Correlation of Mixed Layer Growth in a Double-Diffusive, Salt-Stratified System Heated From Below

1986 ◽  
Vol 108 (1) ◽  
pp. 206-211 ◽  
Author(s):  
T. L. Bergman ◽  
F. P. Incropera ◽  
R. Viskanta
Keyword(s):  
Mathematical Model ◽  
Mixed Layer ◽  
Layer Growth ◽  
Published Data ◽  
Convective Velocity ◽  
Thermally Driven ◽  
Mixed Layers ◽  
Layer Development ◽  
Growth Correlations ◽  
Double Diffusive

Although many mixed layer growth correlations have been developed for stratified solutions which are eroded by mechanically driven mixed layers, little has been done to determine their applicability to solutions for which erosion is thermally driven. In this study entrainment rates have been determined from measurements of mixed layer growth in salt-stratified solutions heated from below. Entrainment data have been obtained for Richardson numbers in the range 80 < Ri < 1000, and when normalized with respect to the mixed layer convective velocity, the data are well correlated in terms of Ri−1. The correlation also agrees with published data obtained at larger and smaller Richardson numbers for both thermally and salt-stratified solutions heated from below. Predictions based on use of the correlation in a mathematical model of mixed layer development are in excellent agreement with measured mixed layer heights and temperatures.

Interferometric study of stable salinity gradients heated from below or cooled from above

1982 ◽  
Vol 116 ◽  
pp. 411-430 ◽  
Author(s):  
W. T. Lewis ◽  
F. P. Incropera ◽  
R. Viskanta
Keyword(s):  
Mixed Layer ◽  
Mixing Layer ◽  
Density Distributions ◽  
Salinity Gradients ◽  
Isothermal Boundary ◽  
Secondary Layer ◽  
Constant Heating ◽  
Mixed Layers ◽  
Layer Development ◽  
Heating From Below

Mixing-layer development is investigated in laboratory experiments of salt-stratified solutions which are cooled from above or heated from below through the imposition of isothermal boundaries. A Mach-Zehnder interferometer is used to infer salt and density distributions within stable regions of the solution and to determine the extent of mixing-layer development. In both heating from below and cooling from above, this development differs significantly from that which has been observed for constant heating from below. Although the formation of a secondary mixed layer is observed, it does not lead to the development of additional mixed layers. Instead, the secondary layer eventually recedes, and the existence of a single mixed layer is restored. This behaviour is due to the isothermal boundary and the effect which it has no decreasing the heat transfer to or from the solution with increasing time. Once the condition of a single mixed layer is restored, extremely large (stable) density gradients develop in the boundary layer separating the mixed and stable regions, and subsequent growth of the mixed layer is slow. In cooling from above, mixing-layer development depends strongly on whether the isothermal boundary is in direct contact with the solution or separated by an air space.

Variations in mixed-layer illite/smectite diagenesis in the rift and post-rift sediments of the Jeanne d'Arc Basin, Grand Banks offshore Newfoundland, Canada

2004 ◽  
Vol 41 (4) ◽  
pp. 401-429 ◽  
Author(s):  
Iftikhar A Abid ◽  
Reinhard Hesse ◽  
John D Harper
Keyword(s):  
Mixed Layer ◽  
Fine Fraction ◽  
Upper Jurassic ◽  
Grand Banks ◽  
Depth Profiles ◽  
Jeanne D'arc Basin ◽  
Central Ridge ◽  
Jeanne D'arc ◽  
Layer I ◽  
Mixed Layers

Mixed-layer illite/smectite (I/S) clays were analyzed from 22 deep exploration wells from the Jeanne d'Arc Basin on the Grand Banks offshore Newfoundland, the host of large commercial hydrocarbon accumulations discovered in the last two and a half decades. The fine fraction of the clays (<0.1 µm) consists mainly of mixed-layer I/S with minor amounts of kaolinite, illite, and chlorite. Smectite and (or) smectite-rich I/S clays were supplied to the Jeanne d'Arc Basin from Upper Jurassic to Tertiary times. Smectite-rich I/S clays occur only in shallow samples irrespective of geologic age. The proportion of illite in I/S mixed-layers, as well as the degree of ordering, increase with depth and temperature indicating that smectite-rich I/S clays have been progressively illitized in both rift and post-rift sediments of the Jeanne d'Arc Basin during burial. The transition from random to R1-ordered I/S occurs between subsurface depths of 1940 and 3720 m and crosses major stratigraphic boundaries. The transition from R1- to R3-ordered I/S generally occurs below 4000 m depth. Variable shapes of I/S depth profiles reflect the influence of temperature, fluid migration, subsidence history, basin structure, lithology, and salt diapirism on I/S diagenesis. Based on these variations, the basin can be subdivided into 4 regions with different illitization gradients. In the Southern Jeanne d'Ac Basin, advanced I/S diagenesis probably reflects uplift and denudation and (or) higher paleogeothermal gradients. Rapid increase of percent illite in I/S with depth in the Trans-Basinal Fault area is most likely controlled by upward flow of hot, K+-bearing fluids along faults. The migration of hydrocarbons probably followed the same pathways as the illitizing fluids. Delayed illitization in the Northern Jeanne d'Arc Basin and Central Ridge area reflects insufficient K+ supply because of a lack of detrital K-feldspar in the host sediment, the absence of faulting, and the presence of thick shale intervals. These findings show that I/S depth profiles may vary within the same sedimentary basin due to a variety of geological factors. Single wells generally cannot be considered representative for the basin as a whole.

Parameterization of Mixed Layer Eddies. Part I: Theory and Diagnosis

2008 ◽  
Vol 38 (6) ◽  
pp. 1145-1165 ◽  
Author(s):  
Baylor Fox-Kemper ◽  
Raffaele Ferrari ◽  
Robert Hallberg
Keyword(s):  
Mixed Layer ◽  
Mixed Layer Depth ◽  
Baroclinic Instability ◽  
Finite Amplitude ◽  
Climate Impacts ◽  
Surface Mixed Layer ◽  
Rotation Rates ◽  
Wide Range ◽  
Horizontal Density Gradient ◽  
Mixed Layers

Abstract Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.

scholarly journals Ultramicrosensors based on transition metal hexacyanoferrates for scanning electrochemical microscopy

2013 ◽  
Vol 4 ◽  
pp. 649-654 ◽  
Author(s):  
Maria A Komkova ◽  
Angelika Holzinger ◽  
Andreas Hartmann ◽  
Alexei R Khokhlov ◽  
Christine Kranz ◽  
...  
Keyword(s):  
Hydrogen Peroxide ◽  
Detection Limit ◽  
Transition Metal ◽  
Prussian Blue ◽  
Electrochemical Deposition ◽  
Mixed Layer ◽  
Scanning Electrochemical Microscopy ◽  
The Stability ◽  
Mixed Layers ◽  
Electrochemical Microscopy

We report here a way for improving the stability of ultramicroelectrodes (UME) based on hexacyanoferrate-modified metals for the detection of hydrogen peroxide. The most stable sensors were obtained by electrochemical deposition of six layers of hexacyanoferrates (HCF), more specifically, an alternating pattern of three layers of Prussian Blue and three layers of Ni–HCF. The microelectrodes modified with mixed layers were continuously monitored in 1 mM hydrogen peroxide and proved to be stable for more than 5 h under these conditions. The mixed layer microelectrodes exhibited a stability which is five times as high as the stability of conventional Prussian Blue-modified UMEs. The sensitivity of the mixed layer sensor was 0.32 A·M−1·cm−2, and the detection limit was 10 µM. The mixed layer-based UMEs were used as sensors in scanning electrochemical microscopy (SECM) experiments for imaging of hydrogen peroxide evolution.

Oceanic wave-balanced surface fronts and filaments

2013 ◽  
Vol 730 ◽  
pp. 464-490 ◽  
Author(s):  
James C. McWilliams ◽  
Baylor Fox-Kemper
Keyword(s):  
Mixed Layer ◽  
Stokes Drift ◽  
Surface Gravity Wave ◽  
Initial Flow ◽  
Coriolis Forces ◽  
Flow Perturbation ◽  
Front Shape ◽  
Oceanic Wave ◽  
Mixed Layers ◽  
Layer Deformation

AbstractA geostrophic, hydrostatic, frontal or filamentary flow adjusts conservatively to accommodate a surface gravity wave field with wave-averaged, Stokes-drift vortex and Coriolis forces in an altered balanced state. In this altered state, the wave-balanced perturbations have an opposite cross-front symmetry to the original geostrophic state; e.g. the along-front flow perturbation is odd-symmetric about the frontal centre while the geostrophic flow is even-symmetric. The adjustment tends to make the flow scale closer to the deformation radius, and it induces a cross-front shape displacement in the opposite direction to the overturning effects of wave-aligned down-front and up-front winds. The ageostrophic, non-hydrostatic, adjusted flow may differ from the initial flow substantially, with velocity and buoyancy perturbations that extend over a larger and deeper region than the initial front and Stokes drift. The largest effect occurs for fronts that are wider than the mixed layer deformation radius and that fill about two-thirds of a well-mixed surface layer, with the Stokes drift spanning only the shallowest part of the mixed layer. For even deeper mixed layers, and especially for thinner or absent mixed layers, the wave-balanced adjustments are not as large.

scholarly journals Influence of Nano-Fluid Lubrication On Single Porous-Layered Journal Bearing: A Hypothetical Approach

2021 ◽  
Author(s):  
BIPLAB BHATTACHARJEE ◽  
PRASUN CHAKRABORTI ◽  
KISHAN CHOUDHURY
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Micropolar Fluid ◽  
Journal Bearing ◽  
Performance Characteristics ◽  
Published Data ◽  
Nano Fluid ◽  
Nano Lubricant ◽  
Output Characteristics ◽  
Modified Darcy’S Law

Abstract In this article a mathematical model of single layered nano-fluid lubricated PJB (porous journal bearing) has been formulated. The nano-lubricant's impact on the efficiency of said journal bearing has been studied using modified Darcy's law and boundary conditions. The different nanoparticles often used as an additive in industrial lubricating oils improve their viscosity significantly. The brief description of dimensionless performance characteristics of the investigated bearing was obtained by the use of the nano-lubricant's modified Krieger-Dougherty viscosity model. The observations revealed that the output characteristics are substantially improved by using nano-lubricant. The present study was validated by comparing the findings of recently published data with micropolar fluid and was found to be completely compatible since data with nano-lubricant are still unavailable.

Double-Diffusive Fluxes in a Salt Gradient Solar Pond

1988 ◽  
Vol 110 (1) ◽  
pp. 17-22 ◽  
Author(s):  
J. F. Atkinson ◽  
E. Eric Adams ◽  
D. R. F. Harleman
Keyword(s):  
Mixed Layer ◽  
Molecular Diffusion ◽  
Numerical Models ◽  
Mechanical Stirring ◽  
Solar Pond ◽  
Salt Gradient ◽  
Layer Region ◽  
Diffusive Fluxes ◽  
Effective Diffusivities ◽  
Double Diffusive

The possible influence of double-diffusive stratification on the vertical transport of salt and heat in a mixed-layer simulation model for a salt gradient solar pond is examined. The study is concerned primarily with the interfacial fluxes across the boundary between the gradient zone and upper convecting zone of solar ponds, though the arguments presented should be applicable to other “diffusive” interfaces as well. In the absence of mechanical stirring in the upper convecting zone (e.g., by wind), double diffusive instabilities could govern the vertical flux of heat and salt by adjusting interfacial gradients of temperature and salinity which control transport by molecular diffusion. Because these gradients are generally too sharp to be resolved by numerical models, the fluxes can either be modeled directly or be parameterized by grid-dependent “effective diffusivities.” It is shown that when mechanical stirring is present in the mixed layer, double-diffusive instabilities will not be allowed to grow in the interfacial boundary layer region. Thus, double-diffusive fluxes become important only in the absence of stirring and, in effect, provide a lower bound to the fluxes that would be expected across the interface.

Calculation of 6-Hour Dip Creatinine Ratio from the 4-Hour Peritoneal Equilibration Test. The Effect of Dwell Duration on the Results

1997 ◽  
Vol 17 (3) ◽  
pp. 273-278 ◽  
Author(s):  
Rajnish Mehrotra ◽  
Ramesh Khanna ◽  
Thomas C.K. Yang ◽  
Pranay Kathuria ◽  
Harold L. Moore ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Peritoneal Dialysis ◽  
University Hospital ◽  
Published Data ◽  
Peritoneal Equilibration Test ◽  
Cardiovascular Research ◽  
Proposed Model ◽  
Margin Of Error ◽  
The University ◽  
Exponential Relation

Objectives Since the introduction of the peritoneal equilibration test (PET), the 4-hour dialysatelplasma creatinine (DIP Cr) has been used by several authors for determining continuous ambulatory peritoneal dialysis (CAPD) prescriptions. However, the results have been unsatisfactory because the 4-hr DIP Cr does not accurately reflect the DIP Cr in 24-hr collections. The PET and the 24-hr dialysate collections differ in the duration of dwell and the tonicity and volume of dialysate, all of which influence the equilibrated DIP Cr. It can be assumed that the DIP Cr in 24-hr collections in these patients is closer to a 6-hr DIP Cr. Because a 6hr PET is inconvenient, we developed a mathematical model to calculate the 5 and 6-hr DIP using the results of a standard PET. Design In a retrospective analysis, DIP Cr ratios in 24-hr collections and DIP Cr ratios calculated from a mathematical formula were correlated. Using a mathematical model, the data collected fit an exponential relation of the type DIP = a(1 -e-t/τ). The values of a and τ are unique for a given patient and were determined using a nonlinear regression technique. The formula performed well on our published data -the true and predicted 6-hr DIP Cr being 0.696 and 0.71, respectively. Setting The University Hospital and Clinics, Dalton Cardiovascular Research Center and Dialysis Clinic, Inc., Columbia, Missouri. Patients All CAPD patients on four 2-L exchangeslday at the time of the 24-hr collections were included. Interventions None. Main Outcome Measures Closeness of 4-hr and 6-hr DIP Cr values to those of 24-hr ratios. Results The study group comprised 74 patients (age, mean ± SEM: 56.4 ± 1.8 yr) with 80 PETs and 145 (24-hr) collections. The interval between the two tests was 8. 3 ± 0.9 months (0 48.7 months). The median 24-hr DIP Cr of 0.760 did not differ significantly from the predicted median 6-hr DIP Cr of 0.755. A subgroup analysis, based on transport type, showed that this relationship was most precise in the high-average transporters. The predicted 6hr DIP Cr was within 100;0 of the 24-hr DIP Cr in 48% of patients and within 20% in 77% of patients. The margin of error was greatest in the low transporters. Conclusions To conclude, the 4-hr DIP Cr from a PET cannot be used interchangeably with the DIP Cr in the 24-hr dialysate collections, hence, the clearances calculated thereof will be inaccurate. Using the proposed model, it is feasible to use the 4 -hr PET results to obtain 5 and 6 -hr DIP Cr values. In our study, using this model, the extrapolated 6-hr DIP Cr is similar to the DIP Cr in 24-hr dialysate collections only in the high-average transporters. Hence, the best way to determine clearances in peritoneal dialysis patients is still by collecting 24-hr dialysates.

A Survey of Stall Propagation—Experiment and Theory

1959 ◽  
Vol 81 (3) ◽  
pp. 409-416 ◽  
Author(s):  
H. W. Emmons ◽  
R. E. Kronauer ◽  
J. A. Rockett
Keyword(s):  
Mathematical Model ◽  
Published Data ◽  
Experimental Literature ◽  
Simple Mathematical Model ◽  
Stall Cells ◽  
Propagation Experiment

The experimental literature on stall propagation is summarized in terms of an idealized compressor which possesses properties typical of the bulk of published data. The published analyses are examined and all are shown to have one fundamental restriction or another which makes them unable to predict all of the relevant features of stall propagation—most notably the number of stall cells. A relatively simple mathematical model is constructed which offers the possibility of a complete prediction.

Sign in / Sign up

Export Citation Format

Share Document