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NASA NTRS2011

The Inner Structure of Collisionless Magnetic Reconnection: The Electron-Frame Dissipation Measure and Hall Fields

It was recently proposed that the electron-frame dissipation measure, the energy transfer from the electromagnetic field to plasmas in the electron s rest frame, identifies the dissipation region of collisionless magnetic reconnection [Zenitani et al., Phys. Rev. Lett. 106, 195003 (2011)]. The measure is further applied to the electron-scale structures of antiparallel reconnection, by using two-dimensional particle-in-cell simulations. The size of the central dissipation region is controlled by the electron-ion mass ratio, suggesting that electron physics is essential. A narrow electron jet extends along the outflow direction until it reaches an electron shock. The jet region appears to be anti-dissipative. At the shock, electron heating is relevant to a magnetic cavity signature. The results are summarized to a unified picture of the single dissipation region in a Hall magnetic geometry.

Zenitani, Seiji↗
NASA NTRS2011

Charging and Subsequent Dissipation of a Rover Wheel in the Lunar Polar Regions

As a roving vehicle moves along the lunar surface, electric charge will build up through tribo-charging. This charge collected by the roving object will have a dissipative path to either the surface or the ambient plasma, depending upon which path is most conductive. At the lunar terminator region and into nightside regions, the surface is very cold and becomes a very poor conductor. leaving the plasma as the dominant remediating current for dissipation. However, within lunar craters, even plasma currents become substantially reduced which then greatly increases electric 'dissipation times, This work will involve the advancement of the stepping astronaut charge model, by considering the charging and plasma dissipation of a rolling rover wheel, The objective of this work is to determine the nature of charging and discharging for a rover wheel as it rolls along the cold, plasma-starved lunar polar regions. The rotating wheel accumulates charge via contact electrification (tribo-charging) with the lunar regolith. This tribo-charging is dependent on the composition of the objects in contact, with insulators and conductors charging differently. Given the environmental plasma in the region, we then determine the dissipation time for the wheel to bleed off its excess charge into the surrounding plasma. A model of the rover wheel rotating continuously over a surface regolith within a polar crater has been applied. The environmental plasma has been described previously. We define a new tribo-charging term specifically for the rotating system, with charge levels defined as a function of the wheel size, area in contact with the regolith, regolith particle size distribution, as well as the velocity at which the wheel is turning. We recognize that as charged dust accumulates and sticks to the wheel, this behaves effectively as a new current. Hence, the overall charging of the system should no longer vary linearly. and begin to show signs of saturation, We are devising a dust current term to model this charge-limiting effect, and will present the results in discussion.

Jackson, T. L.↗
NASA NTRS2013

DNS, Enstrophy Balance, and the Dissipation Equation in a Separated Turbulent Channel Flow

The turbulent flows through a plane channel and a channel with a constriction (2-D hill) are numerically simulated using DNS and RANS calculations. The Navier-Stokes equations in the DNS are solved using a higher order kinetic energy preserving central schemes and a fifth order accurate upwind biased WENO scheme for the space discretization. RANS calculations are performed using the NASA code CFL3D with the komega SST two-equation model and a full Reynolds stress model. Using DNS, the magnitudes of different terms that appear in the enstrophy equation are evaluated. The results show that the dissipation and the diffusion terms reach large values at the wall. All the vortex stretching terms have similar magnitudes within the buffer region. Beyond that the triple correlation among the vorticity and strain rate fluctuations becomes the important kinematic term in the enstrophy equation. This term is balanced by the viscous dissipation. In the separated flow, the triple correlation term and the viscous dissipation term peak locally and balance each other near the separated shear layer region. These findings concur with the analysis of Tennekes and Lumley, confirming that the energy transfer terms associated with the small-scale dissipation and the fluctuations of the vortex stretching essentially cancel each other, leaving an equation for the dissipation that is governed by the large-scale motion.

Balakumar, Ponnampalam↗
NASA NTRS2014

Quantified Energy Dissipation Rates in the Terrestrial Bow Shock: Analysis Techniques and Methodology - 1.

We present a detailed outline and discussion of the analysis techniques used to compare the relevance of different energy dissipation mechanisms at collisionless shock waves. We show that the low-frequency, quasi-static fields contribute less to ohmic energy dissipation, (−j ⋅ E ) (minus current density times measured electric field), than their high-frequency counterparts. In fact, we found that high-frequency, large-amplitude (greater than 100 millivolts per meter and/or greater than 1 nanotesla) waves are ubiquitous in the transition region of collisionless shocks. We quantitatively show that their fields, through wave-particle interactions, cause enough energy dissipation to regulate the global structure of collisionless shocks. The purpose of this paper, part one of two, is to outline and describe in detail the background, analysis techniques, and theoretical motivation for our new results presented in the companion paper. The companion paper presents the results of our quantitative energy dissipation rate estimates and discusses the implications. Together, the two manuscripts present the first study quantifying the contribution that high-frequency waves provide, through wave-particle interactions, to the total energy dissipation budget of collisionless shock waves.

Terrestrial bow↗
NASA NTRS1972

Dissipative effects in the expansion of the universe. I, II.

Consideration of dissipative processes in anisotropic homogeneous world models, showing that dissipation reduces the anisotropy. The viscosity approximation and its range of applicability is discussed. Examples are presented which have been calculated by the use of a simple approximation to the collision-time method, using the cross section appropriate to weak interaction neutrino scattering. It is found that such dissipation is quite effective except for one particular cosmological model which is axisymmetric and in which the entire expansion of the model is taken up by expansion along the axis. A detailed multicomponent model is developed for dissipative processes in Euclidean homogeneous cosmological models. These processes involve neutrinos which might have long mean free times in interaction with other constituents which are thermalized by electromagnetic interactions, and whose weak interactions produce thermal neutrinos.

Matzner, R. A.↗
NASA NTRS1981

The Eulerian- and Lagrangian-mean flows induced by stationary, dissipating planetary waves

The Eulerian- and the Lagrangian-mean flows induced by stationary, dissipating planetary waves are discussed by employing a simple channel model on a beta-plane. It is assumed that the wave is excited by the bottom undulation and dissipated by Newtonian cooling with relaxation time alpha and by Rayleigh friction with (lambda)(alpha), lambda being constant. Three cases where lambda is equal to one are discussed: (1) the basic zonal wind U sub 0 and the dissipation rate alpha are both constant; (2) U sub 0 varies with height while alpha is constant; and (3) U sub 0 and alpha both vary with height. In case (1), the Eulerian- and the Lagrangian-mean fields are shown to depend on the difference between the dissipation scale-height and the density scale-height. In case (2) and case (3), it is shown that the results for case (1) are modified under slightly more realistic situations.

Takahashi, M.↗
NASA NTRS1984

The Laplacian resonance and tidal dissipation

The Laplacian resonance amongst Io, Europa, and Ganymede was examined, taking into account tidal dissipation in Jupiter, Io and Europa. In equilibrium, it is not possible to neglect dissipation in Europa nor the torques of Jupiter on Europa and Ganymede. A formal calculation was made on the assumption that the tidal torques and the torques in orbit-orbit resonance reached an equilibrium such that the rates of decrease of the mean motions of the satellites are in the ratios 4:2:1. Q(j)/k(j)=167 Q(1)/k(1), Q(2)/k(2) = 0.44 Q(1)/K(1), where Q denotes the quality at the body's frequency of rotation, k its second degree Love number and the subscripts J, 1 and 2 denote Jupiter, Io, and Europa. The Q(J) found is at Jupiter's frequency of rotation. The rate of tidal dissipation in Europa comes to 1/5 that of Io. Such a low value of Q(2)/K(2) is plausible if dissipation in both Io and Europa is due to tidal friction in fluid against underlying and overlying solid layers.

Cook, A. F.↗
NASA NTRS1984

Tidal dissipation in the Earth and Moon from lunar laser ranging

The evolution of the Moon's orbit which is governed by tidal dissipation in the Earth while the evolution of its spin is controlled by its own internal dissipation is discussed. Lunar laser ranging data from August 1969 through May 1982 yields the values of both of these parameters. It is suggested that if the Moon was orbited the Earth since its formation, this must be an anomalously high value presumably due to changes in dissipation in the oceans due to continental drift. The explanation that the dissipation occurs at the interface between the mantle and a liquid core of shell is preferred.

Yoder, C. F.↗
NASA NTRS1985

Artificial dissipation models for the Euler equations

Various artificial dissipation models which are used with central difference algorithms for the Euler equations are analyzed for their effect on accuracy, stability and convergence rates. In particular, linear and nonlinear models are investigated using an implicit approximate factorization code (ARC2D) for transonic airfoils. Fully implicit application of the dissipation models is shown to improve robustness and convergence rates. The treatment of dissipation models at boundaries will be examined. It will be shown that accurate, error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model.

Pulliam, T. H.↗
NASA NTRS1985

A nonoscillatory shock capturing scheme using flux limited dissipation

A method for modifying the third order dissipative terms by the introduction of flux limiters is proposed. The first order dissipative terms can then be eliminated entirely, and in the case of a scalar conservation law the scheme is converted into a total variation diminishing scheme provided that an appropriate value is chosen for the dissipative coefficient. Particular attention is given to: (1) the treatment of the scalar conservation law; (2) the treatment of the Euler equations for inviscid compressible flow; (3) the boundary conditions; and (4) multistage time stepping and multigrid schemes. Numerical results for transonic flows suggest that a central difference scheme augmented by flux limited dissipative terms can lead to an effective nonoscillatory shock capturing method.

Jameson, A.↗
NASA NTRS1986

Tidal dissipation in a viscoelastic planet

Tidal dissipation is examined using Maxwell standard liner solid (SLS), and Kelvin-Voigt models, and viscosity parameters are derived from the models that yield the amount of dissipation previously calculated for a moon model with QW = 100 in a hypothetical orbit closer to the earth. The relevance of these models is then assessed for simulating planetary tidal responses. Viscosities of 10 exp 14 and 10 ex 18 Pa s for the Kelvin-Voigt and Maxwell rheologies, respectively, are needed to match the dissipation rate calculated using the Q approach with a quality factor = 100. The SLS model requires a short time viscosity of 3 x 10 exp 17 Pa s to match the Q = 100 dissipation rate independent of the model's relaxation strength. Since Q = 100 is considered a representative value for the interiors of terrestrial planets, it is proposed that derived viscosities should characterize planetary materials. However, it is shown that neither the Kelvin-Voigt nor the SLS models simulate the behavior of real planetary materials on long time scales. The Maxwell model, by contrast, behaves realistically on both long and short time scales. The inferred Maxwell viscosity, corresponding to the time scale of days, is several times smaller than the longer time scale (greater than or equal to 10 exp 14 years) viscosity of the earth's mantle.

Ross, M.↗
NASA NTRS1986

Vortical dissipation in two-dimensional shear flows

An exact expression is derived for the viscous dissipation function of a real homogeneous and isotropic fluid, which has terms associated with the square of vorticity, wave radiation, and dilatation. The implications of the principle of maximal dissipation rate, are explored by means of this equation for a parallel channel flow and a cylindrical vortex flow. The consequences of a condition of maximum dissipation rate on the growth of disturbances in an unsteady, laminar shear layer are apparently consistent with predictions and observations of maximum growth rate of vortical disturbances. Finally, estimates of the magnitudes of several dissipative components of an unsteady vortex flow are obtained from measurements of a periodic wall jet.

Horne, W. Clifton↗
NASA NTRS1988

Tidal dissipation, surface heat flow, and figure of viscoelastic models of Io

The deformation of Io, the tidal dissipation rate, and its interior spatial distribution are investigated by means of numerical simulations based on (1) a three-layer model (with dissipation in the mantle) or (2) a four-layer model (with dissipation in the asthenosphere). The mathematical derivation of the models is outlined; the selection of the input-parameter values is explained; the results are presented in extensive graphs and contour maps; and the constraints imposed on the models by observational data on the hot-spot distribution, tidal deformation, and gravity field are discussed in detail. It is found that both dissipation mechanisms may play a role on Io: model (2) is better able to explain the concentration of hot spots near the equator, while the presence of a large hot spot near the south pole (if confirmed by observations) would favor model (1).

Segatz, M.↗
NASA NTRS1993

Implicit multigrid Euler solutions with symmetric Total-Variation-Diminishing dissipation

A symmetric Total-Variation-Diminishing (TVD) formulation of the numerical dissipation terms has been incorporated into a diagonalized alternating direction implicit multigrid algorithm to solve the Euler equations of inviscid compressible flow. The new treatment of the dissipation makes is possible to capture both very strong and very weak shocks, virtually without oscillation for the steady flows of interest here. In addition, the TVD constraint fixes one of the two previously arbitrary constants in the formulation of the dissipation, and results in both converged solutions and convergence rates which are relatively insensitive to the choice of the remaining dissipation parameter.

Caughey, David A.↗
NASA NTRS1992

Investigation of the dilatational dissipation in compressible homogeneous shear flow

The dilatational dissipation rate within compressible homogeneous turbulent shear flow is studied using data from direct numerical simulations. It is found that the dilatational dissipation rate is mainly associated with large scale acoustic waves. Eddy shocklets are observed; however, they have little contribution to the average dissipation rate. A mechanism for the generation of eddy shocklets is shown to be the focusing of acoustic waves. Turbulence models for the dilatational dissipation rate are compared with data from the simulations. It is found that the formulation of Zeman used by Viegas & Rubesin to calculate a compressible mixing layer agrees well with the numerical simulation results for turbulent Mach numbers less than 0.3. However, it is also found that, for the Mach number range occurring in mixing layers, the model does not accurately represent the theory upon which it is based.

Blaisdell, G. A.↗
NASA NTRS1993

The effect of dissipative inhomogeneous medium on the statistics of the wave intensity

One of the main theoretical points in the theory of wave propagation in random medium is the derivation of closed form equations to describe the statistics of the propagating waves. In particular, in one dimensional problems, the closed form representation of the multiple scattering effects is important since it contributes in understanding such problems like wave localization, backscattering enhancement, and intensity fluctuations. In this the propagation of plane waves in a layer of one-dimensional dissipative random medium is considered. The medium is modeled by a complex permittivity whose real part is a constant representing the absorption. The one dimensional problem is mathematically equivalent to the analysis of a transmission line with randomly perturbed distributed parameters and a single mode lossy waveguide and the results can be used to study the propagation of radio waves through atmosphere and the remote sensing of geophysical media. It is assumed the scattering medium consists of an ensemble of one-dimensional point scatterers randomly positioned in a layer of thickness L with diffuse boundaries. A Poisson impulse process with density lambda is used to model the position of scatterers in the medium. By employing the Markov properties of this process an exact closed form equation of Kolmogorov-Feller type was obtained for the probability density of the reflection coefficient. This equation was solved by combining two limiting cases: (1) when the density of scatterers is small; and (2) when the medium is weakly dissipative. A two variable perturbation method for small lambda was used to obtain solutions valid for thick layers. These solutions are then asymptotically evaluated for small dissipation. To show the effect of dissipation, the mean and fluctuations of the reflected power are obtained. The results were compared with a lossy homogeneous medium and with a lossless inhomogeneous medium and the regions where the effect of absorption is not essential were discussed.

Saatchi, Sasan S.↗
NASA NTRS1996

The Effects of Dissipation and Coarse Grid Resolution for Multigrid in Flow Problems

The objective of this paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For two-dimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density.

Eliasson, Peter↗
NASA NTRS1997

On the Potential Impact of Daytime Surface Sensible Heat Flux on the Dissipation of Martian Cold Air Outbreaks

The Martian daytime soil surface temperature is governed primarily by the net irradiance balance and surface soil heat flux. Thus the outbreak of a cold air mass generates increased sensible heat flux that is conducive to daytime dissipation of the cold air mass thermal characteristics. Conceptual and scaling evaluations of this dissipation are provided while comparison is made with similar situations on Earth. It is estimated that sensible heat flux contribution to the dissipation of the original thermal structure of the cold air could be three times larger than the corresponding situation on Earth. Illustrative numerical model simulations provide scaling of the potential impact on the dissipation of cold air masses for various combinations of background wind speed and latitudes.

Segal, M.↗