Streamtube

A group of streamlines can be taken together to form a streamtube, and thus the whole area for flow can be regarded as being composed of bundles of streamtubes. 

Considering the flow of a fluid through a streamtube, as shown in Figure 2.6, then equating the mass rates of flow at sections 1 and 2 ... 

The rate of change of momentum of the fluid along the streamtube... 

Fig. 4.4.7 (a) Reconstruction of the Stationary Helical Vortex (SHV) mode from MRI data acquired with the spin-tagging spin-echo sequence [27], The axial flow is upwards and the inner cylinder is rotating clockwise. The two helices represent the counter-rotating vortex streamtubes. (b) Construction of Poincare map for SHV [41]. The orbit of a typical particle is... 

Yabusaki, S. B., C. I. Steefel and B. D. Wood, 1998, Multidimensional, multicomponent subsurface reactive transport in non-uniform velocity fields code verification using an advective reactive streamtube approach. Journal of Contaminant Hydrology 30,299-331. 

From the results it has been proven for all the experimental systems studied that the flow rate is constant along the streamtubes defined in the annular zone, such as has been proposed in the model. 

Introduce new variables 0 to follow the stream with its velocity u(x) and a length variable X. Noting that we can chose to follow a stream with constant flowrate 9 in a streamtube X can be written as the RHS of (A4)... 

A discrete view of the transport considers either random trajectories of discrete particles, or random streamtubes of tracer "parcels" carried by a constant flow rate through a network of fractures. For pulse injection of mass Af, we compute the tracer discharge as J(t) = My(t,T), the Laplace transform of y is... 

Modelling Reactive Transport of Organic Solutes in Groundwater with a Lagrangian Streamtube Approach... 

Figure 7.1 Conceptual basis of the streamtube approach (a) aquifer domain between an injection and a control plane, (b) pdf of travel time as description of flow field variability in the aquifer domain.

In the numerical streamtube model, the restriction to nearly uniform flow fields, commonly associated with the streamtube approach, is eliminated by introducing non-planar injection and control surfaces which are perpendicular to the mean flow direction, thus accounting for non-uniform velocity fields (Fig. 7.2). Furthermore, the numerical approach allows to consider even complex physico-chemical relationships among the solutes regarded as well as between the solute and the solid phase. 

Figure 7.2 General scheme of the conceptual transport model ensemble of streamtubes representing the heterogeneous flow field between an injection and a control surface solutes are undergoing various processes solute-solid phase-interactions depend on soil heterogeneity.

If large-scale physico-chemical heterogeneities are present and the individual solute particles encounter quite different physicochemical properties of the aquifer material along their flowpaths, reactive transport must be computed explicitly in terms of r along each and every streamtube (see below and Thiele et al., 1995A,... 

In order to evaluate the reaction function, simulations of one-dimensional advective-reactive transport expressed in terms of the travel time rmust be conducted. A series of concentration profiles with respect to t calculated at distinct times ij (i = 1,2,..., ) approximate the reaction function F (Fig. 7.4). The length of the streamtube is given... 

If the assumption of a representative streamtube is valid, the normalised breakthrough curve (BTC) of a reactive tracer at the control surface (Fig. 7.5) is then given by ... 

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