Showing papers on "Dissipation published in 1980"

Estimates of the Local Rate of Vertical Diffusion from Dissipation Measurements

Abstract: Scaling of the turbulent energy equation suggests the balance of terms in the ocean is between turbulent production, dissipation and the loss to buoyancy. In this paper two models for the source of oceanic turbulence are considered; namely, production by the Reynolds stress working against a time variable mean shear, and the gravitational collapse of Kelvin-Helmholtz instabilities. Both of these shear instabilities are believed to be important in the ocean. Using values for the critical flux Richardson number and the measurements from studies of Kelvin-Helmholtz instabilities, the efficiency of turbulent mixing is shown to be comparable for the two models. Therefore, a general relationship between the dissipation rate and the buoyancy flux due to the small-scale turbulent velocity fluctuations is derived. The result is expressed as an upper bound on the value of the turbulent eddy coefficient for mass Kρ ⩽ 0.2ϵ/N2. Values of Kρ are calculated from recent oceanic measurements of energy dissipation...

The critical velocity in pipeline flow of slurries

Abstract: In slurry transport, the critical velocity is defined as the minimum velocity demarcating flows in which the solids form a bed at the bottom of the pipe (bed load flows) from fully suspended flow. An analysis based on balancing the energy required to suspend the particles with that derived from dissipation of an appropriate fraction of the turbulent eddies is used to develop a correlation for prediction of the critical velocity. Comparison of the results with available experimental critical velocity data, relating to a rather wide variety of slurry systems, confirms that the present correlation does a superior job of prediction than all previously proposed critical velocity correlations.

A note on upwinding and anisotropic balancing dissipation in finite element approximations to convective diffusion problems

Abstract: In one dimension, Petrov—Galerkin nonsymmetric weighting for the convective diffusion equation can be interpreted as an added dissipation. The addition of an appropriate amount of dissipation can therefore give the same oscillation-free solutions as the ‘unwinding’, Petrov—Galerkin, finite element methods. The ‘balancing dissipation’ is optimally chosen so that excessive dissipation does not occur. A scheme is presented for extending this approach to two-dimensional problems, and numerical examples show that the new method can be used with improved computational efficiency.

Study of the superfluid transition in two-dimensional He 4 films

Abstract: We have studied the superfluid transition of thin two-dimensional $^{4}\mathrm{He}$ films adsorbed on an oscillating substrate. The superfluid mass and dissipation support the Kosterlitz-Thouless picture of the phase transition in a two-dimensional superfluid. In addition we observe finitevelocity effects which are not explained by current dynamic theories. We also report data on two-dimensional $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ mixtures.

Fluctuating Temperature Measurements in a Heated Round Free Jet

Abstract: Measurements of the fluctuating temperature in a heated round turbulent free jet have been performed with the aid of a fine wire thermocouple compensated for the effects of thermal inertia. The use of particularly fine thermocouple wires (12.7 μm in diameter) and of digital signal processing represent special features of the experiment. Data are reported for the mean, rms, probability density function, spatial correlation, energy spectrum and, with some reservation, dissipation of the fluctuating temperature. Where possible these are compared with the data of other workers.

Dissipation effects on MHD free convection flow past a semi-infinite vertical plate

Abstract: Viscous and Joule dissipation effects are considered on MHD free convection flow past a semi-infinite isothermal vertical plate under a uniform transverse magnetic field. Series solutions in powers of a dissipation number ∈ (=gβx/cp) have been employed and the resulting ordinary differential equations have been solved numerically. The velocity and temperature profiles are shown on graphs and the numerical values of Φ′1(0)/Φ′0(0) (Φ, temperature function) have been tabulated. It is observed that the dissipation effects in the MHD case become more dominant with increasing values of the magnetic field parameter λ (=M2/(Grx/4)1/2) and the Prandtl number.

Gravity currents entering a two-layer fluid

Abstract: This paper presents a study of steady gravity currents entering a two-layer system, with the current travelling either along the boundary to form a boundary current, or between the two different layers to form an intrusion. It is shown that, at the front of an intrusion, the streamlines meet at angles of 120" at a stagnation point. For an energy-conserving current the volume inflow rate to the current, the velocity of propagation and the downstream depths are determined. In contrast to the pioneering study of Benjamin (1968), it is found that the depth of the current is not always uniquely determined and it is necessary to use some principle additional to the conservation relationships to determine which solution occurs. An appropriate principle is obtained by considering dissipative currents. In general, if the volume inflow rate to a current is prescribed, the current loses energy in order to maintain a momentum balance. We thus suggest the criterion that the energy dissipation is a maximum for a fixed volume inflow rate. It is postulated that the energy which is lost will go to form a stationary wave train behind the current. A nonlinear calculation is carried out to determine the amplitude and wavelength of these waves for intrusions. Such waves have been observed on intrusions in laboratory experiments and the results of the calculation are found to agree well with the experiments. Similar waves have not been observed on boundary currents because the resulting waves have too much energy and break.

Fission in a wall-and-window one-body-dissipation model

Abstract: We calculate the fission of idealized nuclei in a modified liquid-drop model. The potential energy is taken to be a combination of Coulomb energy and nuclear energy obtained by double folding a Yukawa-plus-exponential two-body potential. The collective nuclear kinetic energy is calculated by use of the Werner-Wheeler approximation to incompressible, irrotational flow. The dissipation of collective energy into internal energy is calculated from the one-body wall formula until the neck decreases to a critical size, at which point a transition is made to a combination of the one-body wall formula relative to the centers of mass of the two nascent fragments and the one-body window formula. Experimental fission-fragment kinetic energies for the fission of nuclei throughout the Periodic Table are reproduced optimally when the neck radius at the transition point is 2.5 fm. For the alternative dissipation mechanism of ordinary two-body viscosity, the experimental fission-fragment kinetic energies are reproduced equally well when the viscosity coefficient is 0.015 TP.

Trapped Image Guide For Millimeter-Wave Circuits

Abstract: A novel dielectric waveguide is proposed for use in millimeter-wave integrated circuits, and a simple analysis for dispersion characteristics is developed. Numerical results agree reasonably with measured data. Radiation loss of this waveguide at curved sections are proven to be considerably Iess than those of the image guide. As an application of this waveguide, a leaky-wave radiator has been tested.

The Scaling of Vertical Temperature Gradient Spectra

Abstract: Tests of a formula derived for the cutoff wave number of vertical temperature gradient spectra, using data taken in the upper layers of the North Pacific, show encouraging results. To derive this formula, the cutoff wave number is assumed to be the Batchelor wave number, with kinetic energy dissipation calculated by combining a form used in the atmosphere for calculating the vertical eddy diffusivity in terms of the dissipation with the Osborn-Cox formula for calculating eddy diffusivity from the variance of the temperature gradient spectrum. Kinetic energy dissipation in the water column can be determined in this way; a vertical profile of dissipation shows values of the order of 10 -3 cm 2 s -3 at the base of a stormtossed mixing layer. In the thermocline below, dissipation occurs in patches.

On the entropy balance of the earth‐atmosphere system

Abstract: The entropy balance associated with a Budyko-Sellers climatic model is developed. It is shown that different regimes, associated with decreasing, as well as increasing values of entropy production (which measures the rate of dissipation in the system) in the course of time are possible. This immediately poses the problem of stability of steady states of the climatic system. An explicit criterion of climatic stability is thus derived, which is expressed in terms of thermodynamic quantities related to excess entropy production. The results are illustrated on simple cases involving diffusive energy transport. A comparison with Paltridge's minimum entropy exchange principle is also attempted.

On the correlation between turbulent velocity and temperature derivatives in the atmospheric surface layer

Abstract: Velocity and temperature derivatives were obtained at a height of 4 m in the atmospheric surface layer above land. With the assumption of local isotropy, these measurements are used to obtain some statistics of the turbulent energy and scalar dissipation fields. These statistics include the variances of the logarithms of the scalar and velocity dissipation fields and the correlation between these logarithms. When used in conjunction with the hypotheses for fluctuations in turbulent dissipation rates of Obukhov and Kolmogorov, the statistics suggest that the dependence of the flatness factor of temperature derivative on the turbulent Rynolds number Rλ is not as large as that which had been previously reported in the literature. The experimental data indicate a Rλ0.5 dependence for the kurtosis of the temperature derivative and a Rλ0.15 variation for the strain rate-scalar dissipation correlation.

Viscous heat generation in slit flow

Abstract: The onset of significant departure from isothermality caused by viscous energy dissipation in flow through a slit is determined for isothermal and adiabatic walls. A series solution of the energy equation enables calculation of dimensionless profiles for any power law fluid. Such solutions provide useful standards for judging performances of numerical schemes for solving complex nonisothermal flows.

Combination of Local Heating and Radiometry by Microwaves

Abstract: New methods for combination of microwave heating and microwave radiometry are presented. The processes experimented with here make it possible to collect the thermal signal emitted in the very volume in which the power dissipation is achieved. They can be used for medical (atraumatic control of local hyperthermia) or industrial applications (regulation of microwave heating).

Dynamic spectral characteristics of thermal models for solar hard X-ray bursts

Abstract: The dynamic spectral characteristics of the thermal model for solar hard X-ray bursts recently proposed by Brown et al. (1979) (BMS) are investigated. It is pointed out that this model, in which a single source is heated impulsively and cooled by anomalous conduction across an ion-acoustic turbulent thermal front, predicts that the total source emission measure should rise as the temperature falls. This prediction, which is common to all conductively cooled single-source models, is contrary to observations of many simple spike bursts. It is proposed, therefore, that the hard X-ray source may consist of a distribution of many small impulsively-heated kernels, each cooled by anomalous conduction, with lifetimes shorter than current burst data temporal resolution. In this case the dynamic spectra of bursts are governed by the dynamic evolution of the kernel production process, such as magnetic-field dissipation in the tearing mode. An integral equation is formulated, the solution of which yields information on this kernel production process, from dynamic burst spectra, for any kernel model. With a BMS-type kernel model in one-dimensional form, the derived instantaneous spectra are limited in hardness to spectral indices γ ≳ 4 for any kernel production process, due to the nature of the conductive cooling. Ion-acoustic conductive cooling in three dimensions, however, increases the limiting spectral hardness to γ ≳ 3. Other forms of anomalous conduction yield similar results but could permit bursts as hard as γ ≳ 2, consistent with the hardest observed. The contribution to the X-ray spectrum from the escaping tail of high-energy kernel electrons in the BMS model is calculated in various limits. If this tail dissipates purely collisionally, for example, its thick-target bremsstrahlung can significantly modify the kernel spectrum at the high-energy end. The energetics of this dynamic dissipation model for thermal hard X-ray bursts also are briefly discussed.

Comments on the dissipation of hydromagnetic surface waves

Abstract: A recent paper by Wentzel, which claims to calculate a plasma heating rate due to dissipation of surface waves in an ideal magnetohydrodynamic (MHD) fluid, is found to be in error in interpretation. A well-established general theorem pertaining to the conservative ideal MHD fluid requires that the normal mode calculated by Wentzel be oscillatory in time. Within ideal MHD, dissipation and plasma heating are therefore impossible.

VERTICAL MOTIONS IN AN INTENSE MAGNETIC FLUX TUBE V: Radiative Relaxation in a Stratified Medium

Abstract: It is of interest to examine the effect of radiative relaxation on the propagation of waves in an intense magnetic flux tube embedded in a stratified atmosphere. The radiative energy loss (assuming Newton's law of cooling) leads to a decrease in the vertical phase-velocity of the waves, and to a damping of the amplitude for those waves with frequencies greater than the adiabatic value (o),) of the tube cut-off frequency. The cut-off frequency is generalized to include the effects of radiative relaxation, and allows the waves to be classified as 'mainly progressive' or 'mainly damped'. The phase-shift between velocity oscillations at two different levels and the phase-difference between temperature and velocity pertur- bations are compared with the available observations. Radiative dissipation of waves propagating along an intense flux tube may be the cause of the high temperature (and excess brightness) observed in the network.

The Influence of Realistic Dissipation on Planetary Normal Structures

Abstract: The effect of realistic dissipation on the rotational normal modes of a barotropic atmosphere is investigated. Vertical growth of amplitude of the Lamb(10km equivalent depth)modes is found to diminish with increasing meridional index n. The fastest traveling modes are most sensitive to radiative-photo-chemical damping above 4 scale heights. However, with increasing n, thermal and viscous diffusion dissipate more of the energy below this level. The energy flux is virtually attenuated by 8 scale heights. Thus the particular details above this level should have little bearing on the nature of the modes below. Damping time scales (relaxation periods) are estimated for several modes. These are smallest for wavenumber 1, roughly 10 wave periods, and increase with zonal wavenumber. The role of dissipation in determining these relaxation periods is more than just the local damping of energy. It significantly enhances the “vertical leakage” and thus allows energy to flow more readily to levels of greater ...

Nutation Dampers vs Precession Dampers for Asymmetric Spacecraft

Abstract: The energy dissipation efficiencies of ball-in-tube dampers oriented with their sensitive axes orthogonal to (nutation) and parallel to (precession) the nominal spin axis of an asymmetric spacecraft are studied using the energy-sink method and numerical integration. Energy-sink equations for each of the two types of dampers are obtained in the forms of damped, periodically forced Hill-type equations. The stability of solutions to Mathieu equation approximations to these equations is considered. An approximate analytical expression for the ratio of the average energy dissipation rates of the two types of dampers is obtained. Results for ideally tuned, identical (except for their spring constants and orientations) dampers are presented and compared with those of a previous study. For a particular spacecraft configuration, analytical results for the energy dissipation ratio are compared with numerical results, and excellent agreement is achieved.

Prediction of Two- and Three-Dimensional Asymmetrical Turbulent Wakes, Including Curvature and Rotation Effects

Abstract: Twoand three-dimensional turbulent wakes which develop under the influence of streamline curvature and rotation were calculated with three turbulence closure models. The first model was comprised of transport equations for the turbulent kinetic energy and the rate of energy dissipation. The second model was comprised of equations for the rate of turbulent kinetic energy dissipation and Reynolds stresses, but the effects of the convection and diffusion in the Reynolds stress transport equation were handled collectively. The third model utilizes equations of turbulent kinetic energy dissipation and Reynolds stresses in nearly exact form. All three of the models were modified for the effects of streamline curvature. The second and third models include the effects of rotation through the rotation-originated redistribution term in the transport equation of Reynolds stresses. The numerical results for the wakes of airfoils, cascades, and turbomachinery rotor blades demonstrate that the second and third models provide accurate predictions, but computer time and storage can be considerably saved with the second model.

Effect of dissipation and dispersion on slowly varying wavetrains

Abstract: A kinematic model for disturbance wave motions slowly modulated in space and time is developed, which describes the effects of amplitude and frequency dispersion, modal dependence, flow inhomogeneities, dissipation, and high-order wave dispersion and diffusion. The results, based on general variational principles, apply to waves in arbitrary continuous media, but are discussed primarily in the fluid-dynamic context. The more complete theory presented here reduces to several known wave models in various limits and reconciles, within the framework of a broader unifying approach, a number of differences found among existing, although more specialized, formulations. These latter models are surveyed and, in particular, we emphasize how their domains of applicability may be limited by different kinds of dominant high-order dispersive or diffusive wave mechanisms. **;