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Mass Flux in the Ancient Earth-Moon System and Benign Implications for the Origin of Life on Earth

The origin of life on Earth is commonly considered to have been negatively affected by intense impacting in the Hadean, with the potential for the repeated evaporation and sterilization of any ocean. The impact flux is based on scaling from the lunar crater density record, but that record has no tie to any absolute age determination for any identified stratigraphic unit older than approx. 3.9 Ga (Nectaris basin). The flux can be described in terms of mass accretion, and various independent means can be used to estimate the mass flux in different intervals. The critical interval is that between the end of essential crustal formation (approx. 4.4 Ga) and the oldest mare times (approx. 3.8 Ga). The masses of the basin-forming projectiles during Nectarian and early Imbrian times, when the last 15 of the approx.45 identified impact basins formed, can be reasonably estimated as minima. These in sum provide a minimum of 2 x 10(exp 21)g for the mass flux to the Moon during those times. If the interval was 80 million years (Nectaris 3.90 Ga, Orientale 3.82 Ga), then the flux was approx. 2 x 10(exp 13) g/yr over this period. This is higher by more than an order of magnitude than a flux curve that declines continuously and uniformly from lunar accretion to the rate inferred for the older mare plains. This rate cannot be extrapolated back increasingly into pre-Nectarian times, because the Moon would have added masses far in excess of itself in post-crust-formation time. Thus this episode was a distinct and cataclysmic set of events. There are approx. 30 pre-Nectarian basins, and they were probably part of the same cataclysm (starting at approx. 4.0 Ga?) because the crust is fairly intact, the meteoritic contamination of the pre-Nectarian crust is very low, impact melt rocks older than 3.92 Ga are virtually unknown, and ancient volcanic and plutonic rocks have survived this interval. The accretionary flux from approx. 4.4 to approx. 4.0 Ga was comparatively benign. When scaled to Earth, even the late cataclysm does not produce oceane vaporating, globally sterilizing events. The rooted concept that such events took place is based on the extrapolation of a nonexistent lunar record to the Hadean. The Earth from approx. 4.4 to approx. 3.8 Ga was comparatively peaceful, and the impacting itself could have been thermally and hydrothermally beneficial. The origin of life could have taken place at any time between 4.4 and 3.85 Ga, given the current impact constraints, and there is no justification for the claim that life originated (or re-originated) as late as 3.85 Ga in response to the end of hostile impact conditions.

Ryder, Graham↗

Global Mass Flux Solutions from GRACE: A Comparison of Parameter Estimation Strategies - Mass Concentrations Versus Stokes Coefficients

The differences between mass concentration (mas con) parameters and standard Stokes coefficient parameters in the recovery of gravity infonnation from gravity recovery and climate experiment (GRACE) intersatellite K-band range rate data are investigated. First, mascons are decomposed into their Stokes coefficient representations to gauge the range of solutions available using each of the two types of parameters. Next, a direct comparison is made between two time series of unconstrained gravity solutions, one based on a set of global equal area mascon parameters (equivalent to 4deg x 4deg at the equator), and the other based on standard Stokes coefficients with each time series using the same fundamental processing of the GRACE tracking data. It is shown that in unconstrained solutions, the type of gravity parameter being estimated does not qualitatively affect the estimated gravity field. It is also shown that many of the differences in mass flux derivations from GRACE gravity solutions arise from the type of smoothing being used and that the type of smoothing that can be embedded in mas con solutions has distinct advantages over postsolution smoothing. Finally, a 1 year time series based on global 2deg equal area mascons estimated every 10 days is presented.

Rowlands, D. D.↗

Latitudinal variation of speed and mass flux in the acceleration region of the solar wind inferred from spectral broadening measurements

Spectral broadening measurements conducted at S-band (13-cm wavelength) during solar minimum conditions in the heliocentric distance range of 3-8 R(sub O) by Mariner 4, Pioneer 10, Mariner 10, Helios 1, Helios 2, and Viking have been combined to reveal a factor of 2.6 reduction in bandwidth from equator to pole. Since spectral broadening bandwidth depends on electron density fluctuation and solar wind speed, and latitudinal variation of the former is available from coherence bandwidth measurements, the remote sensing spectral broadening measurements provide the first determination of the latitudinal variation of solar wind speed in the acceleration region. When combined with electron density measurements deduced from white-light coronagraphs, this result also leads to the first determination of the latitudinal variation of mass flux in the acceleration region. From equator to pole, solar wind speed increases by a factor of 2.2, while mass flux decreases by a factor of 2.3. These results are consistent with measurements of solar wind speed by multi-station intensity scintillation measurements, as well as measurements of mass flux inferred from Lyman alpha observations, both of which pertain to the solar wind beyond 0.5 AU. The spectral broadening observations, therefore, strengthen earlier conclusions about the latitudinal variation of solar wind speed and mass flux, and reinforce current solar coronal models and their implications for solar wind acceleration and solar wind modeling.

Woo, Richard↗

Development of a locally mass flux conservative computer code for calculating 3-D viscous flow in turbomachines

The VANS successive approximation numerical method was extended to the computation of three dimensional, viscous, transonic flows in turbomachines. A cross-sectional computer code, which conserves mass flux at each point of the cross-sectional surface of computation was developed. In the VANS numerical method, the cross-sectional computation follows a blade-to-blade calculation. Numerical calculations were made for an axial annular turbine cascade and a transonic, centrifugal impeller with splitter vanes. The subsonic turbine cascade computation was generated in blade-to-blade surface to evaluate the accuracy of the blade-to-blade mode of marching. Calculated blade pressures at the hub, mid, and tip radii of the cascade agreed with corresponding measurements. The transonic impeller computation was conducted to test the newly developed locally mass flux conservative cross-sectional computer code. Both blade-to-blade and cross sectional modes of calculation were implemented for this problem. A triplet point shock structure was computed in the inducer region of the impeller. In addition, time-averaged shroud static pressures generally agreed with measured shroud pressures. It is concluded that the blade-to-blade computation produces a useful engineering flow field in regions of subsonic relative flow; and cross-sectional computation, with a locally mass flux conservative continuity equation, is required to compute the shock waves in regions of supersonic relative flow.

Walitt, L.↗

Experimental comparison of two hot-wire techniques for resolution of turbulent mass flux and local stagnation temperature in supersonic flow

The performance of two constant-temperature normal hot-wire techniques in a supersonic flow is examined. The first technique uses a single-wire and rapid scanning of multiple overheat ratios. Time averages of the signals at all overheats are used to separate the mean and rms mass flux, stagnation temperature and their cross-correlation. The second technique uses a dual-wire probe with each wire operating at different overheat ratios, giving instantaneous mass flux and stagnation temperature. Preliminary results indicate that the separation distance (0.18 mm) between the two hot wires in the dual-wire probe does not introduce significant error. However, the rms mass flux inferred from the dual-wire technique is a factor of two higher than that from the single-wire technique.

Walker, D. A.↗

Mass Flux of ZnSe by Physical Vapor Transport

Mass fluxes of ZnSe by physical vapor transport (PVT) were measured in the temperature range of 1050 to 1160 C using an in-situ dynamic technique. The starting materials were either baked out or distilled under vacuum to obtain near-congruently subliming compositions. Using an optical absorption technique Zn and Se, were found to be the dominant vapor species. Partial pressures of Zn and Se, over the starting materials at temperatures between 960 and 1140 C were obtained by measuring the optical densities of the vapor phase at the wavelengths of 2138, 3405, 3508, 3613, and 3792 A. The amount and composition of the residual gas inside the experimental ampoules were measured after the run using a total pressure gauge. For the first time, the experimentally determined partial pressures of Zn and Se, and the amount and composition of the residual gas were used in a one-dimensional diffusion limited analysis of the mass transport rates for a PVT system. Reasonable agreement between the experimental and theoretical results was observed.

Sha, Yi-Gao↗

Balance Mass Flux and Velocity Across the Equilibrium Line in Ice Drainage Systems of Greenland

Estimates of balance mass flux and the depth-averaged ice velocity through the cross-section aligned with the equilibrium line are produced for each of six drainage systems in Greenland. (The equilibrium line, which lies at approximately 1200 m elevation on the ice sheet, is the boundary between the area of net snow accumulation at higher elevations and the areas of net melting at lower elevations around the ice sheet.) Ice drainage divides and six major drainage systems are delineated using surface topography from ERS (European Remote Sensing) radar altimeter data. The net accumulation rate in the accumulation zone bounded by the equilibrium line is 399 Gt/yr and net ablation rate in the remaining area is 231 Gt/yr. (1 GigaTon of ice is 1090 kM(exp 3). The mean balance mass flux and depth-averaged ice velocity at the cross-section aligned with the modeled equilibrium line are 0.1011 Gt kM(exp -2)/yr and 0.111 km/yr, respectively, with little variation in these values from system to system. The ratio of the ice mass above the equilibrium line to the rate of mass output implies an effective exchange time of approximately 6000 years for total mass exchange. The range of exchange times, from a low of 3 ka in the SE drainage system to 14 ka in the NE, suggests a rank as to which regions of the ice sheet may respond more rapidly to climate fluctuations.

Zwally, H. Jay↗

Carrying the mass flux terms exactly in the first and second moment equations of compressible turbulence

In compressible turbulence models, it is assumed that the Favre-mean velocities are suitable approximations to the Reynolds-mean velocities in order to close unknown terms. This neglects, in the mean momentum and energy equations, the contribution to the stress and work terms by the mean of the fluctuating Favre velocity, a quantity proportional to the turbulent mass flux. As the stress and work terms do not introduce any new unknown correlations requiring closure in either k-epsilon or Reynolds stress closures and because the exact form of the terms can, with little additional work, be carried there is no need to make any modeling assumptions. In the Reynolds stress equations the viscous terms appear naturally in Reynolds variables while the problem is posed in Favre variables. In the process of splitting the viscous terms into the viscous transport terms, carried in Favre variables, and the dissipation terms, carried in Reynolds variables, important contributions from the mass flux appear. The accurate accounting of these terms is important for any consistent near wall modeling and the retention of the mass flux terms is important in complex compressible turbulent flows.

Ristorcelli, J. R.↗

Multiple-Point Mass Flux Measurement System Using Rayleigh Scattering

A multiple-point Rayleigh scattering diagnostic is being developed to provide mass flux measurements in gas flows. Spectroscopic Rayleigh scattering is an established flow diagnostic that has the ability to provide simultaneous density, temperature, and velocity measurements. Rayleigh scattered light from a focused 18 Watt continuous-wave laser beam is directly imaged through a solid Fabry-Perot etalon onto a CCD detector which permits spectral analysis of the light. The spatial resolution of the measurements is governed by the locations of interference fringes, which can be changed by altering the etalon characteristics. A prototype system has been used to acquire data in a Mach 0.56 flow to demonstrate feasibility of using this system to provide mass flux measurements. Estimates of measurement uncertainty and recommendations for system improvements are presented

Mielke, Amy F.↗

Improving Global Mass Flux Solutions from Gravity Recovery and Climate Experiment (GRACE) Through Forward Modeling and Continuous Time Correlation

We describe Earth's mass flux from April 2003 through November 2008 by deriving a time series of mas cons on a global 2deg x 2deg equal-area grid at 10 day intervals. We estimate the mass flux directly from K band range rate (KBRR) data provided by the Gravity Recovery and Climate Experiment (GRACE) mission. Using regularized least squares, we take into account the underlying process dynamics through continuous space and time-correlated constraints. In addition, we place the mascon approach in the context of other filtering techniques, showing its equivalence to anisotropic, nonsymmetric filtering, least squares collocation, and Kalman smoothing. We produce mascon time series from KBRR data that have and have not been corrected (forward modeled) for hydrological processes and fmd that the former produce superior results in oceanic areas by minimizing signal leakage from strong sources on land. By exploiting the structure of the spatiotemporal constraints, we are able to use a much more efficient (in storage and computation) inversion algorithm based upon the conjugate gradient method. This allows us to apply continuous rather than piecewise continuous time-correlated constraints, which we show via global maps and comparisons with ocean-bottom pressure gauges, to produce time series with reduced random variance and full systematic signal. Finally, we present a preferred global model, a hybrid whose oceanic portions are derived using forward modeling of hydrology but whose land portions are not, and thus represent a pure GRACE-derived signal.

Sabaka, T. J.↗

The field-aligned flow approximation for electrons within layers possessing a normal mass flux - A corollary to the deHoffmann-Teller theorem

In this paper, an approximate extension of the deHoffmann-Teller (1950) theorem for electrons within layers possessing a normal mass flux is derived. It is shown that the deHoffmann-Teller frame electron bulk velocity is nearly parallel to the magnetic field everywhere through those one-dimensional time-stationary layers which possess a normal mass flux, even though electric field perpendicular to the magnetic field exists throughout such layers. Examples of layers of this class are the fast and slow shocks as well as rotational discontinuities.

Scudder, J. D.↗

Effect of gas mass flux on cryogenic liquid jet breakup

A scattered-light scanning instrument developed at NASA Lewis Research Center was used to measure the characteristic drop size of clouds of liquid nitrogen droplets. The instrument was calibrated with suspensions of monosized polystyrene spheres. In this investigation of the mechanism of liquid nitrogen jet disintegration in a high-velocity gas flow, the Sauter mean diameter, D32, was found to vary inversely with the nitrogen gas mass flux raised to the power 1.33. Values of D32 varied from 5 to 25 microns and the mass flux exponent of 1.33 agrees well with theory for liquid jet breakup in high-velocity gas flows. The loss of very small droplets due to the high vaporization rate of liquid nitrogen was avoided by sampling the spray very close to the atomizer, i.e., 1.3 cm downstream of the nozzle orifice. The presence of high velocity and thermal gradients in the gas phase also made sampling of the particles difficult. As a result, it was necessary to correct the measurements for background noise produced by both highly turbulent gas flows and thermally induced density gradients in the gas phase.

Ingebo, R. D.↗

The solar wind mass flux

One of the unexplained observations of the solar wind at 1 AU is the relative constancy of the solar wind mass flux. Calculations using a radiative energy balance model with a thermally driven wind suggest that this near constancy of the mass (particle) flux is due to two factors: (1) the role of inward conduction and radiation in cooling the corona, and (2) the finding that the particle flux is proportional to the gas pressure in the outer corona and beyond, where the solar wind flow becomes radial.

Withbroe, George L.↗

Optically thick winds: How is the mass flux determined?

Expanding envelopes of compact objects that possess a buring region at the base of the envelope are commonly observed and modeled. In many cases, such as the late stages of classical nova, the expanding envelope develops into a stationary, optically thick wind of matter escaping from the star. In the usual theoretical formalism there is one more unknown than equations, with closure being obtained by the requirement that the solution pass through the singularity at the sonic point. It is shown analytically that the mass flux, which is one of the unknowns, is almost completely determined by the physical conditions near the base of the envelope just above the burning zone. The sonic point closure relation determines whether the expanding solution can develop into a wind solution. For a given core mass the range of possible wind solutions is an outcome of the great sensitivity of the mass flux to the inner luminosity. Solutions determined through numerical integrations are shown to lie entirely within the narrow analytic boundaries.

Glasner, S. Ami↗