Longitudinal Advection Research Articles

Retention time and dispersion associated with submerged aquatic canopies

The shear layer at the top of a submerged canopy generates coherent vortices that control exchange between the canopy and the overflowing water. Unlike free shear layers, the vortices in a canopy shear layer do not grow continuously downstream but reach and maintain a finite scale determined by a balance between shear production and canopy dissipation. This balance defines the length scale of vortex penetration into the canopy, δe, and the region of rapid exchange between the canopy and overflow. Deeper within the canopy, transport is constrained by smaller turbulence scales. A two‐box canopy model is proposed on the basis of the length scale δe. Using diffusivity and exchange rates defined in previous studies, the model predicts the timescale required to flush the canopy through vertical exchange over a range of canopy density and height. The predicted canopy retention times, which range from minutes to an hour, are consistent with canopy retention inferred from tracer observations in the field and comparable to retention times for some hyporheic regions. The timescale for vertical exchange, along with the in‐canopy velocity, determines the minimum canopy length for which vertical exchange dominates water renewal. Shorter canopies renew interior water through longitudinal advection. Finally, canopy water retention influences longitudinal dispersion through a transient storage process. When vertical exchange controls canopy retention, the transient storage dispersion increases with canopy height. When longitudinal advection controls water renewal, dispersion increases with canopy patch length.

Hurricane-induced destratification and restratification in a partially-mixed estuary

Hurricane Isabel made landfall at the Outer Banks of North Carolina and moved past Chesapeake Bay on 18 –19 September 2003. The baroclinic response of this partially-mixed estuary to the passage of Isabel is investigated using the output from a regional atmosphere-ocean model. The hurricane-forced winds caused gradual deepening of the surface mixed layer, followed by rapid destratification in the water-column. The mixed-layer deepening appears to be driven by velocity shear and can be interpreted by a gradient Richardson number. Although strong winds caused complete mixing locally, a large longitudinal salinity gradient of about 10 4 psu m 1 persisted between the estuary’s head and mouth. After passage of the storm, the horizontal baroclinic pressure gradient drove restratification and a two-layer circulation in the estuary. The averaged buoyancy frequency increased linearly with time during an initial stage, and reached about 0.03 s 1 one day after the destratification. The model results are in good agreement with the theoretical prediction based on gravitational adjustment. Subsequently, turbulent diffusion works against the longitudinal advection to produce quasi-steady salinity distribution.

Extended Graetz problem accompanied by Dufour and Soret effects

Simultaneous heat and mass transfer between parallel plates are analyzed taking into account the Soret and Dufour effects. Both heat and mass transport are examined considering conduction in the axial and transverse directions plus longitudinal advection. The equations differ from the classical heat and mass transfer ones in considering the effect of the temperature gradient upon the mass flux, and conversely the effect of the concentration gradient upon heat flux, in accordance with the dictates of thermodynamics of irreversible processes. The special problems solved evaluate the effect of an imposed temperature difference between the confining walls upon the solute concentration distribution of a multisolute which diffuses against the concentration gradient forced by the prevailing temperature gradient. Details and numerical results are presented only for binary solutions. The asymptotic concentration difference, for a specified temperature difference, depends on the Soret and Dufour coefficients. The approach to the asymptotes is determined by the complete solution of the governing equations.

Retention of conservative and sorptive solutes in streams — simultaneous tracer experiments

The effective transport velocity of solutes in rivers and streams is governed by transient storage in hyporheic zones in which the longitudinal advection velocity is small relative to the main stream flow velocity. Results from a simultaneous tracer experiment using a non-reactive (tritium, 3H 2O) and a sorptive tracer [chromium, 51Cr(III)] have formed the basis of a more accurate interpretation of the retention characteristics of solutes in streams than previously has been possible. By using a simultaneous injection of these two tracers, it was possible to distinguish between their different behaviours. Based on estimations of fluxes, the retained mass of chromium in the storage zones along the 30-km-long study-reach was 76% after 150 h. Independent observations in the bed sediment indicated that the loss of chromium observed in the water was mainly a result of uptake into the bed sediment. To describe the transport in the stream, a model concept including solute sorption kinetics in the bed sediment was proposed. Evaluation of parameters in the model, indicated that the uptake of chromium in the bed sediment is controlled by sorption kinetics.

Two-dimensional nonlinear advection-diffusion in a model of surfactant spreading on a thin liquid film

The spreading of a localized monolayer of dilute, insoluble surfactant, discharged from a point source that moves at constant speed over a thin liquid film coating a planar substrate, is described according to lubrication theory by a pair of coupled nonlinear evolution equations for the monolayer concentration Γand the film depth h. Numerical and asymptotic techniques are here used to show that the extent and structure of such a spreading asymmetric monolayer can be well approximated by a single nonlinear advection–diffusion equation involving Γalone. At large times the solution is composed of three, spatially distinct, asymptotic regions: (i) a quasi-steady ‘nose’ region (containing the source), in which there is a dominant balance between two-dimensional nonlinear diffusion and advection; (ii) an ‘advective’ region, in which longitudinal advection balances transverse diffusion; and (iii) a ‘tail’ region, in which unsteady diffusion is dominant. In each region, local similarity solutions are obtained either exactly (in the advective region) or approximately (elsewhere) by rescaling numerical solutions of the initial-value problem. If the source concentration decreases with time, it is demonstrated that the monolayer’s width is greatest in the tail region, whereas for a source of increasing concentration the monolayer is widest in the advective region. For the simpler one-dimensional problem of a monolayer spreading from a line source, the same balances hold but with transverse diffusion eliminated; here self-similar solutions are found in all three regions that agree closely with numerical solutions of the initial-value problem.

Flow structure in depth‐limited, vegetated flow

Aquatic vegetation controls the mean and turbulent flow structure in channels and coastal regions and thus impacts the fate and transport of sediment and contaminants. Experiments in an open‐channel flume with model vegetation were used to better understand how vegetation impacts flow. In particular, this study describes the transition between submerged and emergent regimes based on three aspects of canopy flow: mean momentum, turbulence, and exchange dynamics. The observations suggest that flow within an aquatic canopy may be divided into two regions. In the upper canopy, called the “vertical exchange zone”, vertical turbulent exchange with the overlying water is dynamically significant to the momentum balance and turbulence; and turbulence produced by mean shear at the top of the canopy is important. The lower canopy is called the “longitudinal exchange zone” because it communicates with surrounding water predominantly through longitudinal advection. In this region turbulence is generated locally by the canopy elements, and the momentum budget is a simple balance of vegetative drag and pressure gradient. In emergent canopies, only a longitudinal exchange zone is present. When the canopy becomes submerged, a vertical exchange zone appears at the top of the canopy and deepens into the canopy as the depth of submergence increases.

Transport Velocity of Flounder Larvae (Platichthys flesus L.) in the Dollard (Ems Estuary)

Larval concentrations of flounder (Platichthys flesus L.), longitudinal current velocity and physical variables were measured simultaneously in the Dollard to calculate the mass transport of the larvae, salinity and suspended matter. Transport velocities of the three substances (salinity, suspended matter and larvae) and of water were calculated and compared. The concept of larval velocity was extended to incorporate the effect of varying vertical larval distribution. The contributions of variations in vertical and temporal concentration to the transport velocity were calculated separately. The differences in velocity between the substances in relation to the vertical and temporal variation provide more insight in estuarine transport processes in the nursery.Temporal salinity variation dominated over vertical variation during flood, and indicated that longitudinal advection was important. Overall, during flood the transport velocity of salinity was 3% lower than that of water. During ebb, there was hardly any difference between the transport velocity of salinity and water. The contributions of temporal and vertical variation in suspended matter were each in the order of 10%, but of opposite signs. The net result is a transport velocity of suspended matter which is 3% (flood) or 4% (ebb) higher than that of water. Erosion-deposition seemed the dominant process. During flood, transport velocity of larvae is 9% higher than that of water, which is mainly caused by vertical concentration variation (6%), while during ebb, larval transport velocity is 9% lower, which is almost exclusively due to the temporal concentration variation (8%). Swimming influences transport during flood, while during ebb it is not clear which process dominates. The results indicate that flounder larvae make use of selective tidal stream transport inside the nursery.

Advection and dispersion of contaminant in a permeable medium embedding fractures in which advection velocity is comparatively slow

This paper concerns the advective migration of an aqueous contaminant in a fractured permeable formation. Calculation and analysis refer to fractures in which advection velocity is comparatively small. The slow advective velocity is created by some local cavities or almost vertical orientation of the fractures. It is shown that the advective contaminant transport is characterized by two dimensionless parameters: (1) the ratio between the permeable block and fracture flow rates, termed the ‘mobility number’; (2) the ratio between the longitudinal advection velocity of the permeable block flow and that of the fracture flow, termed the ‘advection velocity ratio’. For a sufficiently large domain, continuum parameters can be applied to characterization of the fractured permeable formation. Then the mixing between the permeable block flow and the fracture flow is a mechanism leading to contaminant dispersion. For very small values of the advection velocity ratio, the effective dispersivity is fully determined by the mobility number. Its value decreases with increase of the mobility number. Under such conditions, the equivalent porosity is constant, and its value is identical to that of the permeable blocks. A significant value of the advection velocity ratio increases the equivalent porosity of the fractured permeable formation. With regard to the effective dispersivity of the domain, if the advection velocity ratio is equal to unity then the effective dispersivity vanishes. The larger the deviation of the advection velocity from unity, the larger is the effective dispersivity of the fractured permeable medium.

A Lagrangian dispersion model for predicting CO2sources, sinks, and fluxes in a uniform loblolly pine (Pinus taeda L.) stand

A canopy Lagrangian turbulent scalar transport model for predicting scalar fluxes, sources, and sinks within a forested canopy was tested using CO2concentration and flux measurements. The model formulation is based on the localized near‐field theory (LNF) proposed byRaupach[1989a, b]. Using the measured mean CO2concentration profile, the vertical velocity variance profile, and the Lagrangian integral timescale profile within and above a forested canopy, the proposed model predicted the CO2flux and source (or sink) profiles. The model testing was carried out using eddy correlation measurements at 9 m in a uniform 13 m tallPinus taeda L.(loblolly pine) stand at the Blackwood division of the Duke Forest near Durham, North Carolina. The tree height and spacing are relatively uniform throughout. The measured vertical profile leaf area index (LAI) was characterized by three peaks, with a maximum LAI occurring at 6.5 m, in qualitative agreement with the LNF source‐sink predicted profile. The LNF CO2flux predictions were in better agreement with eddy correlation measurements (coefficient of determinationr2= 0.58; and standard error of estimate equal to 0.16 mg kg−1m s−1) thanKtheory. The model reproduced the mean diurnal CO2flux, suggesting better performance over longer averaging time periods. Two key simplifications to the LNF formulation were considered, namely, the near‐Gaussian approximation to the vertical velocity and the absence of longitudinal advection. It was found that both of these assumptions were violated throughout the day, but the resulting CO2flux error at 9 m was not strongly related to these approximations. In contrast to the forward LNF approach utilized by other studies, this investigation demonstrated that the inverse LNF approach is sensitive to near‐field corrections.

Trial of a nonlinear diffusion equation as a model of turbulent diffusion

A nonlinear diffusion equation is demonstrated as a model of turbulent dispersion in the atmosphere. It is based on a similarity solution for two-dimensional dispersion (longitudinal advection and vertical diffusion) from a horizontal line source. The coefficient for the vertical diffusion is a nonlinear function of both concentration and height. The similarity solution for two-dimensional dispersion includes a beta function with arguments that are functions of the parameters for the wind profile and the nonlinear vertical diffusion. The solution is successfully fitted to two sets of Prairie Grass data.

2D Advective-Diffusive Transport of Dissolved Oxygen in Channels

A two-dimensional (2D) theoretical analysis of the dissolved-oxygen (DO) concentration in rectangular channels is performed. It was assumed that the dissolved-oxygen concentration was affected by constant longitudinal advection, constant transverse diffusion, consumption by dissolved biochemical oxygen demand (BOD) and reaeration. The solution obtained presents the same behavior as conservative constituents and first-order decay constituents when expressed in the nondimensional form given by the ratio between the concentration and the cross-sectional concentration for the corresponding cross section. An order-of-magnitude analysis of the constants involved suggests that the location of maximum DO deficit for a bank discharge occurs in a region of the channel where the dissolved oxygen is almost completely mixed across the transverse direction. In this case, both one-dimensional (1D) and 2D dissolved oxygen models yield similar values for the location and value of the critical DO deficit. This solution may be useful as a first estimate of what happens in real situations as well as to provide a way to assess the performance of algorithms that numerically solve the DO transport equation.

Organic substances in the subsurface: Delineation, migration, and remediation

The Electric Power Research Institute (EPRI) and Niagara Mohawk Power Corporation are sponsoring a research program concerning the release, transformation, and migration of organic compounds at a site where coal tar from former manufactured gas plant (MGP) operations was disposed nearly thirty years ago. Work at this site, referred to as EBOS Site 24, has included: determination of the location and chemical content of the tarry source material, delineation of the groundwater contaminant plume, evaluation and implementation of innovative methods for sampling and analysis, and the remediation and restoration of the site. The results of the initial phase of research provided several important insights into the mechanisms of contaminant release and migration. For example, the shape of the groundwater contaminant plume at EBOS Site 24 was dominated by longitudinal advection with little contribution from transverse or vertical dispersion. A long-term monitoring program at EBOS Site 24 was initiated prior to the removal of the source material. The results of the baseline groundwater monitoring along the plume centerline were similar to the values predicted using EPRI's MYGRT TM model for migration of contaminants. After the baseline monitoring was completed, all of the tarry source material was removed in 1991 and used in the production of asphalt and portland cement. The groundwater monitoring program will continue for several years and the field results generated during this time will be used to evaluate and/or calibrate the MYGRT TM model.

Numerical simulation of solute transport in three‐dimensional, randomly heterogeneous porous media

A three‐dimensional solute transport model has been developed to study detailed contaminant movements through large heterogeneous flow systems in porous media. The model is based upon a random walk particle method (RWPM) which can readily treat multidimensional advection and dispersion processes in saturated or unsaturated media in a computationally efficient manner. The transport simulations are used to examine the large time and spatial effects of the variable flow field on developing solute plumes, and, in particular, to investigate the nature of the large‐scale dispersive behavior. Numerical transport experiments were conducted using single realizations of random hydraulic conductivity fields with three different degrees of heterogeneity. Experiments with different source locations were used to investigate preasymptotic and nonergodic effects that would appear as differences in plume evolution among the experiments. Analyses of the simulations indicate the spatial moments of the particle distributions in statistically isotropic saturated media compare favorably with stochastic theory predictions in terms of longitudinal advection and mixing, but differ markedly from predictions of transverse mixing. The simulations also demonstrate that significant nonergodic effects occur, as reflected in strong differences in the second moment evolution curves among the individual experiments and as predicted from the ensemble stochastic theory.

Structure of a fog in the dissipation stage over land

An extensive fog occurred in the northern part of the Kanto Plain in Japan, on the morning of 9 December 1985. The fog was found on visible and i.r. images of Landsat and a Geostationary Meteorological Satellite (GMS). The structure of the fog in the dissipation stage was studied mainly by using these satellite data, together with meteorological data, including those at Tsukuba, which is located in the fog area. Direct sampling of fog droplets was also carried out at Tsukuba, and showed that the maximum radius of the fog droplets at 0656, 0700 and 0704 LST was 25 μm near the ground. Dissipated areas of the fog obtained from the Landsat and GMS images were located in the windward region of the fog. The speed of dissipation was 2.5 times greater than that of the surface wind. Patchy areas of fog were also found in the Landsat images. The dissipated area and the patchy fog areas were located very systematically. It is suggested that the patchy fog areas were closely related to the dissipation process. Fine structures, such as longitudinal and transverse bands and scaly structures, were found at 0943 LST on Landsat images. The longitudinal fog bands were found to be parallel to the direction of surface winds and influenced strongly by complex terrain. It is suggested that these bands were related to longitudinal rolls in an unstable layer of the fog in the presence of vertical shear of wind speed. A quasi-periodic oscillation with a mean period of 9 min was observed in diffuse solar radiation at Tsukuba during the dissipation of the fog. The oscillation was caused by longitudinal advection of the longitudinal fog bands with modulations of nodules and twists.

Influence of Using Purged and Partially Penetrating Monitoring Wells on Contaminant Detection, Mapping, and Modeling

ABSTRACTAn analytical transport model is presented for evaluating vertically averaged concentration data derived from purged and partially penetrating monitoring wells. The model is applicable to continuous contaminant emission from a finite source with longitudinal advection, and three‐dimensional dispersion. The model is used to investigate how screened length may influence contaminant detection, mapping, and modeling. Sensitivity analyses suggest that contaminant concentrations determined from monitoring wells may underestimate the level of aquifer contamination, depending on screened depth, location of the well relative to the contaminant source, the vertical source dimension, and degree of vertical plume spreading. The magnitude of this effect may be comparable to, and in excess of, concentration biases related to construction materials and sampling procedures. Additional screened interval influences may include: underestimates of contamination extent and migration rate; apparent indications of attenuation processes and steady‐state conditions; over‐ estimates of vertical contaminant spreading; increased time of contaminant detection; and poor transport model predictions, owing to well‐biased concentration distributions.

Experimental Investigation of Solute Transport in Stratified Porous Media: 2. The Reactive Case

Laboratory experiments and mathematical simulations were used to investigate the transport of a reactive solute,85Sr, through a sand layer located between two silt layers. The experimental results showed breakthrough curves that were similar in form to those reported in the preceding paper for a nonreactive solute, but were delayed in the time of appearance, had a lower peak concentration, and were more highly dispersed. A mathematical model that accounts for longitudinal advection in the sand layer, transverse diffusion in the silt layers, and retardation in both the sand and silt layers was used to simulate the experimental results. With a trial‐and‐error adjustment of the retardation coefficicents, the mathematical model gave a good representation of the experimental data; however, different parameter values were required in order to simulate breakthrough curves measured at different values of the pore‐water velocity in the sand. The use of measured retardation parameters in the model produced a much better fit to the data compared to that which was obtained when retardation was neglected. Nevertheless, significant discrepancies existed between the measured and simulated results, with the discrepancies becoming greater at lower velocities. In view of the excellent agreement between measured and simulated results obtained in part 1 for nonreactive solutes, the less satisfactory agreement obtained here suggests that there is some physical or chemical aspect of the retardation process that is not adequately represented in the model.

Temporal variability of zooplankton biomass (ATP content and dry weight) in the St. Lawrence Estuary: Advective phenomena during neap tide

In order to assess the temporal variability of living zooplankton in a tidal estuary, the ATP content and dry weight of mixed zooplankton populations (mainly copepods) were measured during a period of 175 h at an anchor station in the Upper St. Lawrence Estuary. Vertical tows were made every 30 min. Hourly vertical profiles of the current speed and direction, temperature and salinity were also obtained during the experiment. A strong tidal influence was found in all series. Maxima and minima of the ATP content (living biomass) and the dry weight (total biomass) were correlated with low and high water slacks. The serial autocorrelation and cross-correlation showed, in both series a 12 to 13-h cycle, and the ATP:dry weight ratio showed a significant 24-h cycle. The cross-correlation with the Kendall τ was used to detect the relationship between biological components and physical indices (stratification and Ri). It is suggested that the proportion of living zooplankton biomass in the Upper St. Lawrence Estuary is most likely the result of a combination of diurnal migration and longitudinal advection.

Temperature profiles in the Barnes Ice Cap, Baffin Island, Canada, and heat flux from the subglacial terrane

Temperature measurements were made in seven boreholes, ranging in depth from 50–276 m, in the Barnes Ice Cap. Holes B4, D4, and T0975 are approximately 1 km from the margin and an average of 8 km apart. Holes T091, T081, T061, and T020 lie along a 10.2 km flow line passing through T0975. Temperature profiles are convex upward in all holes except T020, reflecting the combined effects of longitudinal and upward vertical advection, and frictional heating. The profile in T020 is concave near the bottom of the hole, as a result of downward vertical advection, but convex above mid-depth, owing to a 2.5 °C cooling of the near-surface ice in the early 1940's.Modeling, using a finite difference scheme, suggests that the profiles are in equilibrium with slightly lower vertical velocities and longitudinal advection rates than exist at present, and that temperatures at the glacier surface have increased 0.1–0.5 °C over the last few decades. The modeling further suggests that the heat flux from the subglacial terrane beneath most holes is 0.5–0.8 heat-flow units (HFU), which is somewhat lower than the average geothermal flux on the Canadian Shield. The heat flux seems to decrease down-glacier along the flow line through T0975, apparently reflecting climatic warming of about 2 °at the end of the Little Ice Age. In contrast, the heat flux appears to increase southeastward from the flow line, reaching an anomalously high value of about 1.9 HFU at B4. This trend is unexplained.Measurements of U, Th, and K in rock samples collected near the margin suggest heat production rates of about 5 heat-generation units (HGU), which is slightly higher than previous measurements on Baffin Island.

Annual and Longer Term Variations of Deepwater Properties in the Coastal Waters of Southern British Columbia

Observations of deepwater properties (temperature, salinity, dissolved oxygen, and the derived values of density) have been assembled from the Data Reports of the Institute of Oceanography of the University of British Columbia and values of the first three properties are presented to show the characteristics of their annual variations at 18 locations in the coastal waters of southern British Columbia. Information on the long-term variations (for 6 yr or more) of all properties is presented for eight of the locations. Variations of 1-yr period are evident to 100 m depth at all locations and to 300 m or more at many of them. The variations are of different forms, sinusoidal, peaked or saw-tooth, and there are some differences in phase between the property variations at different locations. Long-term variations (over several years) of annual mean values are small and decrease with increase of depth. Much of the evidence suggests that the changes below 100 m depth are due to longitudinal advection (flow) from elsewhere rather than to vertical transfers from the sea surface in the immediate locality.