation entropy per particle in the early stage of the Universe according to the Bianchi type I in which there are nonvanishing terms for the shear viscosity in the energy-momentum tensorTμν. The viscosity coefficient η is a function of the temperature η=ωTm, where ω andm are constants. We rewrite Einstein equations in such a manner that we can analyse the influence of dissipation on the isotropization. Results of the above analysis reveal that, in the framework of the considered model, the effects of the shear viscosity appear to be significant only under very special initial conditions for the dissipation parameter and form<1; in such a case the radiation entropy increases in the course of the evolution by a substantial factor. The expansion is practically isoentropic in all the remaining cases. The dissipation parameters are found for the lepton and radiation epochs.

Energy relations of density‐current flows: an experimental investigation

Abstract: Three series of density-current experiments were performed in a 5.76 m flume. In the first series, the flume was horizontal, and in the second and third, it was inclined with a positive slope and negative slope, respectively. Energy relations during successive stages of density-current movement were computed from observed data, which showed an appreciable frictional energy dissipation. The computed friction factors of our experimental density-flows were compared to the friction factors for pipe flows (Moody diagram), and while the calculated friction factor increases with increasing Reynold's number within the range of our experiments (Re 2 × 103−2 × 104), it is concluded that with increasing Reynold's number above about 5 × 104 the friction factor decreases. For natural turbidity currents, the Moody diagram gives a reasonable estimate of the friction factor between the current and sediment bed. The value of the friction factor for the interface between the current and overlying water was found to be about 0.2 times the friction factor for the current and flume. However, due to errors inherent in measuring the depth of the current, a value of 0.4 would be more reasonable for density-currents in our range of Reynold's number. Friction tends to decrease the value of the dimensionless coefficient in Keulegan's law of saline front and to decrease the thickness of the flow. In contrast, the presence of a slope in the direction of flow tends to compensate the effect of friction. The angle θc that provides the potential energy to exactly offset the energy losses incurred during movement by the density-currents in our experiments has a calculated value of 31′. An empirical formula φ= 0.935θ—0·57 relating friction, in terms of the hydraulic gradient φ, to the slope angle θ was obtained. Since the thickness of the current can be computed from the relationship between φ and θ, we estimated the thickness of naturally occurring density-currents in Swiss lakes. The results suggest the applicability of our experimental results to small turbidity currents in nature. Our analysis further indicates that large turbidity currents have a small φ and can be expected to flow very long distances on a flat abyssal plain.

Variational-Lagrangian irreversible thermodynamics of nonlinear thermorheology

Abstract: A principle of virtual dissipation generalizing d'Alembert's principle to nonlinear irreversible thermodynamics provides a unifying foundation which leads to an extremely general variational-Lagrangian analysis of dissipative phenomena. Thus a synthesis is achieved between thermodynamics and classical mechanics. The present paper applies this principle to the nonlinear thermomechanics of continua with dissipation and heat conduction. Field equations, constitutive equations and Lagrangian equations with generalized coordinates are derived for nonlinear thermo- viscoelastcity, nonlinear thermoelasticity and heat conduction, plasticity, and com- pressible heat conducting fluids with Newtonian and non-Newtonian viscosity. The thermodynamics of instability is also analyzed from the same fundamental viewpoint. 1. Introduction. A Lagrangian-variational approach to irreversible thermo- dynamics was initiated by the author in 1954-55 (I, 21. It was developed mainly in the context of linearity and applied to thermoelasticity (3, 41 viscoelasticity (l, 2, 41, porous media (5), and initially stressed porous and continuous media (6, 71. The appli- cability of these methods to nonlinear problems was demonstrated in a variety of special cases, such as heat transfer (8), porous solids (9) and nonlinear thermoelasticity (lo). A treatment of nonlinear viscoelasticity based on a Lagrangian thermodynamic approach has also been presented by Schapery (ll). The theory embodied in the publications cited above provides a unified analysis based on Lagrangian formalism and generalized coordinates. Among many advantages, the equations have the same form in any coordinate system. Thus basic reciprocity properties of linear dissipative systems are immediately evident for a very large class of phenomena and boundary conditions. As a consequence, the proof of reciprocity properties does not have to be established for each particular case. Basic properties for systems with heredity are also obtained from the concept of internal coordinates and a general expression derived for the associated operator formalism. The corresponding

Power Reflection from a Lossy One-Dimensional Random Medium

Abstract: We consider the problem of an electromagnetic plane wave normally incident upon a slab of material whose constitutive parameters are subjected to lossy random perturbations. A transmission line model is adopted, wherein the four distributed parameters are assumed to be strongly mixing random functions of distance along the line. We study the reflection of energy at the input in the diffusion limit, an asymptotic limit involving weak random perturbations and long transmission lines. In the presence of dissipation, the probability density function for the modulus of the reflection coefficient approaches a nontrivial limit as the line length approaches infinity. We compute the mean and fluctuations of the voltage and power reflection coefficients with respect to this limiting density as a function of the dissipation.

Energy Dissipation on a Rough Slope

Abstract: Assuming long normally incident waves, described by linear theory, the energy dissipation on a rough slope is accounted for by introducing a term expressing the bottom shear stress. The theoretical development leads to a determination of the reflection coefficient as a function of the horizontal extent of the slope relative to the wave length in front of the slope and an equivalent slope friction factor. A method for the accurate determination of the reflection coefficient from experimental data is developed and used to establish an empirical relationship for the frictional characteristics of a rough slope. The resulting semi-empirical procedure for estimating the reflection coefficient of rough slopes is shown to yield fairly accurate results. The results show that bottom friction may account for the dissipation of 80% of the incident wave energy on a slope as large as 1:3 where the incident waves show no sign of breaking.

Stability of Persistent Currents in Unsaturated Superfluid He 4 Films

Abstract: We report the first measurements of the stability of persistent currents in unsaturated $^{4}\mathrm{He}$ films in an open geometry. Persistent currents are generated without rotation and exhibit several features which place strong restrictions on models of thermally activated dissipation in thin films.