Showing papers on "Dissipation published in 1979"

Ionospheric modification and parametric instabilities

Abstract: Thresholds and linear growth rates for stimulated Brillouin and Raman scattering and for the parametric decay instability are derived by using arguments of energy transfer. For this purpose an expression for the ponderomotive force is derived. Conditions under which the partial pressure force due to differential dissipation exceeds the ponderomotive force are also discussed. Stimulated Brillouin and Raman scattering are weakly excited by existing incoherent backscatter radars. The parametric decay instability is strongly excited in ionospheric heating experiments. Saturation theories of the parametric decay instability are therefore described. After a brief discussion of the purely growing instability the effect of using several pumps is discussed as well as the effects of inhomogeneity. Turning to detailed theories of ionospheric heating, artificial spread F is discussed in terms of a purely growing instability where the nonlinearity is due to dissipation. Field-aligned short-scale striations are explained in terms of dissipation of the parametrically excited Langmuir waves (plasma oscillations); they might be further amplified by an explosive instability (except at the magnetic equator). Broadband absorption is probably due to scattering of the electromagnetic pump wave into Langmuir waves. This absorption is probably responsible for the ‘Overshoot’ effect: the initially observed level of parametrically excited Langmuir waves is much higher than the steady state level.

Climate and thermodynamic systems of maximum dissipation

Abstract: THE Earth–atmosphere is a classic example of a closed, dissipative and nonlinear thermodynamic system which is subject to both regular and irregular impulses causing significant departure from steady state. It is closed because it exchanges energy (solar and thermal radiant energy) but not mass with its environment. It is dissipative because the net input of radiant energy occurs mainly in regions of high temperature towards the Equator and the net output occurs mainly in regions of low temperature towards the poles. It is nonlinear basically because of the multiplicity of internal feedbacks and because of the importance of advective processes. It has steady-state character in the sense that the annual mean radiant energy input is very close to the annual mean output, and parameters such as the annual mean temperature do not vary significantly from one period to another. The regular seasonal variation in solar position ensures significant departure from the steady state so defined, and there are also significant irregular departures arising (for instance) from variations of solar input and IR output caused by variations in the amount and distribution of cloud. Recently I have shown1 that the overall Earth–atmosphere climate system seems to have adopted a format whereby the total thermodynamic dissipation associated with the horizontal energy flows in the atmosphere and ocean is a maximum. ‘Format’ in this context refers to the annual average geographic distribution of cloud, surface temperature and the horizontal energy flows. The practical significance of this is that, if one could accept it as a general principle governing climate behaviour, one could use it directly as a means of a priori prediction of climate and climate change without needing detailed analysis of the internal workings of the system. I could not explain previously why the Earth–atmosphere system should be so constrained. This note points out that the Earth–atmosphere has characteristics such that it might be expected to obey such a constraint. Furthermore, these characteristics are sufficiently general that the same principle of selection of steady-state mode of maximum dissipation may apply to a broad class of non-linear systems.

The fundamental solution in dynamic poroelasticity

Abstract: Summary. In this paper we study Biot’s full, time-dependent equations of dynamic poroelasticity with a view to understanding the effect of pore fluid on seismic wave propagation. Typical values of the constants appearing in the equations which are relevant to the rock surrounding earthquake sources are estimated from values appearing in the recent literature. We investigate the disturbance due to an instantaneous point body force acting in a uniform whole space. In fact we calculate the tensor fundamental solution since this has spherical symmetry, which is strongly exploited in our method of solution. The introduction of four scalar potentials enables us to reduce the problem to two decoupled second-order systems, each consisting of two coupled wave equations with friction in one space and one time dimension. By a further transformation these systems are expressed as symmetric hyperbolic systems of the first order, which are then solved by Laplace transforms. Because the dispersion equations are of higher than second degree only the large time saddle-point contributions are calculated. From these several phenomena emerge. (a) A P wave propagating with the P-wave speed appropriate to the ‘solid’ obtained by constraining the fluid to move with the solid matrix. However, instead of a 6 pulse shape familiar in elastodynamics this P wave has the shape of a Gaussian which appears to diffuse in a frame of reference moving with the P-wave speed. (b) An S wave with similar shape to P. (c) A long-term diffusion which is what one obtains from the equations reduced by setting the inertial terms to zero as in consolidation theory. We also investigate in an appendix a special case of dynamical compatibility in which the P wave remains sharp (i.e. a 6 pulse) and one of our two systems can be solved explicitly. The pulse diffusion amounts to a dissipation of the high frequency content qf seismic waves at a rate proportional to the square of the frequency.

Multiple Layer Series Connected Winding Design for Minimum Losses

Abstract: The classical one dimensional magnetic field and eddy current distribution ("proximity effect") within a series connected multiple layer coil is reexamined with regard to power losses withinthe windings. When the lengthand number of layers ina coilare fixed, the power dissipation within each layer can be minimized by choosing a specific radial thickness for each layer. Above or below this thickness, the losses within the winding increase. The conductor thickness which results in minimum dissipation depends on the relative position of the layer. When compared to a design having a constant thickness for each layer (chosen for minimum total dissipation), it is found that substantial savings in power consumption can be realized by employing a variable thickness of conductor. The one dimensional solution in cylindrical coordinates for the eddy current and skin effect in amultiple layer series connected coil is alsopresented. By solving the problem n cylindrical coordinates, the effect of curvature on the power consumption within each layer is apparent. This analysis should have application to the design of power transformers, armature windings, and inductors for power transmission lines.

Theory of Minimum Rate of Energy Dissipation

Abstract: A general theory of minimum rate of energy dissipation for a class of open channel flows with or without the movement of sediment is proposed in this paper. This theory states that the rate of energy dissipation is a minimum under steady equilibrium or gradually varied flow conditions. The theory is derived from the Navier-Stoke's equations of motion for gradually varied open channel flow without sediment transport. It applies to turbulent and laminar flows as long as the inertia forces due to the time-averaged velocity distribution is small compared with the forces due to gravity and shear. The theory in different degrees of generality can be used to explain the fluvial processes from the movement of sediment to the change of velocity, slope, roughness, channel geometry, pattern, and profile of a river under an eqiulibrium condition or during the process of self-adjustment to reach an equilibrium condition.

On the dissipation associated with equilibrium shocks in finite elasticity

Abstract: Equilibrium fields with discontinuous displacement gradients can occur in finite elasticity for certain materials. The presence of such “equilibrium shocks” affects the energy balance in the elastostatic field, and the present paper is concerned with a notion of dissipation associated with this energy balance. A dissipation inequality is proposed for three-dimensional equilibrium shocks for both compressible and incompressible materials. The consequences of this inequality are studied for weak shocks in plane strain for compressible materials and for shocks of arbitrary strength in anti-plane strain for a class of incompressible materials. A thermodynamic argument for the dissipation inequality is also given.

Buoyancy-Affected Flows In Ventilated Rooms

Abstract: Calculations of velocity and temperature distributions in rooms with ventilation arrangements are reported. The method involves the solution, in finite-difference form, of two-dimensional equations for the conservation of mass, momentum, energy, turbulence energy, and dissipation rate, with algebraic expressions for the turbulent viscosity and heat diffusivity. The results are shown to be in reasonable agreement with available experimental data and the method is then applied to provide additional information useful for design purposes.

Large‐amplitude gravity wave energy production and dissipation in the thermosphere

Abstract: This paper extends some of the analysis of gravity wave generation and dissipation in the thermosphere given in a previous paper [Richmond, 1978] by defining wave energy for gravity waves of arbitrary amplitude and by analyzing several numerical simulations. Wave energy as defined in this paper is closely related to the sum of kinetic energy and available potential energy of the atmosphere. In the absence of production or dissipation mechanisms, wave energy is approximately, but not strictly, conserved. Its dissipation is related to, but in general is not the same as, entropy generation. Numerical simulations substantiate the findings of Richmond (1978) that both the Lorentz force and the Joule heating of auroral currents can generate substantial gravity wave energy but that the waves produced by Joule heating are more capable of traveling to middle and low latitudes. The simulations also reveal that molecular dissipation of wave energy can be relatively less important, in comparison to daytime Joule dissipation, than the simple treatment of Richmond [1978] indicated.

Possible inverse cascade behavior for drift-wave turbulence

Abstract: The turbulent spectral properties of the dynamical equation of Hasegawa and Mima (1978) governing the evolution of the electrostatic potential in drift-wave turbulence is investigated for two formulations of the problem: (1) as a nondissipative initial value problem, with the potential represented by a truncated Fourier series with large number of terms, and (2) as a dissipative problem with a small viscous dissipation at very short spatial scales, and a long wavelength forcing term at longer wavelengths It is found that Hasegawa and Mima's prediction for the nondissipative, truncated initial value modal problem is accurate, but substantial differences exist for the forced dissipative case between computer results and analytical predictions based on a wave kinetic equation of Kadomtsev Much better agreement is found with a simple dual-cascade model based on Kraichnan's generalization of Kolmogorov's cascade arguments

Relaxation times in dissipative heavy-ion collisions

Abstract: The classical model introduced earlier for analyzing experimental data on dissipative heavy-ion collisions, is generalized to include effects from the gradual dissipation of radial kinetic energy and from the development of fragment deformations during the collision. Relaxation times for the dissipation of radial kinetic energy (τ R ) and relative angular momentum (τ l ) as well as for the development of deformations (τα) are fitted to the reaction86Kr (8.18 MeV/u) +166Er and applied to three other reactions. A consistent set of relaxation times isτ R = 0.3 · 10−21 s,τ l =1.5 · 10−21 s andτ α = 5 · 10−21 s. Empirical mass transport coefficients are deduced from comparisons with experimental element distributions. Effects from fluctuations in the deflection function are discussed. Evidence is found for the existence of a relaxation time of the order 10−21 s in the mass-drift coefficient.

Turbulent flow and heat transfer in pipes with buoyancy effects

Abstract: A finite-difference procedure, is employed to predict the turbulent flow and heat transfer in horizontal, inclined and vertical pipes when influenced by buoyancy. The flow is treated as parabolic; and the turbulence model used involves the solution of two differential equations, one for the kinetic energy of turbulence and the other for its dissipation rate. Results are presented for the velocity and temperature fields, and the associated flow-resistance and heat-transfer coefficients. The predictions for horizontal and vertical pipes have been compared with the available experimental results, and the agreement obtained is good.

Steady states and stability properties of a low-order barotropic system with forcing and dissipation

Abstract: A low-order barotropic system with Newtonian forcing and dissipation is investigated. The system has one component in the zonal flow characterized by a Legendre function and two components in the eddy flow having the same longitudinal wave number, but different meridional indices and described by two associated Legendre functions. Five real amplitudes characterizing the system and a system of five ordinary, non-linear differential equations describe the behaviour of the system. The steady states of the system can be determined by a numerical solution of a 9th degree equation for a given intensity of the forcing. Section 3 contains a description of the determination of the steady states and shows that up to five steady states may exist for a given forcing. The most complicated of the steady states have energy in all components of the system and the nonlinear exchange of energy among the components is essential for maintaining the state. Other steady states are either zonal or contain energy in one component only. A general procedure for the determination of the stability of a given steady state is outlined in Section 4 together with a determination of the stability of all steady states within a given parameter range in the forcing. It turns out that among the steady states which have energy in the wave components we find both stable and unstable configurations. It would thus appear that this result is in general agreement with the synoptic experience that some wave configurations can exist in a relatively unchanged form for a long time while others, presumably corresponding to the unstable configurations, will change rapidly. A close correspondence with real atmospheric conditions is impossible in a low-order system. The final part of Section 4 gives the result of some numerical experiments with the simple system to illustrate that the type of initial disturbance given to a steady, unstable state will determine the asymptotic steady state in a case where two or more such states exist. DOI: 10.1111/j.2153-3490.1979.tb00916.x

Nature of 1f frequency fluctuations in quartz crystal resonators

Abstract: The frequency fluctations measured in quartz crystal resonators of quality factor Q are proportional to Q −4.3 . The quantum approach to 1 f noise predicts fundamental fluctuations of the cross sections of elementary dissipative processes. Starting therefore from fluctuations of the total dissipative coefficient, a Q −4 -law is derived. Consequently, the noise is caused by dissipation fluctuations, rather than fluctuations in the density, or the real part of the Young modulus of the crystal.

Degradation and Dissipation of Herbicide Butachior in Paddy Fields

Abstract: 除草剤ブタクロール (マーシェット) を用いて実験室で行なった実験では, ブタクロールの分解は水溶液において異なるpHでは影響を受けず, また湛水状態の土壌中では温度が吸着に著しく影響することがわかった. 0.05M CaCl2溶液中における蒸散も温度が著しく影響する. 土壌カラムを用いて行なった実験ではブタクロールの溶脱は水の流速と薬剤の使用量と関係がある. 培養液におけるイネの生長は0.5ppm, Chlorella vulgaris の生長は0.1ppmの濃度で阻害を受けた.一般の使用法で行なった第二期作 (8月) における圃場試験では使用当日水田の水に最高量2.16ppmを認めたが速やかに減少し4日後には0.1ppm以下となった. 水田表土 (0～3cm) にも使用当日最高量9.17ppm存在したが4日後には0.5ppm以下となった. イネ (茎葉部) におけるブタクロールの吸収量は使用当日最高量31.2ppmを示したが4日後には測定できなかった. 第一期作 (3月) における圃場試験では若干異なる結果が得られたが恐らく気象条件が著しく異なる結果によるものであろうと思われる. ブタクロールを全面的に使用した水田附近の排水溝水 (使用後3～7日に採取) における残留量を調べた結果は何れも0.06ppm以下であり, 約1ヵ月後にはほとんど検出限界値 (0.001ppm) 付近またはそれ以下であった.水田におけるブタクロールの分解および消失はかなり容易でありブタクロールの水田における使用は環境の汚染に大きな影響を及ぼすことがないものと思われる.

Gravity wave propagation in a diffusively separated atmosphere with height-dependent collision frequencies

Abstract: Numerical calculations of gravity wave propagation through a two-component thermosphere with vertically-varying inter-species collision frequencies are performed using a direct integration method. Reflection of upgoing gravity wave energy into downgoing gravity waves appears to be small though nonnegligible at typical thermospheric periods and wavelengths. Coupling into diffusion waves is completely insignificant in most cases and may be determined in part by the relative abundance of the minor species. Temperature perturbation differences between species can be greater than 10% above 300 km altitude even though coupling into diffusion waves is small. Diffusive dissipation of gravity wave energy can be significant in the lower thermosphere and may be comparable to dissipation by viscosity and heat conduction below about 225 km altitude. Heating by diffusive dissipation may also be comparable to direct heating by solar radiation in the lower thermosphere. As a result of dissipative filtering of long-period and short-wavelength waves and the sensitivity of He-N2 density perturbation phase differences to diffusion, the AE-C satellite wave observations can only be fit by internal gravity waves with periods no greater than about 25 min and horizontal wavelengths no less than about 200 km.

Finite-Amplitude Baroclinic Waves in a Continuous Model of the Atmosphere

Abstract: The finite-amplitude dynamics of a weakly unstable baroclinic disturbance in an atmosphere with continuous shear and static stability is investigated. The effects of β (the planetary vorticity gradient), Ekman dissipation and thermal damping are included. The multi-scale analysis demonstrates the existence of two-dynamical regimes. First, under the influence of Ekman friction quasi-steady states are achieved after an oscillatory approach to the equilibrium state. It is shown that under the influence of friction long zonal waves possess a weak instability. Second, under the joint influence of Ekman friction and thermal damping (of the simplest Newtonian cooling model) a true asymptotic state is achieved. The amplitude is calculated and is shown to be independent of the thermal damping κ when κ is small. The rectified beat flux is calculated in the steady finite amplitude state. It is proportional to κ. The beat flux is proportional to the difference between the basic temperature gradient and a cri...

Does Venus wobble

Abstract: The free wobble damping time for Venus due to solar tides and rotational flexing is found to be approximately 700,000 times Q sub omega years, where Q sub omega is the dissipation function associated with the wobble frequency. The slow spin and expected small (nonhydrostatic) J2 predict a very long wobble period of about 100,000 years. As a result, a simple scaling of the earth's Chandler wobble excitation rate to that of Venus suggests that an appreciable wobble could exist. Detection (or lack thereof) of a free wobble may thus place constraints on the dynamic activity (e.g., mantle convection, Venusquakes, etc.) of the Venus interior.

A numerical analysis of the heavy-ion reaction based on the linear response theory

Abstract: Taking the relative distanceR and the deformationδ of each nucleus as the collective variables, we solve the two dimensional coupled dynamical equations of motion with friction in the framework of the linear response theory. In solving the equations of motion, we approximately replace the inertia tensor with the hydrodynamical one and use the modified liquid-drop one as the collective potential energy. As the frictional coefficients we use the microscopically calculated ones in the previous paper.