Stratified Salt Research Articles

Convection in a Continuously Stratified Fluid

This paper begins by commemorating Count Rumford's observations of convection in 1797. Rumford investigated the effects of stewed apples, eiderdown, and other fibrous materials on retarding vertical circulation in liquids. In contrast to Count Rumford's historic experiments, the present paper describes a simple, visually instructive, physical chemistry experiment for demonstrating how a mathematical model can be applied to free convection in a vertically stratified salt solution. In the first part of the experiment, a linear salt concentration profile is created in a beaker of water at room temperature. The salt concentration (and density) is greatest at the bottom of the liquid. When the beaker containing the salt solution is then heated on a hot plate, a well defined convecting bottom layer forms almost immediately. The measured rate of growth in thickness of this convecting layer is compared to that predicted from a model based on density differences. The temperature of the liquid above the bottom conv...

Energetics of grid turbulence in a stably stratified fluid

A biplane grid with a mesh spacing of 10.8 cm was towed horizontally in a towing tank to generate turbulence in a non-stratified fluid and in stratified fluids with different constant density gradients. Turbulence velocity components and density fluctuations were measured using an array of cross-film and conductivity probes. Based on the mesh size of the grid, the nominal values of the (internal) Froude numbers were ∞, 80 and 40, and the corresponding Reynolds number was 4.3 × 104. The decay rates of the (turbulence) kinetic, potential and total energies and the dissipation rates of the kinetic and potential energies were calculated from the experimental data. For each of these quantities, the decay may be represented as a function of the downstream distance raised to a given power. The kinetic energy and its dissipation rate are lower for the stratified cases than for the non-stratified case but are almost compensated for by the corresponding potential energy and its dissipation rate. Our results are consistent with those of direct numerical simulations and agree reasonably well with those obtained in stratified wind and water tunnels. However, the results differ from laboratory results obtained using an optical method to measure the turbulent motion of tracer particles in the wake of a vertically towed grid; these latter results show an abrupt reduction in the decay rate of the turbulence kinetic energy after one Brunt–Vaisala period. A similar trend is also observed in results obtained in facilities with fairly high background turbulence or internal waves. This discrepancy is discussed and an explanation is presented. Furthermore, it is demonstrated that strongly stratified thin sheets with density gradients larger than that of the undisturbed fluid may be generated by local but incomplete mixing. The persistence of such thin sheets is proportional to the Schmidt number (≈ 500) in stratified salt water or the Prandtl number (≈ 0.71) in thermally stratified air.

Effects of molecular diffusivities on counter-gradient scalar and momentum transfer in strongly stable stratification

The effects of molecular diffusivities of heat and mass on the counter-gradient scalar and momentum transfer in strongly stable stratification are experimentally investigated in unsheared and sheared stratified water mixing-layer flows downstream of turbulence-generating grids. Experiments are carried out in two kinds of stably stratified water flows. In the case of thermal stratification, the difference between the turbulent fluxes of an active scalar (heat with the Prandtl number of Pr ≈ 6) and a passive scalar (mass with the Schmidt number of Sc ≈ 600) is investigated. In the case of salt stratification, the effects of the molecular diffusion of the active scalar (salt) with a very high Schmidt number of Sc ≈ 600 on the counter-gradient scalar transfer is studied. Comparisons of the effects of molecular diffusivities are also made between thermally stratified water and air (Pr ≈ 0.7) flows. Further, the effects of mean shear on the counter-gradient scalar and momentum transfer are investigated for both stratified cases. Instantaneous temperature, concentration and streamwise and vertical velocities are simultaneously measured using a combined technique with a resistance thermometer, a laser-induced fluorescence method, and a laser-Doppler velocimeter with high spatial resolution. Turbulent scalar fluxes, joint probability density functions, and cospectra are estimated.The results of the first case show that both active heat and passive mass develop counter-gradient fluxes but that the counter-gradient flux of passive mass is about 10% larger than that of active heat, mostly due to molecular diffusion effects at small scales. The counter-gradient scalar transfer mechanism in stable stratification can be explained by considering the relative balance between the available potential energy and the turbulent kinetic energy as in Schumann (1987). In thermally and salt-stratified water mixing-layer flows with the active scalars of high Prandtl and Schmidt numbers, the buoyancy-induced motions with finger-like structures first contribute to the counter-gradient scalar fluxes at small scales, and then the large-scale motions, which bring fluid back to its original levels, generate the counter-gradient fluxes at large scales. The contribution of the small-scale motions to the counter-gradient fluxes in stratified water flows is quite different from that in stratified air flows. The higher Prandtl or Schmidt number of the active scalar generates both the stronger buoyancy effects and the longer time-oscillation period of the counter-gradient scalar fluxes. The time-oscillation occurs at large scales but the counter-gradient fluxes at small scales persist without oscillating. The mean shear acts to reduce the counter-gradient scalar and momentum transfer at large scales, and therefore the counter-gradient fluxes in sheared stratified flows can be seen only in very strong stratification. The behaviour of the counter-gradient momentum flux in strong stratification is quite similar to that of the counter-gradient scalar flux.

Availability and Persistence of Macronutrients from Lime and Preplant Nutrient Charge Fertilizers in Peat-based Root Media

Using incubation and container culture with subirrigation for up to 28 days, three experiments were conducted with six liming materials of different particle sizes and six blended preplant nutrient charge (PNC) fertilizers. Liming material, particle size, and incorporation rate had an effect on the initial pH (3.5 to 6.1) and the final stable pH (4.8 to 7.8) with one type of Canadian sphagnum peat that did not contain an incorporated PNC. Saturated media extract (SME) Ca and Mg concentrations were <25 and 15 mg·liter-1, respectively, for both pulverized and superfine dolomitic lime at incorporation rates up to 7.2 kg·m-3. For the blended PNC fertilizers in media containing lime, initial electrical conductivity (EC) and SME nutrient concentrations ranged from (EC) 1.0 to 2.9 dS·m-1, (mg·liter-1) 60 to 300 N, 4 to 105 PO4-P, 85 to 250 K, 120 to 400 Ca, and 60 to 220 Mg. However, within two days, the rapid stratification of fertilizer salts within the pot caused macronutrient concentrations to increase in the top 3 cm of root medium (top layer) by an average of 180% and decrease in the remaining root medium in the pot (root zone) by an average of 57% compared to that measured in the medium at planting. Nutrient concentrations in the top layer continued to increase even when those in the root zone fell below acceptable levels recommended for an SME. The importance of fertilizer salt stratification within a pot lies in the reduced availability of nutrients to the plant and illustrates the limited persistence of the PNC fertilizers. Testing nutrients in container media several days after planting rather than in freshly mixed media may be more representative of the starting point for a nutritional management program.

Stratification and wind mixing in the Southern Kattegat

Abstract Changes in salt stratification were investigated by using temperature and fluorescence measurements as tracers. By doing this, information on the short term history of the water column was revealed. Further the dominant processes in mixing and stratification of the upper metres of the water column in the southern Kattegat were identified. Due to the salt content, density increased with depth over most of the water column during the period of measurement., A 50 km intrusion of warm, phytoplankton-rich water from the Great Belt outlet was identified. The density increase was maintained due to the buoyancy input given by the combined effect of a horizontal density gradient and vertical shear. Hence the vertical temperature inhomogeneities lasted for 3–7 days and were not mixed even under an event of strong wing mixing. In this period the nutrient and salt transport are uncoupled, since most of the mixing energy is used to redistribute salt within the nutrient-poor surface layer. A reduction of the horizontal density gradient reduced the buoyancy input and allowed for the homogenization of the upper 15 metres within a few hours. One sharp interface was created. After the formation of the sharp interface salt and nutrient transport can be calculated by using the same entrainment function for both salt and nutrient transport. Only during approximately 5 % of the time there was a direct entrainment of bottom water and only 30% of the available mixing energy could be used to give this entrainment.

Energetics of grid turbulence in a stably stratified fluid

A biplane grid with a mesh spacing of 10.8 cm was towed horizontally in a towing tank to generate turbulence in a non-stratified fluid and in stratified fluids with different constant density gradients. Turbulence velocity components and density fluctuations were measured using an array of cross-film and conductivity probes. Based on the mesh size of the grid, the nominal values of the (internal) Froude numbers were ∞, 80 and 40, and the corresponding Reynolds number was 4.3 × 104. The decay rates of the (turbulence) kinetic, potential and total energies and the dissipation rates of the kinetic and potential energies were calculated from the experimental data. For each of these quantities, the decay may be represented as a function of the downstream distance raised to a given power. The kinetic energy and its dissipation rate are lower for the stratified cases than for the non-stratified case but are almost compensated for by the corresponding potential energy and its dissipation rate. Our results are consistent with those of direct numerical simulations and agree reasonably well with those obtained in stratified wind and water tunnels. However, the results differ from laboratory results obtained using an optical method to measure the turbulent motion of tracer particles in the wake of a vertically towed grid; these latter results show an abrupt reduction in the decay rate of the turbulence kinetic energy after one Brunt–Väisälä period. A similar trend is also observed in results obtained in facilities with fairly high background turbulence or internal waves. This discrepancy is discussed and an explanation is presented. Furthermore, it is demonstrated that strongly stratified thin sheets with density gradients larger than that of the undisturbed fluid may be generated by local but incomplete mixing. The persistence of such thin sheets is proportional to the Schmidt number (≈ 500) in stratified salt water or the Prandtl number (≈ 0.71) in thermally stratified air.

Turbulent mixing in stratified fluids: layer formation and energetics

Water with constant initial salt stratification was mixed with a horizontally moving vertical rod. The initially linear density profile turned into a series of steps when mixing was weak, in agreement with instability theory by Phillips (1972) and Posmentier (1977). For stronger mixing no steps formed. However, in all cases mixed layers formed next to the top and bottom boundaries and expanded into the interior due to the no-flux condition at the horizontal boundaries. The critical Richardson number Rie, dividing experiments with steps and ones without, increases with Reynolds number Re as Rie ≈ exp(Re/900). Steps evolved over time, with small ones forming first and larger ones appearing later. The interior seemed to reach an equilibrium state with a collection of stationary steps. The boundary mixed layers continued to penetrate into the interior. They finally formed two mixed layers separated by a step, and ultimately acquired the same densities so the fluid became homogeneous. The length scale of the equilibrium steps, ls, is a linear function of U/Ni, where U is the speed of the stirring rod and Ni is the buoyancy frequency of the initial stratification. The mixing efficiency Rf also evolved in relation to the evolution of the density structure. During the initiation of the steps, Rf showed two completely different modes of evolution depending on the overall Richardson number of the initial state, Rio. For Rio [Gt ] Rie, Rf increased initially. However for Rio near Rie, Rf decreased. Then the steps reached an equilibrium state where Rf was constant at a value that depended on the initial stratification. The density flux was measured to be uniform in the layered interior irrespective of the interior density gradient during the equilibrium state. Thus, the density (salt) was transported from the bottom boundary mixed layer through the layered interior to the top boundary mixed layer without changing the interior density structure. The relationship between Ril and Rf was found for Ril > 1, where Ril is the Richardson number based on the thickness of the interface between the mixed layers. Rf decreases as Ril increases, consistent with the most crucial assumption of the instability theory of Phillips/Posmentier.

Irrigation Requirements, Root-medium pH, and Nutrient Concentrations of Easter Lilies Grown in Five Peat-based Media with and without an Evaporation Barrier

Subirrigated Easter lilies were grown in five commercially formulated root media using one water-soluble fertilizer applied independently to each medium based on water-holding capacity and water loss. The number of irrigations ranged from 12 to 20 and the amount of applied water ranged from 5.3 to 6.8 liters for the uncovered media treatments. When the root-medium surface was covered with an evaporation barrier, the average amount of applied water was reduced by 35% compared to the uncovered media. The largest effect on root media pH was between uncovered and covered media due to the reduced amount of water applied. Similar macronutrient concentrations were measured in the five media during the experiment with few exceptions. The greatest differences in nutrient concentrations were found within the pots. The top 2.5 cm (top layer) contained nutrient concentrations up to 10 times higher than those measured in the remaining root medium (root zone) of the same pot. Covering the root-medium surface with an evaporation barrier reduced the stratification of fertilizer salts. Root-zone soluble salt concentrations of plants in the covered pots were similar to those of uncovered plants even though 36% less fertilizer was applied to the covered plants.

Closure of a Nuclear Waste Repository Deeply Imbedded in a Stratified Salt Bed

The Waste Isolation Pilot Plant (WIPP) is a repository vault, mined deep into a salt strata. It eventually closes in on itself, encapsulating its contents. At room temperature salt may be regarded as a linear, isotropic, viscoelastic material. In this study, using triaxial compression test results on salt, we determine the relaxation functions and set up the boundary value problem for the encapsulation mechanism of a salt vault. Closure of the repository as a function of time is determined using a three-dimensional finite element model. The Tresca failure criterion is used to predict the stability of the repository. Finally, the study is validated by comparing our results to in-situ measured data.

497 PB 201 Growth and Media Nutrient Concentration of Poinsettia as Influenced by a Pot Cover

The evaporation of water is a major source of water loss from potted plants which can be eliminated by placing a barrier at the exposed surface of media in the pot. To better understand the effect of reducing surface evaporation on growth and media nutrient concentration, 15 cm subirrigated poinsettias were produced with and without a pot cover. Both treatments received the same quantity of fertilizer, 75 mg·week-1 N for a total of 13 fertilizations. Uncovered pots received 12 more irrigations than pots with covers (20 vs. 32). Sixteen weeks after planting, covered plants had significantly less leaf area (2175 vs 2628 cm2), bract area (1655 vs 2137 cm2), height (24.1 vs 27.6 cm), fresh mass (116 vs 144 g) and dry mass (17 vs 20 g) than uncovered plants. Concentrations of N, P, K, Ca and Mg and EC (4.23 vs 2.65 mS·cm-1) were higher in the root-zone of covered plants than in uncovered plant. Covering the media surface did reduce the EC and the concentrations of N, P, K, Ca and Mg in the top layer (eg 13.47 mS·cm-1 vs 15.74 mS·cm-1) but stratification of salts to the top layer still occurred. Fertilizer salts in the top layer were shown to be less available to the plant than those in the root zone.

258 AVAILABILITY AND PERSISTENCE OF MACRONUTRIENTS FROM PREPLANT NUTRIENT CHARGE MATERIALS AND LIME IN PEAT-BASED ROOT MEDIA

Four experiments were conducted with six liming materials of different particle sizes and six commercially available blended preplant nutrient charge (PNC) materials in the laboratory and in container culture with subirrigation for durations up to twenty-eight days. Liming material, particle size, and incorporation rate affected both the initial and final stable pH of one type of peat without an incorporated PNC. Saturated media extract (SME) Ca2+ and Mg2+ concentrations were below the acceptable recommended concentrations for both pulverized and superfine dolomitic lime at incorporation rates up to 7.2 kg·m-3. For the blended PNC materials, initial N, P, K+, Ca2+, and Mg2+ concentrations for five of the six PNC materials were at or above the optimal concentrations recommended for an SME, but did not remain persistent in the root zone. A large percentage of all nutrients tested moved from the root zone into the top 3 cm (top layer) of the pot within two days after planting. Nutrient concentrations in the top layer continued to increase even when nutrient concentrations in the root zone fell below acceptable levels for an SME. The importance of this fertilizer salt stratification within the pot lies in the reduced availability of nutrients to the plant.

Heat-salt finger fluxes across a density interface

The heat and salt fluxes produced by salt fingering at a density interface are studied with a numerical and an analytical model. Specifically, the issue concerning the value of the heat-to-salt flux ratio is addressed. The numerical modeling based on direct numerical computation of the nonlinear governing equations obtains values around 0.5. This value is approximately the average of widely varying experimental values reported in the literature. The large difference between the theoretical flux ratio predicted based on the buoyancy maximization hypothesis and the experimentally derived flux ratio is examined with an analytical model, which includes both effects of salt stratification in the interface and salt discontinuity at the edges of the interface. Combined with the numerical model results, the analysis shows that the disagreement can be traced to the flux maximization hypothesis itself. An alternative hypothesis that maximizes convective velocity amplitude is presented which gives flux-ratio predictions consistent with the measurements. Discussion of the finger width scale and the magnitude of the salt flux is also given as well as comparison of the salt flux with laboratory measurements.

The Importance of Suppression of Turbulence by Stratification on the Estuarine Turbidity Maximum

A simple numerical model demonstrates that the reduction in turbulence due to stratification greatly enhances the trapping of suspended sediment that occurs at the estuarine turbidity maximum. In moderately and highly stratified estuaries the turbulent diffusivity decreases markedly between the region upstream of the salinity intrusion, where the turbulence is uninhibited by salt stratification, and the stratified regime within the salinity intrusion, where turbulence is reduced by the inhibitory influence of salt stratification. This reduction in turbulent diffusion results in a reduction in the quantity of sediment that can be carried by the flow, causing sediment to be trapped near the landward limit of the salinity intrusion. This trapping process occurs at the same location as that due to the estuarine convergence, but it appears to be many times more effective at trapping silt-size particles. A model is formulated that is similar to Festa and Hansen's (1978) model of the estuarine turbidity maximum, with the addition of a stratification-dependent eddy diffusivity. For silt-size sediment particles, the model indicates as much as a 20-fold increase in the trapping rate with inclusion of the stratification effect. it is likely that this mechanism is important in many partially mixed and highly stratified estuaries.

Evidence of the barrier layer in the surface layer of the tropics

Comparisons between isothermal depth to the top of the thermocline, and the mixed layer depth based on a σt criterion were undertaken for the tropical world oceans. In three equatorial regions, a shallower mixed layer than isothermal layer occurs, implying the presence of a strong halocline above the thermocline. This distance separating the top of the thermocline and the bottom of the mixed layer is referred to as the “barrier layer”, in relation to its impediment to vertical heat flux out of the base of the mixed layer. Different mechanisms are responsible for maintaining the barrier layer in each of the three regions. In the western equatorial Pacific Ocean a salinity budget confirmed that heavy local precipitation most likely results in the isothermal but salt‐stratified layer. In the northwest equatorial Atlantic, it is hypothesized that high salinity waters are subducted at the subtropics during winter and advected westward as a salinity maximum in the upper layers of the tropics, resulting in the barrier layer. In the eastern equatorial Indian Ocean, monsoonal related rainfall and river runoff contribute significantly to the freshwater flux, producing salt stratification in the surface. These results suggest the need to include the effects of salinity stratification when determining mixed layer depth.

Visualization of turbulence and internal waves in a stratified fluid

A method for visualizing the velocity field in stratified flow by means of tracer particles made from wooden sawdust is described. The wood particles absorb water and salinity and may match the local density of stratified salt water.

Flow visualization experiments on stably stratified flow over ridges and valleys

Flow visualization experiments on stably stratified flow over ridges and valleys formed by a pair of ridges were conducted in a large towing tank filled with stratified salt water. The ambient flow was normal to the axis of the ridges. Three experimental parameters were varied during the study: the steepness of the ridges, the separation distance between the ridges and the Froude number. The flow field in the valley was strongly influenced by flow separation from the lee side of the upstream ridge. For the gentle and intermediate ridges with maximum slopes of 13° and 27°, this separation was controlled by the lee waves when their wavelength was less than or equal to the width of the ridge. The flow field in the valley was similar to that downstream of a single ridge. For the steep ridge with a maximum slope of 40°, separation from the lee side of the upstream ridge and the flow field in the valley were influenced significantly by the presence of the downstream ridge.

Biogeochemistry of dimethylsulfide [DMS] in a seasonally stratified coastal salt pond

Biogeochemistry of dimethylsulfide [DMS] in a seasonally stratified coastal salt pond

Experimental and numerical investigation of double-diffusive convection induced by a discrete heat source

Various engineering systems, such as those associated with crystal growth techniques or solar ponds, may be characterized by double-diffusive behavior induced by discrete heat sources. Due to the relevance of such systems, the objective of this study is to investigate double-diffusive convection induced by bottom heating with a finite, heated strip placed beneath a salt-stratified layer. Attention is focused on the formation and growth of converting regions in the salt-stratified fluid. Experimental and numerical results reveal that development of convective conditions is characterized by an interaction between Rayleigh-Bénard-type convection and longitudinal convective rolls formed by horizontal temperature gradients. Secondary flow is visualized and predicted to occur above the bottom convection cell. For relatively unstable combinations of the salt stratification and applied heat flux, a complicated interaction between chaotic, double-diffusive convection and a three-dimensional, gravity wave distribution are observed.

Velocity measurements in the field of an internal gravity wave by means of speckle photography

Speckle velocimetry with forward scattering has been applied to measure and visualize the two-dimensional velocity field in an internal gravity wave. The wave was produced by towing a cylinder in vertical direction, normal to its axis, through stratified salt water. Neutrally buoyant tracer particles whose density was matched with the density distribution of the stratification were uniformly distributed in the test fluid. The experimental results verify the results of a linear theory in the far field of the wave.

Visualization of particle displacement and flow in stratified salt water

Visualization of particle displacement and flow in stratified salt water