Net Mass Flux Research Articles

Flow and solute transport through a levee separating fluids with different densities

Steady seepage through a levee or a dam separating reservoirs with different levels and densities is shown to result in five possible flow configurations. If densities are equal, the problem reduces to the classical problem of flow through a dam. If the lower reservoir is less dense, a stationary wedge may or may not form inside the levee near the downgradient reservoir level. If the lower reservoir is more dense, a wedge forms near the toe of the levee, as in the classical problem of saltwater intrusion. Another possibility is that the dense wedge can connect the two reservoirs, thus allowing bidirectional flow. Conditions are derived which define when these different flow configurations occur. For the case of a rectangular dam with vertical walls a closed form solution is obtained for the net mass flux between the reservoirs. Net volumetric flux is determined analytically for all flow configurations except the case of bidirectional flow. The expression for volumetric flux is a generalization of a result based on the Dupuit assumption for the case of constant density. A range of parameters is identified in which net volumetric flux is in one direction and net mass flux in the other. A numerical model based on the boundary integral equation method allows calculation of net volumetric flux for the case of bidirectional flow and also allows simulation of more complex levee geometries. The solution has direct application to levees separating ponds in solar salt production, to the causeway across the Great Salt Lake in Utah, and to the role of exchange flows in the genesis of evaporites in nearshore lagoons.

Charge and Ion Transport in Poly(pyrrole copper phthalocyanine tetrasulfonate) during Redox Switching

The redox switching properties of electrochemically synthesized poly(pyrrole copper phthalocyanine‐3,4′4″,4‴‐tetrasulfonate) (PP‐CuPTS) have been investigated in aqueous electrolytes utilizing the electrochemical quartz crystal microbalance (EQCM) technique. Ion transport during redox switching is found to be cation dominant, indicating that the copper phthalocyanine complex is physically entrapped in the polymer film and is confirmed by the fact that no CuPTS is seen in the switching electrolyte. Coulometric and gravimetric analyses show that the redox switching rate of PP‐CuPTS is related to cation mobility and is a function of ion hydration. Correlation of the charge and mass changes of the polymer during switching reveals that there exists two distinct regimes. An initial mass flux dominant region is followed by a considerable amount of charge flux which is accompanied by no net mass flux. These are likely to be due to ion hydration and simultaneous solvent or co‐ion flux in the opposite direction of the mobile ionic species, respectively.

Present‐day secular variations in the zonal harmonics of Earth's geopotential

We develop a new formalism for the prediction of secular variations in the gravitational potential field of a spherically symmetric, self‐gravitating, (Maxwell) viscoelastic planetary model subjected to an arbitrary surface load which may include a gravitationally self‐consistent ocean loading component. The theory is applied to generate the most accurate predictions to date, of the present‐day secular variations in the zonal harmonics of the geopotential (the so‐called , for degree 𝓁) arising as a consequence of the late Pleistocene glacial cycles. In this respect, we use the very recent ICE‐3G reconstruction of the last late Pleistocene deglaciation event (Tushingham and Peltier, 1991). A comparison of these predictions with those generated using simplified disk models of the ice sheets, which have been used in all previous studies of the , harmonics (𝓁 > 2), indicates that the disk model approximation introduces unacceptably large errors at all spherical harmonic degrees except perhaps 𝓁=2. Predictions have also been made using a eustatic loading approximation (also used in previous studies) in place of a gravitationally self‐consistent ocean loading component, and we have found that the resulting discrepancy is largest at degrees 2, 8 and 10. In the case of the magnitude of the error incurred using the eustatic approximation can be as large as order 10–15% of the predicted value. We have attributed this discrepancy to the present day net flux of water away from the equatorial regions arising from the remnant present‐day adjustment associated with the late Pleistocene glacial cycles. The effect represents a heretofore unrecognized contribution to the harmonics, or alternatively the nontidal acceleration of Earth's axial rate of rotation. In terms of the latter, the maximum anomaly in the length of day is approximately 1.7 μs/yr. We also consider the sensitivity of the data to variations in the radial mantle viscosity profile by using a suite of forward calculations and an examination of Fréchet kernels. The theory required for the computation of those kernels is described herein. We find that the radial variation in sensitivity can be a strong function of the viscosity model used in the calculations. For models with a uniform upper mantle viscosity (νUM) of 1021 Pa s, forward predictions of the harmonics exhibit a pronounced peak when a wide enough range of lower mantle viscosities (νLM) are considered (we denote the νLM value at this peak as ). At the lowest degrees (𝓁 ≤ 4), Fréchet kernels computed for a series of increasing νLM values (1021 Pa s ≤ νLM < 1023 Pa s) indicate a migration of the dominant sensitivity of the data to variations in viscosity from regions below approximately 1200 km depth (for ) to regions above this depth in the lower mantle (for ). The sensitivity of the data to variations in the viscosity profile in the shallowest parts of the lower mantle, for the case , is also reflected in a set of forward calculations described herein. As an example, , predictions made using Earth models in which the viscosity above 1200 km depth is constrained to be 1021 Pa s, do not exhibit the multiple solutions characteristic of the νUM= 1021 Pa s calculations. The same is true of Earth models in which the upper mantle viscosity is weakened an order of magnitude to 1020 Pa s. The theory described herein is also applied to compute the signal (𝓁 ≤ 10) arising from the retreat of small ice sheets and glaciers described by Meier (1984) and also from any potential variations in the mass of the Antarctic and Greenland ice sheets. The present day signal due to the late Pleistocene glacial cycles dominates the signal from Meier's sources at all degrees except 𝓁=3. In contrast, the signal arising from mass variations in the Antarctic and Greenland ice sheets is potentially comparable to the former. A comparison of observational constraints on the data with predictions of the postglacial rebound signal described in this paper, in order to infer mantle rheology, cannot proceed until constraints are placed on the present‐day mass flux of these large polar ice sheets. We show that the constraints required are weakest at degrees 𝓁=2 and 4. Finally, we outline a potentially important procedure for incorporating predictions of the signal due to the late Pleistocene glacial cycles and Meier's sources, with an observational constraint on the datum, to yield bounds on the present‐day net mass flux from the Antarctic and Greenland ice sheets. A rigorous application of this procedure must wait until observational constraints on are reestablished in the literature.

Estimation of S and NOx-N deposition budgets for the United States and Canada

Extensive wet deposition monitoring data, along with much sparser dry deposition monitoring data and isolated field characterizations of droplet deposition, are used to produce an annual deposition budget for S and NOx-N for each contiguous U.S. state and Canadian province. The contribution to wet deposition from natural sources is estimated, and wet deposition is adjusted accordingly, to focus the analysis on deposition associated with anthropogenic emissions. The budgets, which are appropriate for 1985–1987, include adjustments for increased local wet and dry deposition near point sources and urban areas, which are generally avoided in selecting monitoring sites. When aggregated over the United States and Canada, estimated wet, dry, and droplet deposition account for about 30, 29, and 4% of anthropogenic S emissions, respectively, implying that 37% is exported. For NOx-N, estimated wet, dry, and droplet deposition account for 30, 43, and 4% of anthropogenic emissions, with 23% exported. Results are in general agreement with a variety of other observational analyses and regional modeling simulations, particularly for eastern North America, and are consistent with estimates of net horizontal mass fluxes of S and NOx-N across the Atlantic coast of North America.

Quantitative geochemical approach to pedogenesis: importance of parent material reduction, volumetric expansion, and eolian influx in lateritization

Using mass balance techniques we test the prevalent view that laterite genesis is dominated by in situ residual enrichment during chemical weathering of bedrock. Through calculation of net mass fluxes through the laterite soils in Mali, West Africa, we show that residual enrichment by removal of mobile elements with a corresponding increase in bulk porosity and decrease in bulk density, contributes only a very minor fraction of the enrichment of Al, Fe, Si and Au. Instead, we demonstrate that the abundance of these elements is due to the influx and accumulation by selective retention of chemically mature detritus of local and foreign origin clearly evident in micromorphological infilling features. At the same sample depths that accumulation reaches extreme values, we show that volumetric expansion in excess of 200% has occurred locally. We infer that these spatially coincidental zones of mass influx of rock-forming metals Fe, Al, Si, and also Au with dilational hyperstrains result from a mutually reinforcing, mechanical interaction between material influx and the effects of subsurface deformational processes such as shrink-swell cycles and root growth and decay. We propose that with progressive infilling of available connected voids by illuvial microsedimentary deposits of insoluble resistate and neoformed minerals, the capacity for the combined skeleton and plasma to remain isovulumetric is exceeded. We speculate that the resultant space problem is relieved by upwards expansion towards the overlying free surface. Continued translocation and void infilling occur and are limited to the depth where the size of translocational particles is smaller than that of the connected voids. Consequently, progressive hyperstrains accumulate above this critical depth by the long-term influence of a proposed translocational wedge of chemically-resistant minerals against which numerous generations of plant roots have exerted stresses. Eclectic surficial contaminants involved are continuously derived from above leaving no indication of a relict source region within the present soil profile from which they might have been extracted. Instead, the source region is largely the existing regolith column itself which releases local material and in addition, is supplemented by deposition of colluvial detritus shed nearby by escarpment retreat

Sustained patterns in chlorite–iodide reactions in a one-dimensional reactor

We describe an open one-dimensional reaction–diffusion system, the Couette reactor, which provides a permanent feed of fresh reactants and simultaneously preserves the diffusion process. Different compositions of variants of chlorite–iodide reactions are fed at both ends, but there is no net axial mass flux in the reactor. The effective diffusion coefficient is the same for all chemical species, and can easily be varied from 10−2 to 1 cm2/s, permitting large size reaction–diffusion structures. Spatial bistability was obtained with the minimal chlorite–iodide reaction in symmetric feed conditions. A larger variety of patterns was observed with the chlorite–iodide–malonic acid reaction and asymmetric feed conditions: a single steady chemical front, two steady fronts, three steady fronts, a single oscillating front, two oscillating fronts, three oscillating fronts, simple colliding fronts, and a bursting pattern. The patterns were studied as a function of several parameters to determine the sequences of bifurcations. Our observations demonstrate the existence of steady chemical patterns other than Turing patterns.

Mass fluxes in New Mexico mountain thunderstorms from radar and aircraft measurements

AbstractWe have obtained the vertical and detrained mass fluxes through the life cycles of four thunderstorms using measurements from four Doppler radars and an instrumented aircraft. The storms formed over the Magdalena Mountains of central New Mexico, and remained near the mountains through their entire life.Updraughts appeared to entrain a certain amount of surrounding radar‐invisible air. Thermodynamic considerations suggest that this air came from neighbouring towering cumulus clouds rather than directly from the environment. Entrained air did not immediatly mix with cloud‐base air, but tended to maintain its own identity in ascent. Levels with decreasing parcel buoyancy induced significant detrainment from the updraught. Downdraughts were confined primarily to levels below 7–8 km above mean sea level.The net mass flux entering or leaving the underside of the thunderstorms equalled that supplied by the mountain upslope flow. Since this net flux is a combination of updraughts and downdraughts, unstable air at low levels is gradually replaced by stable downdraught air, thus ensuring the demise of the storm.

Cloud draft structure and trace gas transport

Field observations obtained during the second NASA Amazon Boundary Layer Experiment (ABLE 2B), and two‐dimensional moist cloud model simulations are used to determine the dominant transport pathways within a continental tropical squall line. A surface‐based network triangle provided the focus for a multi‐instrumental sampling of the May 6, 1987, squall line which propagated through the central Amazon basin at a rate of 40–50 km h−1. Extensive use is made of the vertical distribution of specific trace gases that are representative of the prestorm and poststorm environment. One‐dimensional photochemical model results suggest the observed poststorm changes in ozone concentration can be attributed to convective transports rather than photochemical production. Two‐dimensional cloud model results detail the dynamic and thermodynamic attributes of the simulated squall convection. The well‐mixed moist troposphere in which the observed squall system developed may have hindered strong downdraft development. Parcel trajectory analyses are conducted to investigate the flow patterns of convective transports. A significant proportion (> 50%) of the air transported to the anvil region originated at or above 6 km, not from the boundary layer via undilute cores. The presence of a midlevel inflow and a strong melting layer at 5.5 km reduced the vertical development of the core updraft and aided in the maintenance of a rotor circulation. The predicted absence of more than one active cell in the model cloud field, the lack of a well‐organized downdraft in the presence of model estimated net upward mass flux, and the initial wind profile suggest the May 6 squall line was unicell in character.

Magnetohydrodynamic modeling of coronal bright points

Coronal bright points are known to be magnetic in nature. A two-dimensional MHD code was devleoped to investigate the rsponse of a stratified atmosphere to a localized magnetic structure. If a bright point occurs at a region where flux tubes of opposite polarity have encountered by chance it is found that, in the presence of stratification, a net upward mass flux results. Upflow velocities of up to one half of the Alfven speed are produced. The implications of the results for mass outflows from bright points in coronal holes are discussed.

An experimental investigation of a wind-generated suspension of particulate matter from a tailings disposal area

A wind tunnel investigation of the wind erosion of uranium mine-tailings material typical of a northern Ontario site has been carried out. The aim of the study was to measure the effects of various parameters, including mean and turbulent wind characteristics of the boundary layer and surface moisture content, upon the erosion process. The analysis of experimental data has yielded a mathematical model for predicting the net vertical mass fluxes. The results show that the dry vertical flux is proportional to u * 2.3and the wet flux to u * 5.0 Partical size analysis was also carried out.

Diagnosis of the net cloud mass flux in GATE : Chen, Yi-Leng, 1985. J. atmos. Sci., 42(16):1757–1769

Diagnosis of the net cloud mass flux in GATE : Chen, Yi-Leng, 1985. J. atmos. Sci., 42(16):1757–1769

Diagnosis of the Net Cloud Mass Flux in Gate

Abstract A diagnostic analysis of the net cloud mass flux for the mean state of Phase III is presented. In the upper troposphere, the environmental mass flux is shown to be slightly larger than the adiabatic sinking motion required by radiative cooling. At the outflow layer of tall clouds, if the moistening effect due to detrainments is balanced primarily by the drying caused by adiabatic sinking in the environment, the computed net detrainment rate would be underestimated. It is hypothesized that a considerable portion of the moisture detrained from tall clouds is transported horizontally toward higher latitudes by horizontal eddy fluxes. The diagnosed environmental subsidence has a maximum in the midtroposphere and is less than 1.5 times the sinking motion required by the radiative cooling in low levels. The vertical profile of the diagnosed net detrainment rate suggests three primary detrainment layers: below 800 mb, between 700 and 500 mb, and above 300 mb. It is shown that overprediction of the cloud...

Fluid motion induced by travelling thermal waves in a rotating fluid

Abstract The mean motion induced by thermal waves travelling along the surfaces of two parallel planes bounding a layer of homogeneous rotating fluid is studied. Under the Boussinesq and long waves approximations, the fluctuating and the mean velocity components are obtained. The asymptotic expressions and numerical calculations of the zonal and meridional mass flux across vertical planes show that the direction of the net mass flux changes for certain combinations of the frequencies of the moving heat source and the inertial oscillations.

Eastern Boundary Ventilation and the Structure of the Thermocline

Abstract The effect of relaxing the zero geostrophic zonal flow condition at the eastern boundary on the structure of the ventilated thermocline is described. It is argued that the effect of dissipation can allow a vertical exchange of mass between layers at the eastern boundary. A model is studied analytically that assumes such an interchange while continuing to forbid a net eastward mass flux at each latitude. The consequences of the relaxation of this condition are striking. Each active layer in the ventilated thermocline can now have a non-zero thickness on the eastern wall. As a result, each such layer has a stagnant shadow zone near the eastern boundary. Each shadow zone extends across the gyre at low latitudes. Hence the isopycnal surfaces, while shallow, remain at finite depth as the equator is approached. The shadow zones are nested, i.e., the shadow zone of the deepest layer is laterally most extensive and the zone shrinks eastward and southward with decreasing depth. The vertical recirculation ...

Sensitivity studies with a coupled ice‐ocean model of the marginal ice zone

An analytical coupled ice‐ocean model is considered which is forced by a specified wind stress acting on the open ocean as well as the ice. The analysis supports the conjecture that the upwelling dynamics at ice edges can be understood by means of a simple analytical model. In similarity with coastal problems it is shown that the ice edge upwelling is determined by the net mass flux at the boundaries of the considered region. The model is used to study the sensitivity of the upwelling dynamics in the marginal ice zone to variation in the controlling parameters. These parameters consist of combinations of the drag coefficients used in the parameterization of the stresses on the three interfaces atmosphere‐ice, atmosphere‐ocean, and ice‐ocean. The response is shown to be sensitive to variations in these parameters in that one set of parameters may give upwelling while a slightly different set of parameters may give downwelling.

Large-Scale Meteorological Conditions Associated with Midlatitude, Mesoscale Convective Complexes

Objective analyses of composited meteorological conditions attending ten Mesoscale Couvective Complexes (MCC) reveal a number of distinctive characteristics and important interactions with the large-scale environment. The systems appear to be linked to eastward progression of a weak, middle-tropospheric, short-wave trough. Initial thunderstorms develop within a region of mesoscale convergence and lifting that is apparently forced primarily by low-level warm advection. The MCC system acquires mesoscale organization while it moves eastward ahead of the short-wave trough. Diabatic heating eventually produces a system that is warm core in the middle troposphere and cold core in upper levels. The mature MCC exhibits many similarities to tropical convective systems, although it occurs within a considerably different large-scale setting. Inflow within the lower half of the troposphere feeds convection within a region characterized by significant net upward mass flux and widespread precipitation. Thickness increases within this region produce anomalously high heights in the upper-troposphere above the MCC and intense outflow develops in the region where the height gradient has increased. Decay typically occurs as the system moves east of the region of conditionally unstable air and low-level warm advection. However, as the system decays, atmospheric response to residual temperature perturbations results in intensification of the precursor short-wave trough within the upper half of the troposphere.

Development and application of a reactive plume model

A reactive plume model has been developed to simulate pollutant concentration distributions across a plume emanating from a major point source. The model, based on a simple mass balance, is composed of a fixed number of cells that can expand in a prescribed fashion as the plume travels downwind. For an inert pollutant species, there is no net mass flux across the expanding cell boundaries. For reactive or background pollutants, an equivalent diffusion coefficient is used to characterize the across-the-cell mass fluxes. An up-to-date kinetic module, the carbon-bond mechanism, has been incorporated into this model to treat photochemical reactions involving hydrocarbons and oxides of nitrogen. This model has been applied to the Widows Creek Power Plant in Alabama and the Oak Creek Power Plant in Wisconsin. Comparisons between the observed distributions of several key pollutant concentrations and the corresponding model predictions seem to indicate that the model has been able to simulate the pertinent transport, diffusion and photochemical processes that take place in a reactive plume.

TREATMENT OF THE NONEQUILIBRIUM VAPOR MOTION NEAR AN EVAPORATING INTERPHASE BOUNDARY

Strong evaporation problems are characterized by the nonequilibrium vapor motion near the interphase boundary. The solution of this nonequilibrium region, known as Knudsen layer, requires the use of kinetic theory. Kinetic equations have been solved numerically for a plane evaporation problem. Numerical solutions have led to the establishment or the validity of a simple kinetic theory approach to calculate the jump conditions across the Knudsen layer and the net mass, momentum, and heat fluxes. This approach can be used together with the conventional continuum method to calculate How parameters at the outer edge of the Knudsen layer for heat transfer problems in which evaporation occurs at the interphase boundary.

Steady-state mass balance approach to substrate biased rf sputtering

An analysis is given of the net mass flux from target to film during steady-state substrate biased rf sputtering. Expressions are derived for film composition and growth rate in terms of relative sputtering rates of atomic species in the surface region of the target and film, and the geometrical transfer efficiencies between target and film. Calculations have been carried out of predicted film composition as a function of substrate bias voltage for several cases, and a comparison is made with experimental data.

The flux of mass across latitude walls in the atmosphere

A formula describing the net flux of mass across latitude walls in the atmosphere is derived which is particularly well suited for evaluation with data from a network of hemispheric upper-air stations. The formula is nearly exact, involving a minimum of assumptions, and accounts for contributions made by both mean and eddy processes. As such, it stands in contrast to the traditional formulation for the net mass flux and hence serves to illustrate the simplifications involved in the latter.