Showing papers on "Momentum published in 1973"

Observations of a Stationary Mountain Wave and its Associated Momentum Flux and Energy Dissipation

Abstract: Analysis is presented of data obtained from instrumented aircraft flying in a mountain wave of moderate amplitude west of Denver, Colo., on 17 February 1970. Emphasis is placed on determination of the downward flux of westerly momentum generated by the wave, for which accurate measurements of vertical velocities on scales of order 50 km are essential. Three different methods are applied and compared: direct aircraft measurement, using vanes and an inertial platform; evaluation from the steady-state equation for conservation of potential temperature; and integration of the steady-state continuity equation. Each method produces errors, but by combining the results of the three methods a profile is obtained which agrees. fairly well with a steady-state theoretical prediction. An important side result is the discovery that gust-probe equipment is apparently not necessary for the direct aircraft measurement of wave momentum flux, but an inertial platform or similarly stable attitude reference level is...

Decay of poloidal rotation in a tokamak plasma

Abstract: Radial electric fields may be built up in a tokamak by several mechanisms such as nonambipolar particle transport or loss, or the inhomogeneous deposition of electric charge which occurs as a result of the injection of fast neutral atoms. The initial effect of the radial fields is to produce a poloidal rotation of the plasma. Such rotation, however, subjects the moving elements of the plasma to energy dissipation by magnetic pumping, which damps the rotation in a period of the order of the ion‐ion collision time. The problem is analyzed for the “plateau” and “banana” regimes by applying the drift kinetic equation, with a simple relaxation collision term, to a slab‐model low‐β plasma. The calculation may be more generally applied to the problem of momentum dissipation for any low‐β long‐mean‐free‐path plasma in a periodic or stochastic magnetic field.

Energy and momentum theorems in magnetospheric processes

Abstract: This review deals with the several energy and momentum theorems that relate to magnetospheric processes that have been developed. The region of primary consideration in this paper is the magnetospheric domain that extends between the ionosphere and the interplanetary medium, although, for studying certain phenomena, ionospheric and solar wind properties are of central importance and must be included. Both energy theorems and momentum theorems with their applications are presented. Since energy is an integral property of the system variables, analytical results can be found without knowledge of detailed dynamical processes. Thus, relations are derived between particle and magnetic system energies, and application is made to the shape of the magnetopause and various phases of a magnetic storm. Particular attention is given to symmetric and asymmetric ring currents, including energy and momentum equilibrium conditions; a review of nonlinear self-consistent models and a discussion of how charge exchange and energy diffusion participate in the recovery phase are presented. Comprehensive expressions for the storm time disturbance field are given in terms of both ring current and boundary current energies, and changes that occur during magnetospheric compressions are discussed. The momentum theorems center around the requirement of static force balance during geomagnetically quiet intervals. Whereas the energy theorems give expressions for the average disturbance field over the earth, the momentum theorems give the gradient in the disturbance field across the earth. The forces between earth and the boundary current, the ring current, and the tail current are derived for various models. It is noted that existing vacuum models of the geomagnetic tail are deficient in meeting the combined requirements of energetics and dynamics of the quiet time tail. Introducing the plasma sheet removes the difficulty by allowing an extra degree of freedom in adjusting the force between the earth and the tail. The role of the plasma sheet in making force adjustments is shown to be consistent with the observed thinning of the plasma sheet before sub storms.

A numerical simulation of the cavity filling process with PVC in injection molding

Abstract: : In this work a numerical simulation of the mold cavity filling process was attempted. The mold filled in this simulation is a disk which hot polymer melt enters through a tubular entrance located at the center of the top plate. The tube is 2.54 cm. long and has a radius of 0.24 cm. The plate separation and outer radius of the disk cavity may be varied. A constant pressure applied at the entrance of the tube causes the flow. The cavity walls are kept at various low temperatures. The reported results are for rigid PVC. Continuity, momentum, and energy transport equations for a constant density power law fluid are used to solve the flow problem. It is assumed that the outer radius of the disk is very much greater than the plate separation, that there is axisymmetry, that only one of the viscous terms in the momentum equation is significant, and that in the flow direction heat conduction is negligible compared with convection. Constant values for the thermal conductivity and heat capacity of the melt are used. The resulting differential equations are transformed into difference equations explicity, except for the energy equation. In this case a Six Point Crank- Nicholson implicit differencing technique was necessary to assure thermal stability of the solution. The difference equations were solved by using a Fourth Order Ruhge-Kutta integration formula for the velocity profiles and the Thomas method for the temperature profiles. Convergence to the differential solutions is guaranteed but since a lower limit was imposed on the time increment by the core storage limit of the computer facilities (27K) and long execution times, all results are semi-quantitative for the problem as stated. (Author, modified-PL)

Observed generation of an atmospheric gravity wave by shear instability in the mean flow of the planetary boundary layer

Abstract: Observations of a single boundary-layer event — the generation of an atmospheric gravity wave by an unstable shear flow at Haswell, Colorado on November 12, 1971 — are briefly described and discussed. The observations were made using: (a) an acoustic echo sounder, (b) anemometers mounted at two fixed levels on a 150-m tower, (c) an anemometer and a thermometer mounted on a movable carriage on the tower, and (d) a microbarograph array, including one microbarograph mounted atop the tower. The wave phase velocity (−3.5–4.0 m s−1) was found to equal the wind velocity in the middle of the shear flow, as assumed by other authors. The wave-associated vertical fluxes of momentum and energy measured just above the wave critical layer were estimated to be −5 dyn cm−2 and −800 erg cm−2 s−1, respectively. These are large values. The annual average vertical flux of momentum at temperate and high latitudes is −0.25 dyn cm−2, while the average kinetic energy dissipation rate in a unit column of atmosphere is −5 × 103 erg cm−2 s−1. If the region of wave generation was itself propagating horizontally, its propagation velocity was large compared with the horizontal phase speed of the small-scale waves generated. Wave generation appeared to occur over an area large compared with the size of the microbarograph array (i.e., ≫ 2 km).

On the mechanism of sound production in organ pipes

Abstract: It is shown that both the Cremer‐Ising and Coltman mechanisms for sound production in organ pipes are comprehended by a more general approach, based on conservation of linear momentum. By calculating force per unit area exerted by the jet on a control volume containing the mixing region, and equating this to the difference in pressure along the pipe axis, it is possible to derive an expression for acoustic particle velocity in the standing wave as a function of the jet driving flow spectrum. The momentum model of the jet‐pipe interaction is able to explain the Coltman radiation symmetry effect, and also accounts for the role of entrained air in sound production. Additional spectral interaction terms, not previously noted, are found to play a significant role in the production of sound‐pressure fluctuations in the pipe. The fluctuating lift force at the edge is found to contribute to the sustenance of the pipe‐cavity oscillation below resonance, opposing it above resonance. In the near vicinity of the resonant frequency, edgetone effects are relatively small.

The momentum of a light wave in a refracting medium

Abstract: Elementary considerations support the result of Abraham, by which the momentum is, for given energy, inversely proportional to the refractive index, rather than proportional to it, as predicted by Minkowski. This conclusion disagrees, however, with the experiment of Jones & Richards.

Some problems of quantum mechanics possessing a non-negative phase-space distribution function

Abstract: In order to clarify physical consequences due to the presence of a set of auxiliary functionsφ k (q,t) in quantum mechanics with a non-negative phase-space distribution function, the simplest quantum-mechanical problems are solved. It is shown thatφ k (q,t) influence upon the results of a problem. Therefore it is supposed thatφ k (q, t) reflect some physical reality (subquantum situation), interacting with a mechanical system. In particular the ‘subquantum situation’ determines the minimum coordinate and momentum uncertainties ((δq)2 and (δp)2) as well as the coordinate distribution of a ‘fixed’ system and the momentum distribution of a ‘free’ system. These results provide the opportunity to formulate the notion of a stationary homogeneous isotropic ‘subquantum situation’. Supposing thatδq andδp are small an attempt is made to develop an approximate method of solutions (quasi-orthodox approximation). Energy spectrum of an electron in a hydrogen atom is found in the second order of this approximation.

Wave equation and propagation parameters for sound propagation in suspensions

Abstract: A wave equation has been formulated for the propagation of sound in suspensions and emulsions, taking into consideration the different viscosities and thermodynamic properties of the suspension components. The suspension has been assumed to be homogeneous in the sound field for the particle size to be much smaller than the incident wavelength and to be a continuous fluid which enters and leaves the control volume element at volume‐averaged values of velocity and momentum. This equivalent continuous fluid has been assumed to possess a density equal to the volume‐averaged density and a compressibility equal to the effective compressibility of the suspension or emulsion (calculated from the scattering theory). The formulated wave equation immediately yields the acoustical properties of suspensions or emulsions, such as sound velocity and viscous and thermal attenuation coefficients.

Asymmetric wave-stress tensors and wave spin

Abstract: Linearized wave-stress tensors derived from Hamilton's variational principle may be asymmetric. If interpreted as momentum fluxes, they would lead to lack of conservation of orbital angular momentum. It is shown that changes in internal angular momentum or spin of waves and torque coupling to external fields can adequately provide conservation of total angular momentum in such cases, Examples are given for acoustic, internal gravity, Rossby and plasma waves.

Quantum-mechanical analogue of particle creation caused by the expansion of the universe

Abstract: Free spin-1/2 particles in an expanding isotropic and homogeneous universe are treated in the framework of the quantum mechanics of unquantized matter fields. The curved space-time acts thereby as an unquantized external field. The eigenvalues of energy and momentum are time dependent. They are, after a simultaneous energy and momentum measurement, related by the special-relativistic relationE(t) = = ±c √p2(t) +m2c2. A freely moving plane wave (solution of the dynamical equation which is an eigenfunction of the momentum) contains in general cigenfunctions of both signs of the energy, which in special relativity remain decoupled. This is also the case in the universe above for particles with vanishing rest mass (neutrinos) and massive particles with vanishing momentum. For other particles one finds an expansion-induced time-dependent mixing of positive- and negative-energy parts. One can interpret this with regard to the corresponding creation and annihilation operators of quantum field theory as the analogue of particle production. The probability of finding particles of opposite sign of the energy differs with the aget of the universe and is of the order ϱ(t), where ϱ(t) isħ/mc2 times the Hubble parameter at the timet. For electrons ϱ(t) ≈ 10-21t-1 s. While ϱ(t) is today only about 10-39, one can expect considerable particle production for times with ϱ(t) ≥ 1, i.e. during the first 10-21 seconds of the Universe.

The conservative “flow” method and the calculation of the flow of a viscous heat-conducting gas past a body of finite size

Abstract: A METHOD for the numerical solution of gas dynamical problems, based on a difference approximation of the conservation laws, is presented. Examples of calculations of the flow past a body of finite size are given. This paper presents a numerical method, based on a difference approximation of the conservation laws, recorded for each cell of the difference grid. In the field variables the method generates an explicit difference scheme which, as is shown by calculations and studies of a model example, is conditionally stable and monotonic. From the method of construction, the scheme is conservative with respect to mass, the momentum components and the total energy. The method is used to calculate the flow past a sphere of a viscous, heat conducting gas at a given surface temperature. Various formulations of this problem have been considered in [1–3]. In [1] the “shortened” Navier—Stokes equations were solved by the method of integral ratios; in [2] a numerical solution of the complete Navier—Stokes equations was found by a finite-difference method. In [3] the method of integral ratios was also used for the complete system of Navier-Stokes equations.

Note on shock‐wave velocity in high‐speed liquid‐solid impact

Abstract: A better relationship between the shock‐wave and impact velocities in high‐speed water‐solid impact is determined from the fundamental equations of continuity, momentum, and state. A second‐order relationship is hypothesized and the necessary coefficients then found using the Tait equation of state. Very good agreement is found with available experimental data for water.

Hartree–Fock Alpha Cluster Density Distributions in Light A = 4n Nuclei Using Density Dependent Effective Interactions

Abstract: Hartree-Fock calculations have been performed for the A = 4n nuclei /sup 12/C to /sup 40/Ca, employing a selection of density-dependent effective interactions. This selection consists of two density and momentum dependent delta function interactions, similar to the Skyrme interaction, and two density and momentum dependent finite-range interactions whose radial forms are given as a sum of two Gaussian functions. A basis of single-particle axially deformed harmonic oscillator functions is used. Special emphasis is given to the study of the occurrence of alpha-particle type clustering in the density distributions of light A = 4n nuclei and the influence of the strength of the one-body spin-orbit field. (auth)