scholarly journals ALGORITHM FOR VERTICAL DIFFUSION

1976 ◽  
Vol 1 (15) ◽  
pp. 190
Author(s):  
Soren Peter Kjeldsen
Keyword(s):  
Diffusion Coefficients ◽  
Vertical Mixing ◽  
Computing Methods ◽  
Vertical Diffusion ◽  
Governing Parameter ◽  
High Frequencies ◽  
One Dimensional ◽  
Two Fluids ◽  
Cyclic Frequency ◽  
Constant Coefficients

A mathematical method and a computer algorithm is developed for the case of one-dimensional vertical mixing for an estuary with rather small advection. In the case under consideration varies the diffusion coefficients both with time and depth, and the case is therefore closer to actual estuaries than earlier computing methods that applies constant coefficients. Model experiments with a small grid oscilliating with high frequencies in two fluids with different densities were performed to test the algorithm. Reynolds number for turbulence was near 1.6-101'. The results showed that the ratio between the stabilizing Brunt-Vaisala frequency and the agitating cyclic frequency was a governing parameter for the system, and dimensionless. diffusion coefficients could be expressed as a function of this parameter.

Ad- and Desorption of Oxygen at Metal-Oxide Interfaces: Numerical Approach for Concentration-Dependent Diffusion Coefficient

2006 ◽  
Vol 258-260 ◽  
pp. 360-365
Author(s):  
M. Stasiek ◽  
Andreas Öchsner
Keyword(s):  
Diffusion Coefficients ◽  
Atomic Oxygen ◽  
Coupled System ◽  
Numerical Approach ◽  
Time Dependent ◽  
General Boundary Conditions ◽  
Oxide Interfaces ◽  
One Dimensional ◽  
Concentration Dependency ◽  
Constant Coefficients

A numerical approach for the segregation of atomic oxygen at Ag/MgO interfaces is presented. A general segregation kinetics is considered and the coupled system of differ- ential equations is solved due to a one-dimensional finite difference scheme which accounts for concentration-dependent diffusion coefficients. Based on a model oxide distribution, the influence of the concentration-dependency is numerically investigated and compared with the solution for constant coefficients. In addition, the numerical approach allows for the consider- ation of general boundary conditions, specimen sizes and time-dependent material and process parameters.

scholarly journals Red Cell Membrane Permeability Deduced from Bulk Diffusion Coefficients

1974 ◽  
Vol 64 (6) ◽  
pp. 706-729 ◽  
Author(s):  
W. R. Redwood ◽  
E. Rall ◽  
W. Perl
Keyword(s):  
Cell Membrane ◽  
Membrane Permeability ◽  
Diffusion Coefficients ◽  
Bulk Diffusion ◽  
Red Cells ◽  
Cell Membrane Permeability ◽  
Red Cell ◽  
Cell Column ◽  
Red Cell Membrane ◽  
One Dimensional

The permeability coefficients of dog red cell membrane to tritiated water and to a series of[14C]amides have been deduced from bulk diffusion measurements through a "tissue" composed of packed red cells. Red cells were packed by centrifugation inside polyethylene tubing. The red cell column was pulsed at one end with radiolabeled solute and diffusion was allowed to proceed for several hours. The distribution of radioactivity along the red cell column was measured by sequential slicing and counting, and the diffusion coefficient was determined by a simple plotting technique, assuming a one-dimensional diffusional model. In order to derive the red cell membrane permeability coefficient from the bulk diffusion coefficient, the red cells were assumed to be packed in a regular manner approximating closely spaced parallelopipeds. The local steady-state diffusional flux was idealized as a one-dimensional intracellular pathway in parallel with a one-dimensional extracellular pathway with solute exchange occurring within the series pathway and between the pathways. The diffusion coefficients in the intracellular and extracellular pathways were estimated from bulk diffusion measurements through concentrated hemoglobin solutions and plasma, respectively; while the volume of the extracellular pathway was determined using radiolabeled sucrose. The membrane permeability coefficients were in satisfactory agreement with the data of Sha'afi, R. I., C. M. Gary-Bobo, and A. K. Solomon (1971. J. Gen. Physiol. 58:238) obtained by a rapid-reaction technique. The method is simple and particularly well suited for rapidly permeating solutes.

scholarly journals Explicit Numerical Solution of High - Dimensional Advection - Diffusion

2013 ◽  
Vol 2 (3) ◽  
pp. 17-22
Author(s):  
Elham Bayatmanesh
Keyword(s):  
High Dimensional ◽  
Numerical Techniques ◽  
Science And Engineering ◽  
Numerical Examples ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Constant Coefficients ◽  
The Subject ◽  
The One

The Several numerical techniques have been developed and compared for solving the one-dimensional and three-dimentional advection-diffusion equation with constant coefficients. the subject has played very important roles to fluid dynamics as well as many other field of science and engineering. In this article, we will be presenting the of n-dimentional and we neglect the numerical examples.

scholarly journals Comparison of ocean vertical mixing schemes in the Max Plank Institute Earth System Model (MPI-ESM1.2)

2020 ◽  
Author(s):  
Oliver Gutjahr ◽  
Nils Brüggemann ◽  
Helmuth Haak ◽  
Johann H. Jungclaus ◽  
Dian A. Putrasahan ◽  
...  
Keyword(s):  
Vertical Mixing ◽  
Global Scale ◽  
Earth System Model ◽  
System Model ◽  
The Arctic ◽  
Earth System ◽  
Max Planck ◽  
Vertical Diffusion ◽  
Mixing Schemes ◽  
Mean State

Abstract. We compare the effects of four different ocean vertical mixing schemes on the ocean mean state simulated by the Max Planck Institute Earth System Model (MPI-ESM1.2) in the framework of the Community Vertical Mixing (CVMix) library. Besides the PP and KPP scheme, we implemented the TKE scheme and a recently developed prognostic scheme for internal wave energy and its dissipation (IDEMIX) to replace the often assumed constant background diffusivity in the ocean interior. We analyse in particular the effects of IDEMIX on the ocean mean state, when combined with TKE (TKE+IDEMIX). In general, we find little sensitivity of the ocean surface, but considerable effects for the interior ocean. Overall, we cannot classify any scheme as superior, because they modify biases that vary by region or variable, but produce a similar pattern on the global scale. However, using a more realistic and energetically consistent scheme (TKE+IDEMIX) produces a more heterogeneous pattern of vertical diffusion, with lower diffusivity in deep and flat-bottom basins and elevated turbulence over rough topography. In addition, TKE+IDEMIX improves the circulation in the Nordic Seas and Fram Strait, thus reducing the warm bias of the Atlantic water (AW) layer in the Arctic Ocean to a similar extent as has been demonstrated with eddy-resolving ocean models. We conclude that although shortcomings due to model resolution determine the global-scale bias pattern, the choice of the vertical mixing scheme may play an important role for regional biases.

scholarly journals Measurements of Enhanced Turbulent Mixing near Highways

2012 ◽  
Vol 51 (9) ◽  
pp. 1618-1632 ◽  
Author(s):  
Mark Gordon ◽  
Ralf M. Staebler ◽  
John Liggio ◽  
Paul Makar ◽  
Shao-Meng Li ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Traffic Flow ◽  
Power Law ◽  
Vertical Mixing ◽  
Weather Forecast ◽  
Early Morning ◽  
Highway Traffic ◽  
Vertical Diffusion ◽  
Global Environmental

AbstractIn August and September of 2010, measurements of turbulent fluxes and turbulent kinetic energy were made on highways in the Toronto area (Ontario, Canada). In situ turbulence measurements were made with a mobile laboratory while driving on the highway with traffic. Results demonstrate that the turbulent kinetic energy (TKE) spectrum is significantly enhanced on and near the highway by traffic for frequencies above 0.015 Hz. The decay of TKE with distance behind vehicles is well approximated by power-law curves. The strongest increase in TKE is seen while following heavy-duty trucks, primarily for frequencies above 0.7 Hz. From these results, a parameterization of on-road TKE enhancement is developed that is based on vehicle type and traffic-flow rate. TKE with distance downwind of the highway also decays following a power law. The enhancement of roadside TKE is shown to be strongly dependent on traffic flow. The effect of vehicle-induced turbulence on vertical mixing was studied by comparing parameterized TKE enhancement with the typical TKE predictions from the Global Environmental Multiscale weather forecast to predict the potential increase in vertical diffusion that results from highway traffic. It is demonstrated that this increase in TKE by traffic may be locally significant, especially in the early morning.

Numerical Experiments Analysis of Wave-Induced Vertical Mixing’s Effects on Sea Surface Wind-Induced Momentum Transfer

2010 ◽  
Author(s):  
Bingchen Liang ◽  
Ying Liu ◽  
Lili Yang
Keyword(s):  
Fresh Water ◽  
Yellow River ◽  
Vertical Section ◽  
Vertical Mixing ◽  
Three Dimensional ◽  
Velocity Profiles ◽  
Dimensional Model ◽  
One Dimensional ◽  
Wave Induced ◽  
Sediment Model

A hydrodynamic sediment coupled model COHERENS-SED, which has been developed by the present authors through introducing wave-enhanced bottom stress, wave dependent surface drag coefficient, wave-induced surface mixing, SWAN, damping function of sediment on turbulence and sediment model to COHERENS, is modified to account for wave-induced vertical mixing. One equation k–ε turbulence model is taken into account in calculating vertical viscosity coefficient. COHERENS-SED consists of sediment model SED, current model COHERENS and wave generation model SWAN. The model can also calculate one-dimensional, two-dimensional and three-dimensional current separately. One-dimensional model and three-dimensional model are adoptted to study the wave-induced vertical mixing’s effects. The horizontal current velocity profiles given by the model, with same input conditions as what to get analytical results, are in nice agreement with analytical velocity profiles. Therefore the model can be reliable to identify wave-induced vertical mixing’s effects on horizontal velocity profiles and momentum transferring. Two group numerical experiments are built based on 130m water depth and 20m water depth for the one-dimensional model. Results show that higher wave height can generate larger vertical eddy viscosity and lower horizontal velocity generally. In order to find out such effects on fresh water flume momentum transfer towards down in vertical section of estuary, Yellow River delta is chosen to study the effects of wave-induced vertical diffusion on sediment vertical mixing and the Yellow River estuary vertical cross-section is chosen to study fresh water disperse range in vertical section. The results of fresh water shows that wave-induced vertical mixing increases the momentum of fresh water transferring ability towards down to seabed. So fresh water flume length is compressed obviously.

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