Advection time scale

At 24 h after the start of the release the plume maximum had spht into two separate parts (Fig. 5.2). The head received cyclonic rotational momentum from a meso-scale disturbance and reached DK02 after 26 h giving rise to the first peak. As the latter part of the cloud progressed it received anti-cyclonic momentum and after 36 h the plume attained a U-shaped deformation which was advected towards DK02. The rotational time scale of the eddies was not large enough (compared to the advective time scale of the plume) to cause a full revolution in the plume. 

The front velocity v/ is the result of the interplay among the flow characteristics (i.e., intensity U and length scale L), the diffusivity D, and the production time scale x. In this chapter we shall study the problem of front propagation in the case of cellular flows. In particular, introducing the Damkohler number Da = L/(Ux) (the ratio of advective to reactive time scales) and the Pec let number Pe = UL/D (the ratio of diffusive to advective time scales), we shall discuss how the front speed can be expressed as a nondimensional function such as Vf/vo = < >(Da,Pe). A crucial role in determining i >(Da. Pe) is played by the renormalization of the diffusion coefficient and chemical time scale [13] induced by the advection. 

In Eq. 6, / and v are the length and velocity scales for the physical problem under consideration. Equation 6 can also be interpreted as the ratio of two timescales, namely, freiax = and fadvection = Uv, where treiax IS the charge relaxation timescale and fadvection is the advection time-scale. With a typical value of / 10 pm and V 200 pm s fadvection IS of the order of 0.1 s, which is several orders of magnitude higher than the typical values of freiax in an aqueous... 

Fig. 8 Agglomeration time normalised by the particle advection time scale upx/dp as a function of both the particle Stokes number St and the considered particle size distribution...

Time scales of transport can also be applied to situations when no well-defined reservoirs can be defined. If the dominant transport process is advection by mean flow or sedimentation by gravity, the time scale characterizing the transport between two places is simply tadv = L/V where L is the distance and V the transport velocity. Given a t)q)ical wind speed of 20 m/s in the mid-latitude tropospheric westerlies, the time of transport around the globe would be about 2 weeks. 

In choosing a model, the user can optimize fate assessment efforts by delineating first, the source release patterns and second, the dominant dynamical processes. Taking the intramedia processes first, one can address model criteria by considering the ratio of characteristic times. The advection time is the principal length scale of the domain L divided by the average flow speed u i.e. 

An important characteristic of a property distribution is encapsulated in the Peclet number, Pe = ULIk, which is the ratio of diffusive time-scale to advective timescale of the system. In this definition, U and L are the characteristic velocity and length scales of the flow. The Peclet number is a measure of the relative importance of advection versus diffusion, where a large number indicates an advectively dominated distribution, and a small number indicates a diffuse flow. Numerical modeling indicates that certain tracer distributions, in particular tracer-tracer relationships, are significantly affected by the Peclet number, and consequently can be used to determine the nature of the fluid flow (Jenkins, 1988 Musgrave, 1985, 1990). 

Patterns of chemical distributions within the ocean are primarily controlled by biological processes and ocean circulation. Major features of this biogeochemical mosaic include removal of nutrients from warm surface ocean waters, concentration of these same nutrients in deep-ocean waters, and depletion of dissolved oxygen at intermediate water depths. These patterns are imprinted as mixing and advection carry nutrient-laden water from ocean depths into the sunlit upper water. These nutrients are used during photosynthesis to generate particulate and dissolved products that sink or are mixed into the interior ocean, where they are respired back into dissolved metabolites. Interactions of these physical and biological processes occur on time scales of days to hundreds of years and are expressed by the vertical concentration profiles of a variety of dissolved chemical... 

Note that the dispersion terms described in equation (6.18) are valid only in the limit of Fickian behavior. From the central limit theorem, this regime is reached when every particle has amply sampled each region (wakes, gaps, recirculation zones). The average time-scale to advect through a wake is (a(u)Yl, and the average time-scale to experience trapping within a recirculation zone is r/ (yad). Then, the Fickian limit is reached at time t r/ (yad) and (fl(M 1. 

From sect 1.2.7 we reitrate that Taylor s simplification is useful for flow situations where the turbulent eddies evolve with a time scale longer than the time it takes an eddy to be advected past a fixed spatial point (e.g., the location of a sensor). If an eddy of diameter A is advected at a mean velocity of magnitude, juj, (i.e., considering a uniform flow with mean velocity, v, of low... 

Equation (7.143) can be made dimensionless by a proper choice of characteristic length and time scales. It is easy for a specific system to identify a characteristic length L and a characteristic velocity 1/ resulting in a characteristic advection time tm = L/ Z/. Once the steady state has been reached, it is straightforward to calculate average values for the internal coordinates ... 

By using these values, it is possible to estimate the characteristic rate of change for the internal coordinates, which can in turn be used to define characteristic time scales for phase-space advection for each internal coordinate = [ i/ i( i),..., m/ m( m)]-Analogously for diffusion a characteristic time scale is easily defined tdjj = jlDij. Also for the source term for point processes some characteristic time scales can be defined. For... 

We begin our analysis of Eq. (7.145) by noticing that, since all the terms are normalized, the importance of the different terms is dictated by the values of the time scales. If, for example, tm is much greater than td, , tj, rn, and r, then particle advection is much slower than the other particulate processes, and the term on the left-hand side is negligible with respect to the terms on the right-hand side. In contrast, when tm is much smaller than T, TD,p, Tj, Tn, and ti, particle advection is much faster than the particulate processes involved, and the term on the left-hand side is more important than the terms on the right-hand side. 

If large-scale advection alone was responsible for the transport of air parcels from the tropopause to any location in the middle atmosphere, the calculation of the transit time between these two locations would be straightforward. Air parcels, however, do not maintain their integrity over long time scales, because they are rapidly distorted by wave-induced mixing processes into many smaller-scale components. Therefore, the transit time from any point Pq to point P in the atmosphere cannot... 

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