Advection systems

The fundamental engine of the Earth s endogenous fluid advection system is the irreversible... 

Here we also assume that the reaction term does not depend explicitly on the spatial coordinate, therefore the dynamics of the medium is uniform in space. It is easy to see that the spatially uniform time-periodic oscillation is a trivial solution of the full reaction-diffusion-advection system, so the question is whether this uniform solution is stable to small non-uniform perturbations and more generally, if there are any persistent spatially non-uniform solutions in which the spatial structure does not decay in time. 

Zhao, S., Ovadia, J., Liu, X., Zhang, Y.-T., Nie, Q. Operator splitting implicit integration factor methods for stiff reaction-diffusion-advection systems. J. Comput. Phys. 230, 5996-6009 (2011)... 

Regardless of the source, the resultant oil slicks are essentially surface phenomena that are affected by several transportation and transformation processes. With respect to transportation, the principal agent for the movement of slicks is the wind, but length scales are important. Whereas small (i.e. relative to the slick size) weather systems, such as thunderstorms, tend to disperse the slick, cyclonic systems can move the slick essentially intact. Advection of a slick is also affected by waves and currents. To a more limited extent, diffusion can also act to transport the oil. 

At times when the surface pressure gradient is weak, resulting in light winds in the atmosphere s lowest layers, and there is a closed high-preSsure system aloft, there is potential for the buildup of air pollutant concentrations. This is especially true if the system is slow-moving so that light winds remain in the same vicinity for several days. With light winds there will be little dilution of pollutants at the source and not much advection of the polluted air away from source areas. 

The Gaussian Plume Model is the most well-known and simplest scheme to estimate atmospheric dispersion. This is a mathematical model which has been formulated on the assumption that horizontal advection is balanced by vertical and transverse turbulent diffusion and terms arising from creation of depletion of species i by various internal sources or sinks. In the wind-oriented coordinate system, the conservation of species mass equation takes the following form ... 

Its equations account for advection, Coriolis effects, turbulent heat, momentum, moisture iran.sport, and viscosity. The system treats diurnaliy varying winds such as the land-sea breeze and... 

Hundreds to thousands of km - the synoptic scale, in which motions are those of whole weather systems. Advection is the dominant transport process. 

The motions on the largest spatial scales amount to the aggregate of the world s synoptic weather systems, often called the general circulation. Both with respect to substances that have atmospheric lifetimes of a day or more and with regard to the advection of water, it is useful to depict the nature of this general circulation. The mean circulation is described to some extent in terms of the Hadley and Ferrell cells shown in Fig. 7-4. They describe a coupled circulation... 

Three regions of the atmosphere are seen to have significant zonal components of flow and thus of advection. The mid-latitude troposphere at the surface tends to exhibit westerly flow (i.e., flow from west to east) on the average. This region contains the familiar high- and low-pressure systems that cause periodicity in mid-latitude weather. Depending on the lifetime of the substances of concern, the motion in these weather systems may be important. 

Biofilms adhere to surfaces, hence in nearly all systems of interest, whether a medical device or geological media, transport of mass from bulk fluid to the biofilm-fluid interface is impacted by the velocity field [24, 25]. Coupling of the velocity field to mass transport is a fundamental aspect of mass conservation [2]. The concentration of a species c(r,t) satisfies the advection diffusion equation... 

The RTD quantifies the number of fluid particles which spend different durations in a reactor and is dependent upon the distribution of axial velocities and the reactor length [3]. The impact of advection field structures such as vortices on the molecular transit time in a reactor are manifest in the RTD [6, 33], MRM measurement of the propagator of the motion provides the velocity probability distribution over the experimental observation time A. The residence time is a primary means of characterizing the mixing in reactor flow systems and is provided directly by the propagator if the velocity distribution is invariant with respect to the observation time. In this case an exact relationship between the propagator and the RTD, N(t), exists... 

Advection is important in fragmentation processes, and an initially homogeneous system may evolve spatial variations due to spatially dependent fragmentation rates. For example, Fig. 36 shows the spatial distribution of eroded clusters in the journal bearing flow operating under good mixing... 

Logical Structures. When a synthetic organic chemical is released into an aquatic system, the entire array of transport, transfer, and transformation processes begins at once to act on the chemical. Transport from the point of entry into the bulk of the system takes place by advection and by turbulent dispersion. Transfers to sorbed forms and irreversible transformation processes proceed simultaneously with the transport of the chemical. After the elapse of sufficient time, the chemical comes to be distributed throughout the system, with relatively smooth concentration gradients resulting from dilution, speciation, and... 

In addition to dissipation of the substance from the model system through degradation, other dissipative mechanisms can be considered. Neely and Mackay(26) and Mackay(3) have also introduced advection (loss of the chemical from the troposphere via diffusion) and sedimentation (loss of the chemical from dynamic regions of the system by movement deep into sedimentation layers). Both of these mechanisms are then assumed to act in the unit world. This approach makes it possible to investigate the behavior of atmosphere emissions where advection can be a significant process. Therefore, from a regulatory standpoint if the emission rate exceeds the advection rate and degradation processes in a system, accumulation of material could be expected. Based on such an analysis reduction of emissions would be called for. 

The environmental compartments are represented by boxes and the concentration of a chemical in these boxes is affected by processes that cause mass flows of the chemical to and from the boxes. The chemical can be input into a box from outside the system, output from a box to outside the system, or transported by means of advective or diffusive processes to and from other boxes. A mass balance equation can be written for each of the boxes representing the mass flow of the chemical. Generally, the magnitude of these mass flows depends on the concentration of the chemical in the boxes. If mathematical expressions which relate the mass flows to the concentrations are available, the set of mass balance equations (one for... 

The Level II calculations at pH 5.1 include the reaction half-lives of 550 h in air, 550 h in water, 1700 h in soil and 5500 h in sediment. No reaction is included for suspended sediment or fish. The steady-state input of 1000 kg/h results in an overall fugacity of 3.43 x 1(H Pa, which is about 24 times the Level I value. The concentrations and amounts in each medium are thus about 24 times the Level I values. The relative mass distribution is identical to Level I. The primary loss mechanism is reaction in soil, which accounts for 936 kg/h, or 94% of the input. Most of the remainder is lost by reaction and advection in water. The air and sediment loss processes are unimportant largely because so little of the PCP is present in these media. The overall residence time is 2373 h thus, there is an inventory of PCP in the system of 2373 x 1000 or 2,373,000 kg. 

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