On the spreading of a turbulent spot in the absence of a pressure gradient

1982 ◽  
Vol 123 ◽  
pp. 69-90 ◽  
Author(s):  
I. Wygnanski ◽  
M. Zilberman ◽  
Joseph H. Haritonidis
Keyword(s):  
Scalar Field ◽  
Effective Diffusion ◽  
Effective Diffusivity ◽  
Passive Scalar ◽  
Turbulent Spot ◽  
Path Integral Representation ◽  
Long Time ◽  
Negative Effect ◽  
Diffusion Function ◽  
Markovian Limit

We derive a path-integral representation for the effective diffusion function of a passive scalar field. We use it to calculate the long-time effective diffusivity in Gaussian turbulence in the near-Markovian limit. Our results confirm the negative effect of vorticity predicted by previous discussions. They also demonstrate that the helicity of the turbulence when present may be as important an influence as the vorticity.

Path-integral methods for turbulent diffusion

1982 ◽  
Vol 123 ◽  
pp. 59-68 ◽  
Author(s):  
I. T. Drummond
Keyword(s):  
Path Integral ◽  
Effective Diffusion ◽  
Effective Diffusivity ◽  
Passive Scalar ◽  
Path Integral Representation ◽  
Integral Methods ◽  
Long Time ◽  
Negative Effect ◽  
Diffusion Function ◽  
Markovian Limit

We derive a path-integral representation for the effective diffusion function of a passive scalar field. We use it to calculate the long-time effective diffusivity in Gaussian turbulence in the near-Markovian limit. Our results confirm the negative effect of vorticity predicted by previous discussions. They also demonstrate that the helicity of the turbulence when present may be as important an influence as the vorticity.

The effective long-time diffusivity for a passive scalar in a Gaussian model fluid flow

1978 ◽  
Vol 89 (2) ◽  
pp. 241-250 ◽  
Author(s):  
R. Phythian ◽  
W. D. Curtis
Keyword(s):  
Diffusion Processes ◽  
Fluid Velocity ◽  
Gaussian Model ◽  
Effective Diffusivity ◽  
Passive Scalar ◽  
Random Motion ◽  
Velocity Correlation ◽  
Molecular Diffusivity ◽  
Velocity Correlation Function ◽  
Long Time

The problem considered is the diffusion of a passive scalar in a ‘fluid’ in random motion when the fluid velocity field is Gaussian and statistically homogeneous, isotropic and stationary. A self-consistent expansion for the effective long-time diffusivity is obtained and the approximations derived from this series by retaining up to three terms are explicitly calculated for simple idealized forms of the velocity correlation function for which numerical simulations are available for comparison for zero molecular diffusivity. The dependence of the effective diffusivity on the molecular diffusivity is determined within this idealization. The results support Saffman's contention that the molecular and turbulent diffusion processes interfere destructively, in the sense that the total effective diffusivity about a fixed point is less than that which would be obtained if the two diffusion processes acted independently.

scholarly journals Diffusion and the formation of vorticity staircases in randomly strained two-dimensional vortices

2009 ◽  
Vol 638 ◽  
pp. 49-72 ◽  
Author(s):  
MATTHEW R. TURNER ◽  
ANDREW P. BASSOM ◽  
ANDREW D. GILBERT
Keyword(s):  
Diffusion Equation ◽  
Surf Zone ◽  
Spatial Scales ◽  
Effective Diffusion ◽  
Effective Diffusivity ◽  
Angular Frequency ◽  
Asymptotic Model ◽  
Two Dimensional ◽  
Fine Scale ◽  
Long Time

The spreading and diffusion of two-dimensional vortices subject to weak external random strain fields is examined. The response to such a field of given angular frequency depends on the profile of the vortex and can be calculated numerically. An effective diffusivity can be determined as a function of radius and may be used to evolve the profile over a long time scale, using a diffusion equation that is both nonlinear and non-local. This equation, containing an additional smoothing parameter, is simulated starting with a Gaussian vortex. Fine scale steps in the vorticity profile develop at the periphery of the vortex and these form a vorticity staircase. The effective diffusivity is high in the steps where the vorticity gradient is low: between the steps are barriers characterized by low effective diffusivity and high vorticity gradient. The steps then merge before the vorticity is finally swept out and this leaves a vortex with a compact core and a sharp edge. There is also an increase in the effective diffusion within an encircling surf zone.In order to understand the properties of the evolution of the Gaussian vortex, an asymptotic model first proposed by Balmforth, Llewellyn Smith & Young (J. Fluid Mech., vol. 426, 2001, p. 95) is employed. The model is based on a vorticity distribution that consists of a compact vortex core surrounded by a skirt of relatively weak vorticity. Again simulations show the formation of fine scale vorticity steps within the skirt, followed by merger. The diffusion equation we develop has a tendency to generate vorticity steps on arbitrarily fine scales; these are limited in our numerical simulations by smoothing the effective diffusivity over small spatial scales.

Use of immunocorrectors in patients with chronic lymph leukemia

1986 ◽  
Vol 67 (2) ◽  
pp. 99-101
Author(s):  
V. Ya. Shustov ◽  
N. A. Afanasyeva ◽  
P. P. Kuznetsov ◽  
A. K. Myshkina
Keyword(s):  
Immune System ◽  
Outpatient Treatment ◽  
Infectious Complications ◽  
Chronic Lymphatic Leukemia ◽  
Cytostatic Drugs ◽  
Ability To Work ◽  
Lymphatic Leukemia ◽  
Long Time ◽  
Negative Effect

Chronic lymphatic leukemia is second only to acute leukemia in the frequency of infectious complications. In most cases, severe infectious complications are the cause of death in these patients. Modern chemotherapy makes it possible to preserve the ability to work and the life expectancy of patients for a long time. However, the negative effect of cytostatic drugs on the already altered immune system leads to an even greater suppression of immunity and an increase in the number of infectious complications. The search for new ways to combat infections has shown the advisability of long-term outpatient treatment with antibacterial drugs.

Expressions for the effective diffusivity in materials with interphase boundaries

2004 ◽  
Vol 819 ◽  
Author(s):  
Irina V. Belova ◽  
Graeme E. Murch
Keyword(s):  
Polycrystalline Material ◽  
Effective Diffusivity ◽  
Poor Agreement ◽  
Two Phase ◽  
Interphase Boundaries ◽  
Long Time ◽  
Simulation Results ◽  
The Individual ◽  
Individual Grains ◽  
Good Agreement

AbstractWe address the problem of calculating the long-time-limit effective diffusivity in stable two- phase polycrystalline material. A phenomenological model is used where the high diffusivity interphase boundaries are treated as connected “coatings” of the individual grains. Derivation of expressions for the effective diffusivity with segregation is made along Maxwell lines. Monte Carlo simulation using lattice-based random walks is used to test the validity of the expressions. It is shown that for the case analysed the derived expressions for the effective diffusivity are in very good agreement with simulation results. The equivalent of the Hart equation is also derived. It is shown to be in poor agreement with simulation results.

scholarly journals Long-term investigation of phosphorus removal by iron electrocoagulation in small-scale wastewater treatment plants

2018 ◽  
Vol 78 (6) ◽  
pp. 1304-1311 ◽  
Author(s):  
I. Mishima ◽  
M. Hama ◽  
Y. Tabata ◽  
J. Nakajima
Keyword(s):  
Wastewater Treatment ◽  
Phosphorus Removal ◽  
Wastewater Treatment Plants ◽  
Phosphorus Release ◽  
Small Scale ◽  
Operational Conditions ◽  
Long Time ◽  
Negative Effect ◽  
Iron Electrolysis

Abstract Small-scale wastewater treatment plants (SWTPs), called Johkasou, are widely used as decentralized and individual wastewater treatment systems in sparsely populated areas in Japan. Even in SWTPs, nutrients should be removed to control eutrophication. An iron electrolysis method is effective to remove phosphorus chemically in SWTPs. However, it is necessary to determine the precise conditions under which phosphorus can be effectively and stably removed in full scale SWTPs for a long period. Therefore, long-term phosphorus removal from SWTPs was investigated and optimum operational conditions for phosphorus removal by iron electrolysis were analyzed in this study. Efficient phosphorus removal can be achieved for a long time by adjusting the amount of iron against the actual population equivalent. The change of the recirculation ratio had no negative effect on overall phosphorus removal. Phosphorus release to the bulk phase was prevented by the accumulated iron, which was supplied by iron electrolysis, resulting in stable phosphorus removal. The effect of environmental load reduction due to phosphorus removal by iron electrolysis was greater than the cost of power consumption for iron electrolysis.

scholarly journals INTEGRATED SYNOPTICAL METHOD FOR CALCULATING ASSIMILATION CAPACITY OF SEA WATERS

2017 ◽  
pp. 115-120
Author(s):  
Hikmat Hamid oglu Asadov ◽  
Sima Ajdar gizi Askerova
Keyword(s):  
Sea Water ◽  
Water Masses ◽  
Optimum Regime ◽  
Optimization Task ◽  
Maximum Value ◽  
Long Time ◽  
Negative Effect ◽  
Optimum Order ◽  
Assimilation Capacity ◽  
The Given

Pollution of sea waters is one of major attributes of coastal industrial centers and the norming of such emissions is one of major countermeasures. The assimilation capacity of sea waters is a major factor relevant at norming and planning of outflows into sea waters. At present time the synoptical method has been developed, which doesn’t require carrying out long time and repeated observing of the level of pollution of sea waters. This method has formed the basis for developing the integrated synoptical method for calculating sea water assimilation capacity. The suggested method provides for division of the sea waters into separated homogenous water masses. The aim of the study is to develop an inverse integrated synoptical method allowing synthesizing of such an optimum order for loading separate water masses with pollutants upon, at which the calculated total value of assimilation capacity would reach its maximum. The article shows the possibility of utilization of known synoptical method for determining assimilation capacity of sea waters in the inverse order, i.e. for calculating the maximum value of pollutant put into the fixed zone of sea waters, upon a condition of reaching the given amount of assimilation capacity and absence of essential negative effect on ecosystem. The task of calculating an optimum regime function of discrete type, upon which the integrated value of assimilation capacity would reach the maximum value, has been formulated. The solution of analogue equivalent of the formed optimization task is carried out using the Euler equation for a non-conditional variation optimization task, taking into account the accepted limitation condition. The recommendations on optimum loading of different sea water zones with determined type of pollutant have been given.

scholarly journals Drying kinetics of crushed mass of ‘jambu’: Effective diffusivity and activation energy

2018 ◽  
Vol 22 (7) ◽  
pp. 499-505 ◽  
Author(s):  
Francileni P. Gomes ◽  
Resende Osvaldo ◽  
Elisabete P. Sousa ◽  
Daneil E. C. de Oliveira ◽  
Francisco R. de Araújo Neto
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Agricultural Research ◽  
Effective Diffusion ◽  
Effective Diffusivity ◽  
Information Criterion ◽  
Drying Kinetics ◽  
Coefficient Of Determination ◽  
Chi Square ◽  
Chi Square Test

ABSTRACT The aim of this paper was to analyze the drying kinetics, test the Akaike information criterion (AIC) and Schwarz’s Bayesian information criterion (BIC) in the selection of models, determine the effective diffusivity and activation energy of the crushed mass of ‘jambu’ leaves for different conditions of temperature and layer thicknesses. The experiment was carried out at the Food Laboratory of the Brazilian Agricultural Research Corporation (Embrapa) in Macapá-AP. Drying was carried out in air circulation oven with speed of 1.0 m s-1 at various temperatures (60, 70 and 80 ºC) and layer thicknesses (0.005 and 0.010 m). The experimental data were fitted to 11 mathematical models. Coefficient of determination (R2), mean relative error (P), mean estimated error (SE), Chi-square test (χ2), AIC and BIC were the selection criteria for the models. For the effective diffusivity, the Fick’s diffusion model was used considering the flat plate geometry. It was found that Midilli and Logarithmic models showed the best fit to the experimental data of drying kinetics. Effective diffusion coefficient increases with increment in the thickness of the material and with the temperature elevation. Activation energy of the material was of 16.61 kJ mol-1 for the thickness of 0.005 m, and 16.97 kJ mol-1 for the thickness of 0.010 m. AIC and BIC can be additionally included to select models of drying.

Homogenization theory for a replenishing passive scalar field

2009 ◽  
Vol 30 (5) ◽  
pp. 631-644 ◽  
Author(s):  
Peter R. Kramer ◽  
Shane R. Keating
Keyword(s):  
Scalar Field ◽  
Passive Scalar ◽  
Homogenization Theory

Finite-Péclet-number effects on the scaling exponents of high-order passive scalar structure functions

2012 ◽  
Vol 713 ◽  
pp. 453-481 ◽  
Author(s):  
J. Lepore ◽  
L. Mydlarski
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Passive Scalar ◽  
Structure Functions ◽  
High Order ◽  
Field Boundary ◽  
Scaling Exponents ◽  
Heated Cylinder ◽  
Scalar Structure ◽  
The Difference

AbstractThe effect of scalar-field (temperature) boundary conditions on the inertial-convective-range scaling exponents of the high-order passive scalar structure functions is studied in the turbulent, heated wake downstream of a circular cylinder. The temperature field is generated two ways: using (i) a heating element embedded within the cylinder that generates the hydrodynamic wake (thus creating a heated cylinder) and (ii) a mandoline (an array of fine, heated wires) installed downstream of the cylinder. The hydrodynamic field is independent of the scalar-field boundary conditions/injection methods, and the same in both flows. Using the two heat injection mechanisms outlined above, the inertial-convective-range scaling exponents of the high-order passive scalar structure functions were measured. It is observed that the different scalar-field boundary conditions yield significantly different scaling exponents (with the magnitude of the difference increasing with structure function order). Moreover, the exponents obtained from the mandoline experiment are smaller than the analogous exponents from the heated cylinder experiment (both of which exhibit a significant departure from the Kolmogorov prediction). Since the observed deviation from the Kolmogorov $n/ 3$ prediction arises due to the effects of internal intermittency, the typical interpretation of this result would be that the scalar field downstream of the mandoline is more internally intermittent than that generated by the heated cylinder. However, additional measures of internal intermittency (namely the inertial-convective-range scaling exponents of the mixed, sixth-order, velocity–temperature structure functions and the non-centred autocorrelations of the dissipation rate of scalar variance) suggest that both scalar fields possess similar levels of internal intermittency – a distinctly different conclusion. Examination of the normalized high-order moments reveals that the smaller scaling exponents (of the high-order passive scalar structure functions) obtained for the mandoline experiment arise due to the smaller thermal integral length scale of the flow (i.e. the narrower inertial-convective subrange) and are not solely the result of a more intermittent scalar field. The difference in the passive scalar structure function scaling exponents can therefore be interpreted as an artifact of the different, finite Péclet numbers of the flows under consideration – an effect that is notably less prominent in the other measures of internal intermittency.

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