Showing papers on "Dissipation published in 1970"

Longshore currents generated by obliquely incident sea waves: 1

Abstract: By using known results on the radiation stress associated with gravity waves, the total lateral thrust exerted by incoming waves on the beach and in the nearshore zone is rigorously shown to equal (E0/4) sin 2θ0 per unit distance parallel to the coastline, where E0 denotes the energy density of the waves in deep water and θ0 denotes the waves' angle of incidence. The local stress exerted on the surf zone in steady conditions is shown to be given by (D/c) sin θ per unit area, where D is the local rate of energy dissipation and c is the phase velocity. These relations are independent of the manner of the energy dissipation, but, because breaker height is related to local depth in shallow water, it is argued that ordinarily most of the dissipation is due to wave breaking, not to bottom friction. Under these conditions the local mean longshore stress in the surf zone will be given by (5/4)ρumax2 s sin θ, where ρ is the density, umax is the maximum orbital velocity in the waves, s is the local beach slope, and θ is the angle of incidence. It is further shown that, if the friction coefficient C on the bottom is assumed constant and if horizontal mixing is neglected, the mean longshore component of velocity is given by (5π/8)(s/C) umax sin θ. This value is proportional to the longshore component of the orbital velocity. When the horizontal mixing is taken into account, the longshore currents observed in field observations and laboratory experiments are consistent with a friction coefficient of about 0.010.

An eddy cell model of mass transfer into the surface of a turbulent liquid

Abstract: Experimental gas absorption studies for bubbles transported in turbulent pipe flow of water strongly indicate that liquid phase controlled mass transfer is due to surface renewal by turbulent eddies. Predictions of transport behavior from the conditions of turbulent flow cannot be made in support of this mechanism because no satisfactory theory of turbulent transport near a gas-liquid interface is available. This work considers a model of the hydrodynamic behavior near the surface which provides a link between the observed mass transfer behavior and the state of the turbulent field. In this model, the very small scales of turbulent motion are considered to be controlling. These motions are idealized, and their flow and mass transfer behavior are solved analytically. The overall result for eddies of various sizes is related to the turbulent energy spectrum by using only the easily accessible parameter ϵ, the energy dissipation rate. This model gives quantitative agreement to within a factor of 2 for three widely different experimental situations including gas-liquid and liquid-solid interfaces. However, the predicted Reynolds number dependence is somewhat higher than the experimental result. The model attempts to clearly define the basic physical process at the interface. Therefore, it indicates the direction for further experimentation needed to clarify the basic relationship between the mass transfer rates in the liquid phase and the hydrodynamic behavior of the turbulent liquid.

Damping of Solitary Waves

Abstract: The Korteweg‐de Vries equation is modified to include energy dissipation. In the cases treated the dissipative term is the Fourier transform of the linear damping. The effect of a small amount of such dissipation on the time evolution of a solitary wave is obtained.

The propagation of electromagnetic energy through an absorbing dielectric

Abstract: The energy associated with an electromagnetic wave passing through a dielectric resides partly in the electromagnetic field and partly in the accompanying excitation of the dielectric. The theory of energy propagation through an absorbing classical dielectric having a single resonant frequency is presented in this paper. Simple expressions are derived for the velocity of energy transport associated with an electromagnetic wave, and for the finite energy relaxation time caused by the damping mechanism. The variations of these quantities, and of the absorption coefficient, with the relative values of the damping constant and dipole moment of the classical oscillator are investigated. This information is used to throw light on the basic mechanism of irreversible dissipation of energy by an electromagnetic wave in a dielectric. The similarities between the calculations of the dielectric constant by classical dispersion theory and by quantum mechanics are discussed.

Finite-Amplitude Baroclinic Waves

Abstract: A theory is presented for the finite-amplitude behavior of unstable baroclinic waves in a quasi-geostrophic two-layer model. It is shown that in the absence of dissipation the equilibrated finite-amplitude state exhibits an oscillation, both of the mean flow and the baroclinic wave. On the other hand, if sufficient dissipation is present, the final state is a wave whose amplitude is steady and the approach to that state is non-oscillatory.

Minimal energy dissipation in logic

Abstract: Minimal energy dissipations for the logic process based on thermodynamics and general phase space considerations are known. The actual availability of these minimal dissipations has not, however, been demonstrated. These minimal dissipation sources in a computing system also act as noise sources and thereby lead to questions about the ultimate available reliability of the computing process. A new and hypothetical device is presented in this paper and used to construct a physically analyzable computing system. It is demonstrated that this system has dissipations larger than, but of the same order of magnitude as, the original minimal quantities. It is also shown that any required reliability can be obtained with this device, without increased energy expenditure, but at the expense of an increasing time per computational step.

Airplane Measurements of Planetary Boundary Layer Structure

Abstract: Measurements of air velocity and temperature from an airplane in the planetary boundary layer with strong surface heating are used to calculate vertical heat, momentum and energy fluxes, as well as spectral densities and probability distributions of velocity and temperature. Airplane traverses parallel to the wind are compared to crosswind traverses and a definite elongation of the heat transporting eddies, or thermals, parallel to the wind is observed. The terms in the turbulent kinetic energy balance equation (with the exception of the pressure fluctuation term) and the temperature variance balance equation are estimated. The turbulent kinetic energy dissipation is almost constant with height between the lowest flight level of 100 m above the surface, and the highest flight level of 1000 m, which is just below the top of the boundary layer, while the generation term due to the buoyancy force decreases and the divergence of the vertical transport of kinetic energy increases with height to mainta...

Thermal properties of very fast transistors

Abstract: Recent predictions that thermal effects will limit future transistor speed improvement motivated an interest in predicting and measuring these effects. A mathematical model of the three-dimensional transient heat flow problem is presented which takes into account the physical structure of the device and the actual region of power dissipation. At any point within the device, the model predicts the time-dependent temperature response to a change in power dissipation. A new method of measuring the local time-dependent thermal behavior of small bipolar transistors is described and used to verify the model. It was found that the thermal spreading resistance becomes important in silicon transistors when the emitter stripe dimensions approach 1 µ. Furthermore, the thermal response is much slower than the electrical response. Also, it was confirmed that adjacent devices in integrated circuits are essentially thermally isolated as far as thermal spreading resistance is concerned.

Turbulence and Flocculation

Abstract: Designers of flocculators are required to select the residence time, the number of flocculation compartments, the stirrer characteristics and the energy requirements, such that these function in an optimum manner in the treatment of a particular water. This paper presents a rational performance equation incorporating these parameters and demonstrates its validity with measurements employing a continuously operating model flocculation apparatus. Performance is shown to be determined by both the energy dissipation rate and the type of stirring equipment, but excessive energies result in floc breakup and reduced performance. At any particular performance a minimum residence time is shown to exist corresponding to an optimum energy dissipation. Anemometric measurements demonstrate a linear relationship between the mean square fluctuating velocity and the root mean velocity gradient computed from energy measurements. Whereas different stirrers have similar turbulence spectra, they display quite different performance coefficients.

Kelvin–Helmholtz instability of finite amplitude

Abstract: Non-linear Kelvin–Helmholtz instability, of two parallel horizontal streams of inviscid incompressible fluids under the action of gravity, is studied theoretically. The lower stream is denser and there is surface tension between the streams. Some progressing waves of finite amplitude are found as the development of a slightly unstable wave of infinitesimal amplitude. In particular, the non-linear elevation of the interface between the fluids is calculated. The finite amplitude of the waves does not equilibrate to a constant after a long time, but varies periodically with time. In practice, slight dissipation should lead to equilibration at an amplitude close to a value given by the present theory.

Dissipation discontinuities in hydromagnetic shock waves

Abstract: Within the hydromagnetic approximation, the effects of resistive, viscous, and thermal conduction dissipation on the structure of shock waves is studied. A Perturbation analysis about the upstream and downstream stationary points is developed, which, when coupled with the shock evolutionary conditions, determines the conditions for the formation of discontinuities in the shock structure. The Viscous subshock for fast shock waves and the hydromagnetic analogue of the gas dynamic isothermal discontinuity for fast and slow shocks are analyzed. Very oblique fast shocks require both resistive and viscous dissipation for a steady shock structure. Strong slow shocks propagationg nearly along the magnetic field fail to steepen if only resistive dissipation is included. The rotational discontinuity does not possess a stable shock structure for any of the dissipation processes considered.

Model for Reverse‐Domain Nucleation in Ferromagnetic Conductors

Abstract: Recent reports indicate that the average dynamic domain size in a material undergoing a change in magnetization may be significantly smaller than the static domain size. This finer dynamic domain structure can be predicted by an application of the principle of minimum entropy production Eddycurrent dissipation and dissipative domain nucleation and annihilation processes are considered as the dominant mechanisms for entropy production. Expressions for their contributions are derived and the total entropy production is minimized with respect to the density of domains. The theoretical average domain width thus derived is found to vary with frequency as (f)−1/2 and with peak induction as (Bmax)−1, in accord with observations. A comparison of the theoretical with observed domain densities permits an evaluation of the dissipation per unit wall area associated with the dynamic process of nucleating a reverse‐domain wall. This energy is an order‐of‐magnitude larger than domainwall surface energy.

Energy-dissipation theorem and detailed josephson equation for ideal incompressible fluids.

Abstract: The dissipation of energy in the flow of an ideal incompressible fluid is described by a theorem whose derivation relies upon the exact three-dimensional Magnus formula discussed in the previous paper. The theorem, which explicitly demonstrates the role of vortex motion in the process of energy dissipation, can be used to calculate the trajectories of vortices. Also derived is a detailed Josephson equation - an extension of Anderson's "new corollary in classical hydrodynamics" - which provides an exact non-time-average relation between chemical potentials and vortex motion.

Weak Nonlinear Magneto-Acoustic Waves in a Cold Plasma in the Presence of Effective Electron-Ion Collisions

Abstract: Nonlinear perturbation method is applied to describe the behaviour of unsteaby magneto-acoustic waves of small but finite amplitude propagating in a cold plasma in the presence of effective electron-ion collisions. It is shown under an assumption of small effective collision frequency that the original system of equations can be reduced to a single nonlinear equation which has a combined form of the Korteweg-de Vries and the Burgers equations. The dispersion term is just the same as that of collisionless case, whereas the dissipation term is found to be proportional to the magnetic viscosity. A qualitative discussion is given concerning the steady solutions of this equation.

Aie entrainment and energy dissipation in breakers

Abstract: Even m shallow water, only a part of wave energy is lost by turbulent viscosity and bottom friction, most of wave energy transfer takes place m the narrow zone of surf at the shore. Till to the point of breaking, the theoretical conception of an one-phase flow may be applied to the problem. From beginning of breaking, however, the effect of aeration can not be neglected. Prom a simple physical consideration, the sudden reduction of wave height and wave energy inside the surf zone can be explained by the entrainment of air bubbles into the water. Except compression and surface tension effects, most of wave energy is stored at first by the static energy of the air bubbles which are driven into the water. Using idealized assumptions for calculation (uniform concentration of air bubbles a.s.o.), it can be shown that m a plunging breaker the wave energy is dissipated on a very short way (less than on wave length), for a spilling breaker however, this way is of the order of some wave lengths.

Steady-state quantum analysis of linear systems

Abstract: A rigorous basis for the quantum analysis of the steady state of linear distributed systems is established. The analysis of a distributed system of finite length requires, for self-consistency, that excitations be stated at the boundaries of the system even in the absence of externally applied excitations. The commutators of the amplitudes at the boundaries are stated and a useful analogy with thermal noise of classical systems is established. The use of these boundary conditions enables one to formulate the theory of the steady state for distributed quantum systems. When the system under consideration is coupled to a dissipation mechanism, operator-noise sources have to be assigned to the dissipative elements. The commutation relations that must be obeyed by these noise sources are derived. This formalism enables one to analyze the steady-state operation of an attenuator and of a maser amplifier. Finally, properties of multiterminal-pair networks are discussed using the steady-state quantum approach.

Analytical Treatment of Radiation and Conduction Losses in Thermal Induction Plasmas

Abstract: Approximate solutions have been obtained of the Elenbaas‐Heller equation for a two‐zone model of thermal induction plasmas. Most of the heat production takes place in the external zone, where it is kept in balance by conduction losses. The major portion is lost to the wall, the minor transferred to the internal zone. This heat supply accounts for most of the radiation losses, which are confined to the internal zone. A small fraction of radiation is balanced by direct dissipation. Under these conditions, the distribution of the heat conduction potential assumes a parabolic shape for the inner zone, whereas it is described by Bessel functions in the external zone. A coordinate transformation in this zone accounts for the nonuniformity of the induced electric field and explicitly shows the effect of skin depth upon the profile shape. Matching of the zonewise solutions yields temperature distributions that are continuous to the first derivative and display the characteristic minimum at the axis known from exp...

Measurement of fine‐scale atmospheric structure using an optical propagation technique

Abstract: A propagation experiment was performed with a coherent beam of optical-frequency radiation transmitted over a 10-meter path. The combination of short path length and short wavelength makes the experiment sensitive to the fine-scale structure of the turbulent atmosphere. From the propagation measurements, we are able to infer both the characteristic size of the small-scale eddies known as the microscale l0 and the functional form of the spectrum of permittivity fluctuations at wave numbers in the region of dissipation (i.e., wave numbers of the order of the microscale).

Effect of dissipation on nonlinear coupling phenomena.

Abstract: The coupling coefficients, which account for the nonlinear interaction between three longitudinal plasma waves, are calculated. The results depend significantly on effects which are due to energy-dependent collision-frequencies and carrier masses.

Energy dissipation near an interface: a more realistic approach to electron range and stopping power.

Abstract: Spencer's (1) treatment of the energy dissipated near point isotropic electron sources is incorporated into the convenient formalism introduced by Charlton and Cormack (2) in their treatment of the interface problem. This approach leads to functions which are dependent both upon the initial electron energy and the medium in which the energy is being dissipated-factors not introduced into prior treatments (2-4). Dose distributions based on the functions derived in this paper are compared to distributions calculated from data presented by other authors. These comparisons suggest that dose distributions predicted by some of the simpler models of electron passage through matter are remarkably good and that one of the frequently-referred-to models must be rejected as a basis for dosage calculation. Functions are presented in tabular and graphical form for plane and spherical interfaces for electrons with "high" and "low" initial energies traveling through various media.

A theoretical study of the annual variation of atmospheric energy

Abstract: The zonally averaged equation for a two-level, quasi-geostrophic model are used to calculate the annual mean values and the first harmonic of the annual variation of the midtropospheric temperature and the zonal winds at the upper and lower levels. The diabatic heating in the model is of a simple Newtonian form. The effects of surface skin friction and of internal friction are included together with a simple parameterization of the meridional eddy transport of sensible heat, while the transport of zonal relative momentum by the eddies is neglected, thereby restricting the motion to the largest meridional scale. From the solution of the equations it is possible to calculate the annual mean values and the first harmonic of the annual variation of the amounts of zonal available potential energy and zonal kinetic energy and, also, the generation of zonal available potential energy, the convertions from this form of energy to eddy available potential energy and to zonal kinetic energy, and the dissipation of zonal kinetic energy by friction. The results show that the simplified model is capable of reproducing several important aspects of the annual variation of atmospheric energetics. The phase relationships involving the time lag between the generation of zonal available potential energy and the dissipation of kinetic energy as well as the time lag between the seasonal forcing and the maxima of zonal available potential energy and zonal kinetic energy are well reproduced. There are differences between the theoretical results and observational studies with respect to the intensity of the general circulation and the amounts of energy. The sensitivity of the theoretical solution to the numerical values of the physical parameters is investigated. DOI: 10.1111/j.2153-3490.1970.tb01931.x

On the meridional distribution of source and sink terms of the kinetic energy balance1,, 2

Abstract: The latitude-height distributions of the kinetic energy generation and dissipation over North America are presented in a series of cross sections from 25° to 70° N, and from the surface to the 50-mb level. The generation was computed using the twice-daily observed wind and geopotential data for a 1-yr period. The dissipation was obtained for a 3-mo summer period as the residual term of the kinetic energy equation. Throughout all latitudes, the generation and dissipation have a maximum in the planetary boundary layer. They gradually reach a minimum in the mid-troposphere, then increase to another maximum at the jet stream level except in middle latitudes. In the upper troposphere, there seems to be a characteristic meridional distribution both for generation and dissipation. The generation is significantly large north and south of the middle latitude where the kinetic energy is adiabatically destroyed. Those latitudes of large generation in the upper troposphere are also characterized by high fric...

Critical power dissipation in a superconductor

Abstract: The magnetic breakdown field Hp′ is calculated which, if applied at the surface of a super‐conductor, produces a critical power dissipation leading to a steep rise in the power loss. Generally Hp′ < Hc, the critical field of the material. The functional dependence of the Q of a microwave cavity for values of Hp near Hp′ is also found.