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1.
Vertical eddy diffusivities (Kv's) have been estimated at fourteen widely separated locations from fourteen222Rn profiles and two228Ra profiles measured near the ocean floor as part of the Atlantic and Pacific GEOSECS programs. They show an inverse proportionality to the local buoyancy gradient [(g/?)(??pot/?z)] calculated from hydrographic measurements. The negative of the constant of proportionality is the buoyancy flux [?Kv(g/?)(??pot/?z)] which has a mean of ?4 × 10?6 cm2/sec3. Our results suggest that the buoyancy flux varies very little near the ocean floor. Kv's for the interior of the deep Pacific calculated from the relationship Kv = (4 × 10?6cm2/sec3)/[(g/?)(??pot/?z)] agree well with published estimates. Kv's calculated for the pycnocline are one to two orders of magnitude smaller than upper limits estimated from tritium and7Be distributions.Heat fluxes calculated with the model Kv's obtained from the222Rn profiles average 31 μcal cm?2 sec?1 in the Atlantic Ocean and 8 μcal cm?2 sec?1 in the Pacific Ocean.  相似文献   

2.
Vertical profiles of excess bottom222Rn and potential temperature were measured at 23 stations in the northwestern Pacific Ocean. The Rn profiles were classified into the following three types: quasi-exponential (type E), benthic boundary layer (type B), and horizontally disturbed (type H). The ratio among types E, B and H was approximately 2 : 3 : 1.An apparent vertical eddy diffusivity (K) was calculated by applying a one-dimensional diffusion model to the Rn profiles of types E and B. Type E had K values ranging from 15 to 180 cm2 s?1 (average: 70 cm2 s?1). As to type B, K values for the benthic boundary layer (4.5–260 cm2 s?1, average: 120 cm2 s?1) were always more than an order of magnitude larger than those for the upper layer (0.2–35 cm2 s?1, average: 7 cm2 s?1), indicating more active vertical mixing in the benthic boundary layer than in the upper layer.Rn profiles were measured in regions where the bottom topography is known. It was verified that the occurrence of type H related closely with local bottom topographic features accompanied by lateral transient supply of Rn-rich or Rn-poor water.A couple of Rn profiles at the same location, measured at time intervals of several years, were compared with each other for three locations. The general characteristics of Rn profiles were shown to remain unaltered with time, while the fine structure of Rn profiles may have short-term variations caused by local bottom topography and fluctuations of bottom current as indicated in type H.  相似文献   

3.
The concentrations of222Rn and226Ra in the water column and in the sediments of Santa Barbara and San Nicolas Basins have been measured semi-annually over the last four years. Approximately one-third of excess radon profiles obtained in the water column in these basins can be adequately fit with a one-dimensional eddy diffusion-decay model. Exponential profiles in the center of San Nicolas Basin yield a vertical eddy diffusivity of 26±16 cm2/s and 3.4±1.0 cm2/s for Santa Barbara Basin. The application of a two-dimensional eddy diffusion-decay model to profiles obtained in the center and on the margins of San Nicolas Basin produces a better fit than is found using a one-dimensional vertical eddy diffusivity. The two-dimensional model for San Nicolas Basin predicts a vertical eddy diffusivity of 17 cm2/s and a horizontal eddy diffusivity of 105 cm2/s. These values are in reasonable agreement with those predicted from the vertical buoyancy gradient and the horizontal length scale.The vertically integrated radon excess (standing crop) in the water column of Santa Barbara Basin averages 53±23 atoms/m2 s. This is in good agreement with the flux across the sediment-water interface of 60±15 atoms/m2 s, calculated by measuring radon emanation in the sediments as a function of depth and applying a molecular diffusion-reaction model. Hence, one-dimensional molecular diffusion accurately predicts the flux of radon from the laminated Santa Barbara Basin sediments. In San Nicolas Basin the integrated radon excess in the water column is 376±143 atoms/m2 s, but the diffusive randon flux from San Nicolas Basin sediments averages only 190±53 atoms/m2 s. This descrepancy indicates that a non-diffusive process, probably macrofaunal irrigation, supplies much of the flux of radon from San Nicolas Basin sediments.  相似文献   

4.
We present the distribution of226Ra in eight vertical profiles from the eastern Pacific. The profiles are located along a meridional trend near 125°W, from 43°S to 29°N. Surface226Ra concentrations are about 7 dpm/100 kg, except for the two stations south of 30°S where the higher values are due to the Antarctic influence. Deep waters show a distinctive south-to-north increase in the226Ra content, from about 26 to 41 dpm/100 kg near the bottom. Unlike in the Atlantic and Antarctic Oceans, the effect of226Ra injection from bottom sediments is clearly discernible in the area. The presence of this primary226Ra can be traced up to at least 1–1.5 km above the ocean floor, making this part of the sea bed among the strongest source regions for the oceanic226Ra. Numerical solutions of a two-dimensional vertical advection-diffusion model applied to the deep (1.2–4 km)226Ra data give the following set of best fits: upwelling velocity(Vz) = 3.5m/yr, vertical eddy diffusivity(Kz) = 0.6cm2/s, horizontal (north-south) eddy diffusivity(Ky) = 1 × 107cm2/s, and water-column regeneration flux of226Ra(J) = 3.3 × 10?5dpmkg?1yr?1 as an upper limit. These parametric values are in general agreement with one-dimensional (vertical) model fits for the Ra-Ba system. However, consideration of226Ra balance leads us to suspect the appropriateness of describing the vertical exchange processes in the eastern Pacific with constantVz and Kz. If future modeling is attempted, it may be preferable to treat the area as a diffusion-dominant mixing regime with depth-dependent diffusivities.  相似文献   

5.
Abstract

A new non-linear model of mixing and convection based on a modelling of two buoyant interacting fluids is applied to penetrative convection in the upper ocean due to surface cooling. In view of simple algebra, the model is one-dimensional. Dissipation is included, but no mean shear is present. A non-similar analytical solution is found in the case of a well-mixed layer bounded below by a sharp thermocline treated as a boundary layer. This solution is valid if the Richardson number, R i , defined as the ratio of the total mixed-layer buoyancy to a characteristic rms vertical velocity, is much greater than unity. The model predicts a deepening rate proportional to R i ?3/4. The thermocline remains of constant thickness, and the ratio thermocline thickness to mixed-layer depth decreases as R i ?3/4 as the mixed layer deepens. If the surface flux is constant, the mixed-layer depth increases with time as t ½. The vertical structure throughout the mixed layer and thermocline is given by the analytical solution, and vertical profiles of mean temperature and vertical fluxes are plotted. Computed profiles and available laboratory data agree remarkably well. Moreover, the accuracy of the simple analytical results presented here is comparable to that of sophisticated turbulence numerical models.  相似文献   

6.
This study investigated the influence of the regional flow on the streambed vertical hydraulic conductivity (Kv) within the hyporheic zone in three stream reaches of the Weihe River in July 2016. The streambed Kv with two connected depths was investigated at each test reach. Based on the sediment characteristics, the three test reaches could be divided into three categories: a sandy streambed without continuous silt and clay layer, a sandy streambed with continuous silt and clay layer, and a silt–clay streambed. The results demonstrate that the streambed Kv mainly decreases with the depth at the sandy streambed (without continuous silt and clay layer) and increases with the depth at the other two test reaches. At the sandy streambed (with continuous silt and clay layer) where streambed Kv mainly decreases with the depth, the regional upward flux can suspend fine particles and enhance the pore spacing, resulting in the elevated Kv in the upper sediment layers. At another sandy streambed, the continuous silt and clay layer is the main factor that influences the vertical distribution of fine particles and streambed Kv. An increase in streambed Kv with the depth at the silt/clay streambed is attributed to the regional downward movement of water within the sediments that may lead to more fine particles deposited in the pores in the upper sediment layers. The streambed Kv is very close to the bank in the sandy streambed without continuous silt and clay layer and the channel centre in the other two test reaches. Differences in grain size distribution of the sediments at each test reach exercise a strong controlling influence on the streambed Kv. This study promotes the understanding of dynamics influencing the interactions between groundwater and surface water and provides guidelines to scientific water resources management for rivers.  相似文献   

7.
Summary An instrument for use with a captive balloon has been developed for the investigation of the vertical distribution of222Rn and its daughter ions of high mobility. The system consists of a light weight ion collector of the Gerdien type and an automatic air sampler. Simultaneous collections of222Rn and its daughter ions having mobilities of known limits makes it possible to determine the concentration of the radioactive ions relative to the ambient concentration of222Rn in different atmospheric conditions in the air layer adjacent to the ground where aircraft and tower measurements are not practicable. Vertical profiles taken over a mountain ridge in a well-mixed atmosphere show almost constant concentrations of222Rn and its daughter ions with altitude. In some cases a slight increase in the concentrations of222Rn and its daughter ions with altitude has been observed. The radioactive ion concentration relative to the ambient concentration of222Rn in the boundary layer is of the order of 3%.  相似文献   

8.
Measurements of turbulent fluctuations of horizontal and vertical components of velocity, salinity and suspended particulate matter are presented. Turbulent Prandtl numbers are found to increase with stratification and to become larger than 1. Consequently, the vertical turbulent mass transport is suppressed by buoyancy forces, before the turbulent kinetic energy (TKE) and vertical turbulent momentum exchange are inhibited. With increasing stratification, the buoyancy fluxes do not cease, instead they become countergradient. We find that buoyantly driven motions play an active role in the transfer of mass. This is in agreement with trends derived from Monin–Obukhov scaling. For positive Richardson flux numbers (Ri f ), the log velocity profile in the near-bed layer requires correction with a drag reduction. For negative Ri f , the log velocity profile should be corrected with a drag increase, with increasing |Ri f |. This highlights the active role played by buoyancy in momentum transfer and the production of TKE. However, the data do not appear to entirely follow Monin–Obukhov scaling. This is consistent with the notion that the turbulence field is not in equilibrium. The large stratification results in the decay of turbulence and countergradient buoyancy fluxes act to restore equilibrium in the energy budget. This implies that there is a finite adjustment timescale of the turbulence field to changes in velocity shear and density stratification. The energy transfers associated with the source and sink function of the buoyancy flux can be modeled with the concept of total turbulent energy.  相似文献   

9.
Five near-bottom excess-radon profiles have been measured at the Geosecs-I station in the northeast Pacific, at varying intervals over a period of two and a half years. These profiles vary considerably in both structure and radon concentration, indicating transient characteristics of the bottom water in the deep Pacific. Only two of the five profiles are of the quasi-exponential type (Y. Chung and H. Craig); the stationary vertical eddy diffusivities calculated from these two profiles are 129 cm2/sec in November, 1971, and 22 cm2/sec obtained five months later.A single bottom-radon profile was measured in the western-boundary-current region of the South Pacific at the Geosecs-III station. This profile is also of the quasi-exponential type, with a vertical diffusivity of 32 cm2/sec. Although the radon concentrations of the three quasi-exponential profiles and the calculated diffusivities are quite different, the integrated excess-radon inventory in the water column, and the calculated flux of radon across the sediment—water interface, vary by only a factor of two in the two areas studied.  相似文献   

10.
A model framework is presented for simulating nitrogen and carbon cycling at the sediment–water interface, and predicting oxygen consumption by oxidation reactions inside the sediments. Based on conservation of mass and invoking simplifying assumptions, a coupled system of diffusive–reactive partial differential equations is formulated for two-layer conceptual model of aerobic–anaerobic sediments. Oxidation reactions are modeled as first-order rate processes and nitrate is assumed to be consumed entirely in the anoxic portion of the sediments. The sediments are delineated into a thin oxygenated surface layer whose thickness is equal to the oxygen penetration depth, and a lower, but much thicker anoxic layer. The sediments are separated from the overlying water column by a relatively thin boundary layer through which mass transfer is diffusion controlled. Transient solutions are derived using the method of Laplace transform and Green’s function, which relate pore-water concentrations of the constituents to their concentrations in the bulk water and to the flux of decomposable settling organic matter. Steady-state pore-water concentrations are also obtained including expressions for the extent of methane saturation zone and methane gas flux. A relationship relating the sediment oxygen demand (SOD) to bulk water oxygen is derived using the two-film concept, which in combination with the depth-integrated solutions forms the basis for predicting the extent of oxygen penetration in the sediment. Iterative procedure and simplification thereof are proposed to estimate the extent of methane saturation zone and thickness of the aerobic layer as functions of time. Sensitivity of steady-state solutions to key parameters illustrates sediment processes interactions and synergistic effects. Simulations indicate that for a relatively thin diffusive boundary layer, d, oxygen uptake is limited by biochemical processes inside the sediments, whereas for a thick boundary layer oxygen transfer through the diffusive boundary layer is limiting. The results show an almost linear relationship between steady-state sediment oxygen demand and bulk water oxygen. For small d methane and nitrogen fluxes are sediment controlled, whereas for large d they are controlled by diffusional transfer through the boundary layer. It is shown that the two-layer model solution converges to the one-layer model (anaerobic layer) solution as the thickness of the oxygenated layer approaches zero, and that the transient solutions approach asymptotically their corresponding steady-state solutions.  相似文献   

11.
Depth variable vertical eddy diffusion coefficients for heat (K z) were calculated from continuously measured temperature profiles in Überlinger See (western part of Lake Constance). The temperatures were averaged over vertical intervals of 10 m yielding 14 discrete values (maximum depth of Überlinger See: 147 m). A linear fit from 10 June to 29 September 1987 was used to smooth the significant temperature fluctuations caused by internal seiches of Lake Constance.Assuming horizontal homogeneity for the smoothed data the Gradient-Flux-Method was applied to compute vertical diffusion coefficientsK z at different depths using the depth variable volumes and surfaces of the 14 layers. The resulting mean diffusion coefficients for the period from June to September are 0.04 cm2/s near the thermocline and up to 0.8 cm2/s in deeper strata (accuracy: ± 50%). It is shown that horizontal mixing between Überlinger See and Obersee (main lake) alters the computation ofK z by less than 50%.A relationship betweenK z and stability (Brunt-Väisälä) frequencyN is found which corresponds well to the theory of internal wave induced turbulence.Combining the diffusion coefficients with measured phosphorus profiles, a phosphorus flux from the hypolimnion to the epilimnion of (0.7 ± 0.4) mg P m–2 d–1 was calculated, corresponding to about 20% of the average external loading per area of Lake Constance in 1986.  相似文献   

12.
We have conducted RASS (Radio Acoustic Sounding System) observations with the MU (Middle and Upper atmosphere) radar on 28–31 July 1994 at Shigaraki, Japan (34°51′ N, 136°06′ E) and determined the characteristics of turbulence energy dissipation rate (ε) and vertical eddy diffusivity (K) in the troposphere and lower stratosphere. We have first examined the accuracy of the Brunt Väisälä frequency squared (N2) derived from RASS temperature profiles. Then, ε and K are determined by using N2 and the Doppler spectral width of turbulence echoes (σ2turb). We found that the structures of ε and K are sometimes affected by the local variations of N2. We found that sometimes ε became small, even though σ2turb was large, because N2 was small. On the contrary, K was enhanced due to small N2, although σ2turb was small.  相似文献   

13.
In earthquake prediction studies, the regional behaviour of accurate 222Rn measurements at a set of sites plays a significant role. Here, measurements are obtained using active and passive radon detector systems in an earthquake-active region of Turkey. Two new methods are proposed to explain the spatial behaviours and the statistical uncertainties in the 222Rn emission measurements along fault lines in relation to earthquake occurrence. The absolute point cumulative semivariogram (APCSV) and perturbation method (PM) help to depict the spatial distribution patterns of 222Rn in addition to the joint effects of the K dr, the radon distribution coefficient, and the perturbation radon distribution coefficient (PRDC). The K dr coefficient assists in identifying the spatial distributional behaviour in 222Rn concentrations and their migration along the Earth’s surface layers. The PRDC considers not only the arithmetic averages but also the variances (or standard deviations) and the correlation coefficients, in addition to the size of the error among the 222Rn measurements. The applications of these methodologies are performed for 13,000 222Rn measurements that are deemed to be sufficient for the characterization of tectonics in the Keban Reservoir along the East Anatolian Fault System (EAFS) in Turkey. The results are evaluated for the ?çme earthquake (M L 5.4, 5.7 km, 23 June 2011), which occurred in the vicinity of the EAFS.  相似文献   

14.
The “anomalous” layer in the lowermost mantle, identified as D″ in the notation of K.E. Bullen, appears in the PREM Earth model as a 150 km-thick zone in which the gradient of incompressibility with pressure, dKdP, is almost 1.6, instead of 3.2 as in the overlying mantle. Since PREM shows no accompanying change in density or density gradient, we identify D″ as a thermal boundary layer and not as a chemically distinct zone. The anomaly in dKdP is related to the temperature gradient by the temperature dependence of Ks, for which we present a thermodynamic identity in terms of accessible quantities. This gives the numerical result (?Ks/?T)P=?1.6×107 Pa K?1 for D″ material. The corresponding temperature increment over the D″ range is 840 K. Such a layer cannot be a static feature, but must be maintained by a downward motion of the lower mantle toward the core-mantle boundary with a strong horizontal flow near the base of D″. Assuming a core heat flux of 1.6 × 1012 W, the downward speed is 0.07 mm y?1 and the temperature profile in D″, scaled to match PREM data, is approximately exponential with a scale height of 73 km. The inferred thermal conductivity is 1.2 W m?1 K?1. Using these values we develop a new analytical model of D″ which is dynamically and thermally consistent. In this model, the lower-mantle material is heated and softened as it moves down into D″ where the strong temperature dependence of viscosity concentrates the horizontal flow in a layer ～ 12 km thick and similarly ensures its removal via narrow plumes.  相似文献   

15.
In a limno-corral (diameter 12 m, depth to sediments 10 m), located in Baldeggersee (Switzerland), vertical mixing has been measured during more than one year and compared to the conditions in the open lake (maximum depth 65 m, surface area 5.3 km2). The temperature method by McEwen and Hutchinson yields Kz values between 5×10−2 cm2s−1 at the upper boundary of the thermocline and 2×10−3 cm2s−1 at the bottom, a value near the molecular diffusion of heat at 4°C (1.36×10−3 cm2s−1). Kz calculated from profiles of excess radon-222 generally agree with those from the temperature data. Compared to the open lake, the corral has a more shallow epilimnion. However, during calm meteorological conditions, vertical mixing in the upper 10 m is similar outside and inside the corral. Supported by the Swiss National Science Foundation within the framework for its National Research Program on ‘Lake Currents.’  相似文献   

16.
Recent advances in the measurement and interpretation of geoid height anomalies provide a new way to estimate the thickness of the oceanic lithosphere as a function of crustal age. GEOS-III satellite altimetry measurements show abrupt changes in sea level across fracture zones which separate areas of lithosphere with different ages. These changes have the correct location, amplitude, and wavelength to be caused by the combined gravitational attraction of the relief across the fracture zone and the isostatic support of this relief. Eight profiles of geoid height and bathymetry across the Mendocino fracture zone are inverted to determine the depth of the isostatic compensation, assuming that the compensation occurs in a single layer. These depths are then interpreted with a thermal boundary layer model of lithospheric growth. To explain satisfactorily the geoid measurements, the thermal diffusivity of the upper mantle must be 3.3 × 10?3 cm2 s?1 and the thickness of the lithosphere, defined as the depth at which the geotherm reaches 95% of its maximum value, must be9.1km m.y.?1/2 × t1/2, where t is lithospheric age.  相似文献   

17.
Abstract

This paper analyzes the linear stability of a rapidly-rotating, stratified sheet pinch in a gravitational field, g, perpendicular to the sheet. The sheet pinch is a layer (O ? z ? d) of inviscid, Boussinesq fluid of electrical conductivity σ, magnetic permeability μ, and almost uniform density ρ o; z is height. The prevailing magnetic field. B o(z), is horizontal at each z level, but varies in direction with z. The angular velocity, Ω, is vertical and large (Ω ? VA/d, where VA = B0√(μρ0) is the Alfvén velocity). The Elsasser number, Λ = σB2 0/2Ωρ0, measures σ. A (modified) Rayleigh number, R = gβd2/ρ0V2 A, measures the buoyancy force, where β is the imposed density gradient, antiparallel to g. A Prandtl number, PK = μσK, measures the diffusivity, k, of density differences.  相似文献   

18.
Three ferromanganese nodules handpicked from the tops of 2500 cm2 area box cores taken from the north equatorial Pacific have been analysed for their U-Th series nuclides.230Thexc concentrations in the surface 1–2 mm of the top side of the nodules indicate growth rates of 1.8–4.6 mm/106 yr. In two of the nodules a significant discontinuity in the230Thexc depth profile has been observed at ～0.3 m.y. ago, suggesting that the nodule growth has been episodic. The concentration profiles of231Paexc (measured via227Th) yield growth rates similar to the230Thexc data. The bottom sides of the nodules display exponential decrease of230Thexc/232Th activity ratio with depth, yielding growth rates of 1.5–3.3 mm/106 yr.The230Thexc and231Paexc concentrations in the outermost layer of the bottom face are significantly lower than in the outermost layer of the top face. Comparison of the extrapolated230Thexc/232Th and230Thexc/231Paexc activity ratios for the top and bottom surfaces yields an “age” of (5?15) × 104 yr for the bottom relative to the top. This “age” most probably represents the time elapsed since the nodules have attained the present orientation.The210Pb concentration in the surface ～0.1 mm of the top side is in large excess over its parent226Ra. Elsewhere in the nodule, up to ～1 mm depth in both top and bottom sides,210Pb is deficient relative to226Ra, probably due to222Rn loss. The absence of210Pbexc below the outermost layer of the top face rules out the possibility of a sampling artifact as the cause of the observed exponentially decreasing230Thexc and231Paexc concentration profiles. The flux of210Pbexc to the nodules ranges between 0.31 and 0.58 dpm/cm2 yr. The exhalation rate of222Rn, estimated from the226Ra-210Pb disequilibrium is ～570 dpm/cm2 yr from the top side and >2000 dpm/cm2 yr from the bottom side.226Ra is deficient in the top side relative to230Th up to ～0.5–1 mm and is in large excess throughout the bottom. The data indicate a net gain of226Ra into the nodule, corresponding to a flux of (24?46) × 10?3 dpm/cm2 yr. On a total area basis the gain of226Ra into the nodules is <20% of the226Ra escaping from the sediments. A similar gain of228Ra into the bottom side of the nodules is reflected by the high228Th/232Th activity ratios observed in the outermost layer in contact with sediments.  相似文献   

19.
Vertical mixing in Überlingersee is studied by releasing sulfur hexafluoride (SF6) as a tracer at a central hypolimnic depth of 60 m and measuring its subsequent vertical dispersion over a period of three months. The experiment started with a streaky tracer injection of 1 liter gaseous SF6 (STP) in August 1990. At that time the lake showed a typical strong summer stratification which in a weakened form lasts until November. From the SF6 profiles of fifteen surveys at three sampling sites vertical diffusivitiesK z are calculated compensating internal seiche displacement and horizontal tracer loss. Except of the bottom region no sampling site or time period is marked by significant differences in the hypolimnicK z profile. So vertical mixing in the whole Überlingersee is described by mean diffusivities decreasing from 1.7 cm2/s at 120 m depth to 0.4 cm2/s in 30 m. The minimal value of 0.3 cm2/s in the thermocline region at 20 m depth is only based on observations in autumn. For a strong summer stratification it is certainly lower. The gradient-flux-method for heat was applied to compute a meanK z (T) profile from continuously measured temperature profiles. Significant differences resulting from the two tracers showed, that theK z (T) values are underestimated by up to a factor of 5 if cooling by lateral exchange is neglected. Particularly, internal seiche pumping of colder water from the adjacent Lake Obersee over the separating sill of Mainau into the deep Überlingersee basin is observed in 1990 from August onward, obviously controlling the heat budget below the sill level.  相似文献   

20.
We present an upscaled model for the vertical migration of a CO2 plume through a vertical column filled with a periodic layered porous medium. This model may describe the vertical migration of a CO2 plume in a perfectly layered horizontal aquifer. Capillarity and buoyancy are taken into account and semi-explicit upscaled flux functions are proposed in the two following cases: (i) capillarity is the main driving force and (ii) buoyancy is the only driving force. In both cases, we show that the upscaled buoyant flux is a bell-shaped function of the saturation, as in the case of a homogeneous porous medium. In the capillary-dominant case, we show that the upscaled buoyant flux is the harmonic mean of the buoyant fluxes in each layer. The upscaled saturation is governed by the continuity of the capillary pressure at the interface between layers. In the capillary-free case, the upscaled buoyant flux and upscaled saturation are determined by the flux continuity condition at the interface. As the flux is not continuous over the entire range of saturation, the upscaled saturation is only defined where continuity is verified, i.e. in two saturation domains. As a consequence, the upscaled buoyant flux is described by a piecewise continuous function. Two analytical approximations of this flux are proposed and this capillary-free upscaled model is validated for two cases of heterogeneity. Upscaled and cell averaged saturations are in good agreement. Furthermore, the proposed analytical upscaled fluxes provide satisfactory approximations as long as the saturation set at the inlet of the column is in a range where analytical and numerical upscaled fluxes are close.  相似文献   

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