Showing papers on "Dissipation published in 1968"

Gravity currents and related phenomena

Abstract: This paper presents a broad investigation into the properties of steady gravity currents, in so far as they can be represented by perfect-fluid theory and simple extensions of it (like the classical theory of hydraulic jumps) that give a rudimentary account of dissipation. As usually understood, a gravity current consists of a wedge of heavy fluid (e.g. salt water, cold air) intruding into an expanse of lighter fluid (fresh water, warm air); but it is pointed out in Q 1 that, if the effects of viscosity and mixing of the fluids at the interface are ignored, the hydrodynamical problem is formally the same as that for an empty cavity advancing along the upper boundary of a liquid. Being simplest in detail, the latter problem is treated as a prototype for the class of physical problems under study: most of the analysis is related to it specifically, but the results thus obtained are immediately applicable to gravity currents by scaling the gravitational constant according to a simple rule. In Q 2 the possible states of steady flow in the present category between fixed horizontal boundaries are examined on the assumption that the interface becomes horizontal far downstream. A certain range of flows appears to be possible when energy is dissipated; but in the absence of dissipation only one flow is possible, in which the asymptotic level of the interface is midway between the plane boundaries. The corresponding flow in a tube of circular cross-section is found in $3, and the theory is shown to be in excellent agreement with the results of recent experiments by Zukoski. A discussion of the effects of surface tension is included in 0 3. The two-dimensional energy-conserving flow is investigated further in Q 4, and finally a close approximation to the shape of the interface is obtained. In Q 5 the discussion turns to the question whether flows characterized by periodic wavetrains are realizable, and it appears that none is possible without a large loss of energy occurring. In $6 the case of infinite total depth is considered, relating to deeply submerged gravity currents. It is shown that the flow must always feature a breaking ‘head wave’, and various properties of the resulting wake are demonstrated. Reasonable agreement is established with experimental results obtained by Keulegan and others.

Turbulence, viscosity, and dissipation in the solar-wind plasma

Abstract: Solar wind magnetic field power spectra and plasma velocity, discussing turbulence, viscosity and dissipation

Recent spectra of atmospheric turbulence

Abstract: Spectra of atmospheric turbulence recently measured at various heights and sites under a variety of stability conditions have been analysed and compared. The results are: (i)In regions over which the spectra obey −5/3 power laws, the ratio of the lateral to the longitudinal spectra shows fair agreement with the 4/3 ratio predicted by the Kolmogorov hypothesis for the inertial sub-range. The vertical-longitudinal ratio has a similar tendency. (ii)Dissipation rates computed from the longitudinal spectra seem to be consistent with the hypothesis that dissipation is balanced by the total production of mechanical and convective turbulent energy, provided that the turbulence is in equilibrium. In transition from rough to smooth terrain, dissipation exceeds the other terms. (iii)Vertical-velocity spectra obey Monin-Obukhov similarity theory up to a height of about 50 m. Their shapes are reasonably uniform, the major change with stability being a change of scale of the wave number axis, i.e., any characteristic nondimensional wave number is a function of z/L only. This function appears to be the same as the relation between the normalized dissipation and z/L. These results are consistent with previously measured Kolmogorov constants and with measured ratios of standard deviation of vertical velocity to friction velocity. Up to about a height of 50 m the wavelengths of the maxima of the logarithmic spectra increase linearly with height and more slowly thereafter, up to about 300 m. The spectra in stable air above 50 m suggest the existence of a buoyant sub-range. (iv)Longitudinal spectra do not obey similarity theory in a number of ways. The wavelengths do not scale with height, and there may be differences between sites when the spectra are plotted in similarity coordinates. (v)Spectra over the sea seem to have relatively more energy at low frequencies than those over land.

Resonant Oscillations of Water Waves. I. Theory

Abstract: A theory is presented to describe the oscillations of a liquid in a tank near a resonant frequency, where linearized theory is invalid. It is shown that although the oscillations are described adequately by the classical wave equation, the boundary conditions cannot be properly satisfied unless the non-linear terms are included. The effects of dissipation and dispersion are also significant in the determination of the oscillations, even though the terms to which they give rise in the equations are multiplied by small parameters under normal laboratory conditions. When the former is dominant a weak bore is formed which travels to and fro in the tank and is continually reflected at either end. When dispersion is significant the surface profile can be likened to a series of cnoidal waves which also travel along the tank and suffer reflexion. Several novel features appear. The amplitude does not increase monotonically as the nominal resonant frequency is approached. There are several distinct frequencies at which there is a sharp change in amplitude and in the form of the profile. More than one stable oscillation is possible at some frequencies. Near a resonant frequency higher than the fundamental, subharmonic oscillations are possible over part of the range.

On the generation, dissipation, and prediction of ocean wind waves

Abstract: A method based on the equation of radiative transfer has been developed for predicting the two-dimensional wind wave spectrum in the North Atlantic Ocean. The model takes account of wave generation by both resonance and instability mechanisms. A simple representation for wave breaking is also included, as are the effects of nonlinear wave interactions. This combination of energy transfer mechanisms is used to compute wave spectra that are in reasonable accord with observations. The results question the concept of a ‘fully developed’ spectrum. The work also points up a lack of understanding of the particulars of various energy transfer mechanisms, as well as the shortcomings of the basic predictive input data.

Instantaneous Energy Dissipation Rate in a Lap Joint—Uniform Clamping Pressure

Abstract: Instantaneous energy dissipation rate and load deflection of lap joints under uniform clamping pressure

Mechanism of Energy Dissipation in High-Damping-Capacity Manganese-Copper Alloys

Abstract: The results are described of some studies of a mechanism of energy dissipation due to strain-induced reorientation of tetragonality in binary manganese-copper alloys containing 60–90 wt.-% Mn. The dependence of the structure upon the progress of ageing and the temperature of observation is reported. A high damping capacity is associated with the presence of a tetragonal structure, and the damping capacity varies approximately as (strain)n, where n lies between 0.15 and 0.44. The reorientation of tetragonal domains has been investigated by X-ray techniques, and, the corresponding movement of domain boundaries has been observed and recorded by optical microscopy.

Generalized critical-state model of type II superconductors

Abstract: A modified form of the critical-state model of type II superconductors is described which takes account of Hc1 and surface sheath currents. The penetrating flux, hysteresis loop characteristics, a.c. losses and rate of penetration of flux into the superconductor when exposed to a sinusoidal magnetic field are evaluated. The model implies zero power dissipation for peak applied fields less than Hc1+ΔH and rapidly increasing dissipation just above this region, asymptotically approaching that derived from the Bean-London model.

Vertically propagating waves in an atmosphere with Newtonian cooling inversely proportional to density

Abstract: The behavior of vertically propagating waves is investigated for an atmosphere with Newtonian cooling, where the cooling rate coefficient is very small near the ground and increases inversely with the atmosphere's density away from the ground. This model for dissipation is unrealistic. However, the results obtained are very similar to those obtained by Yanowitch (1967a, b), who investigated the behavior of waves in a viscous atmosphere where the kinematic viscosity is inversely proportional to atmospheric density. The present calculations are, in general, far simpler than those of Yanowitch, and suggest that many of his results follow from the variation of dissipation with height and not from specific details of the physics. It is suggested that the present calculations may provide convenient estimates of the effects of dissipation in more realistic situations.

On the intensity of the general circulation of the atmosphere

Abstract: The intensity of the general circulation can be measured by the generation of available potential energy, the conversion of available potential energy to kinetic energy, or the dissipation of kinetic energy by frictional forces. Various estimates of the intensity are reviewed with special emphasis on the assumptions made in each investigation. There is a difference in principle between a nonhydrostatic and a hydrostatic system. In a hydrostatic system the internal and potential energies are proportional to each other, although the potential energy communicates directly with reservoirs of kinetic energy in a nonhydrostatic atmosphere. The review of the concept of available potential energy shows that the approximate form is exact for a quasi-geostrophic formulation of atmospheric dynamics. A critical evaluation is made of the generation of available potential energy and the dissipation of kinetic energy.

Time-Translation Invariance for Certain Dissipative Classical Systems

Abstract: Time-translation invariance of the equation of motion for an arbitrary one-dimensional classical system has been shown to generate a conservation law. For conservative systems, this conserved quantity is shown here to be the usual energy. For the linearly damped harmonic oscillator, the explicit form of this constant is found, as well as for quadratically damped systems. In both cases, as the damping approaches zero, the conserved quantity is shown to approach a function of the usual energy. For both types of dissipation, Lagrangians are given which yield the equations of motion.

Lower Atmospheric Energy Sources for the Upper Atmosphere

Abstract: The question of energy sources for the region above 70 km is considered together with the necessarily concomitant questions of energy transmission and conversion. Brief attention is devoted to energy reaching the upper atmosphere by radiation and diffusion. Energy carried to the upper atmosphere by advection by the mean field and by vertically propagating waves is treated in greater detail. The explicit excitations of gravity waves, planetary waves and thermal and gravitational tides, and the factors influencing their transmission to the upper atmosphere are discussed. In the case of tides a quantitative description of the magnitudes and energetics is presented. A simple model for evaluating the thermal effects of wave dissipation is also presented.

Finite Strain Elastic-Plastic Theory

Abstract: In the generation of plane waves in metal plates by detonation of contact explosives, the pressures reached can be sufficiently high to produce finite elastic and plastic strain components, and appreciable changes in temperature due to thermo-mechanical coupling effects. A theory of elastic-plastic deformation is developed to include these conditions. Finite elastic and plastic deformations are represented in terms of the initial and final configurations of the body, and an unstressed configuration at the constant base temperature subject only to plastic flow. In general this configuration cannot be represented by a continuous displacement function. The analysis of the kinematics of these three states is carried out for general deformation history. The elastic strain component is related to the stress through thermo-elastic theory for finite strains. A plasticity law is developed which includes the influence of temperature change and the finite elastic strain existing during the duration of plastic deformation. Thermo-mechanical coupling is included in the plasticity theory according to experiments on the dissipation of mechanical work into heat energy during plastic flow. Following plastic flow the internal energy and the entropy are greater than in a body of the same material under the same stress and at the same temperature, but not subject to plastic flow. However, these contributions are not considered to modify the elastic law appreciably, as has been found experimentally.

Wake-temperature turbulent fluctuation decay rates deduced from O sub 2 radiation.

Abstract: The effects of temperature fluctuations in a hypersonic turbulent wake on a chemical reaction with a strong temperature dependence are analyzed to determine the appropriate turbulence parameters for several different turbulent wake models. The chemical reaction selected for its temperature sensitivity is the atomic-oxygen chemiluminescent recombination. This radiation has been measured behind nonablating spheres in air in the General Motors Ballistic Range by Reis. The wake turbulence models are: a) random inviscid convection (so-called "marble cake"), b) homogeneous mixing, c) partial dissipation or bimodal model, d) mixinglag models, and e) gaussian mean-temperature profile with superimposed fluctuations. The data are interpreted in terms of each model. It is shown that models a, b, and d are inconsistent with the data. The radiation is interpreted in terms of the unmixed volume fraction of the partial dissipation model to obtain the rms turbulent temperature and mass density fluctuations and the turbulent dissipation function, which is then applied to predict the rms fluctuations of electron density. It is found that the resulting predictions are consistent with other measurements. The dissipation function indicates that the mixing-lag length is equal to about 20 wake radii. The model involving the Gaussian mean-temperature profile and fluctuations is consistent with the data for a thermal half width equal to slightly less than ha]f the mean turbulent front wake radius, with the temperature fluctuation ratio on the axis between 0.3 and 0.5. This is consistent with the measured mean-temperature profiles and temperature fluctuations, but the results are very sensitive to the mean temperature in the wake.

Prediction of Finite-Amplitude Waveform Distortion with Dissipation and Spreading Loss

Abstract: A new technique recently used for solution of the plane‐wave Burgers' equation in a lossless medium has led to the development of an approximate analytical solution to Burgers' equation with dissipation for plane, cylindrical, and spherical sinusoidal waves. The solution is valid for the initial propagation zone prior to sawtooth formation for Gol'dberg numbers larger than 5 as indicated by comparison with a previous numerical solution of Burgers' equation for a plane wave. The approximate solution is expressed as a series that converges rapidly enough to permit calculations of harmonic levels by hand. For more viscous cases, where the approximate solution fails, the above technique leads easily to a numerical solution of Burgers' equation. By comparing the harmonic levels predicted by the numerical solution with empirical data taken on distorting spherical waves, it is concluded that numerical results tend to be below the measured values. It is felt that the numerical method can be of use in predicting distortion levels for practical underwater systems that exploit finite‐amplitude effects.

Transient temperature distributions in viscoelastic solids subject to cyclic deformations

Abstract: When a viscoelastic solid is deformed, mechanical energy is necessarily dissipated in the form of heat. The present paper is concerned with the effect of this dissipation on the temperature field in the solid. The coupled heat equation is used to calculate the transient and steady-state temperature distributions in two situations: (1) simple-shear of an infinite slab, and (2) torsional oscillations of a circular rod.

On the energy release by magnetic field dissipation in the solar atmosphere

Abstract: The energy release by Joule magnetic-field dissipation in the solar atmosphere is discussed. It is shown that the heating is unimportant in the case of granulation and intergranular space. In the case of spot features the additional temperatures ΔTr with the accounting of the radiation losses are no more than 30° for small new spots, ≈ 1° for the large umbrae and 300° for bright points in large umbrae. This effect gives the possibility to suggest a hypothesis on the source of temperature inhomogeneity in the spot umbra and the nature of bright points. In the chromosphere the dissipation is negligible.

Energy transfer of a quasi-monochromatic wave in an inhomogeneous medium

Abstract: The paper presents the derivation of more general expressions than those usually obtained for the energy density W, the energy flux density , and the energy dissipation Γ of a quasi-monochromatic wave. The corrections as computed can be substantial, for example, in an inhomogeneous plasma in the region of frequencies ω for which the drift effects play an important role.

Motion of normal regions along a superconducting strip.

Abstract: The local temperature and heat current density in a superconducting strip whose ends are maintained at constant temperature are calculated for the case of periodically repeating motion of magnetic-flux-containing normal regions along the strip. The effective transport entropy per unit length per flux quantum, associated with the motion, is calculated; reasonable agreement with experiment is found. The power dissipation arising from the presence of temperature gradients is found to be small by comparison with the electrical dissipation in pure, but not in impure, superconductors. The presence of local thermal gradients is estimated to have an important influence upon the thermogalvanomagnetic effects in superconductors.

Diagnosis of Early Baroclinic NWP Models

Abstract: On the basis of the evidence available to date it is concluded that the two most important faults of early baroclinic models, 1) overdevelopment in terms of a general increase in kinetic energy and 2) failure to amplify cyclone-scale, baroclinic wave disturbances which amplify in the atmosphere, were due, respectively, to the absence of a dissipation term to balance the kinetic energy generated in the model and to space truncation which imposed too large a minimum scale for amplification. The solution to these problems is to reproduce in a model the scale dependence in the atmosphere of net development (development minus dissipation). The three paths available to achieve this goal are: 1) decrease the minimum resolvable scale (grid size), 2) reduce the space truncation of finite difference operators, and 3) increase the scale dependence of the dissipation term so that it removes energy only from the smallest permitted scales. The current best estimate of the residence time for the total kinetic e...

Effect of Sudden Change of Wall Temperature in a Thermal Radiating Gas

Abstract: Overall behaviours of a radiating grey gas bounded by a black infinite plane wall are investigated for small disturbances caused by an implusive change of the wall temperature. On the assumption that molecular dissipation is negligible in the conservation equation and the radiative transfer term in the energy equation can be approximated by the method of kernel substitution, approximate analytical solutions of these equations are obtained which are valid in the four limiting cases of strong and weak radiation, and small and large times. It is found that for large time and for weak radiation the wave front precedes the maximum of pressure. Except this, separation of wave from heat transport part is not very significant for large time, as expected. For small time, formation of an acoustic wave is distinct together with diffusion based on heat transport. For weak radiation and for small time, radiation slip is remarkable.