This discussion is again split up into four principle sections, which refer to the calibration stage, the evolution of particle cloud with downstream distance, the prediction stage, and several comparisons between models having similar properties
4.5.4.1 Calibration stage for over-bank flow.
The centroids of the particle distributions differed from the data by between 3 and 6 cm, and again showed a positive bias. The discrepancy between the modelled and measured centroids was however of the order of the resolution of the
measurements (3cm) and was considered acceptable at 4m downstream.
All of the spreads in the particle distributions at a depth of 159mm agreed to within the estimated experimental uncertainty with the spread in the concentration distributions (the coefficient of variability was in the range from less than 1% to 4%), which is confirmed by the example particle distribution for the model NSCALE
labelled ‘nscale 40’ on fig. 4.17. The predicted particle distribution at 16m downstream (labelled ‘nscale 160’) on the same figure shows, however, that there are problems to come.
4.5.4.2 Evolution of particle distributions with downstream distance for over bank flow.
The graphs (fig. 4.15 and 4.16) showing the evolution of the spread at 159mm with downstream distance show that most of the modelled distributions over-predict the measured spread in the concentration distribution. Only one of the models, JSCALE predicts the observed behaviour to within the uncertainties at all of the
measurement sites in the downstream direction, although the characteristic shape of the curve is representative of several of the models (NSCALE, JUMP, CORJ3 and
CORJ4). This will again be discussed in section 4.7.
The centroids in the particle distributions showed a non-trivial drift in the centroids of approximately 15 cm by cross-section 7, but remained relatively steady in the data as shown in table 4.8 for the model NEWJUMP:
Table 4.8 Variation of centroids with downstream distance for data and two different models. distance downstream data centroid (m) NEWJUMP centroid (m) NEWJUMP (modified with boundary reflection about angle of incidence) centroid (m) 4m 1.073 1.116 1.084 8m 1.095 1.143 1.111 12m 1.065 1.185 1.129 16m 1.046 1.213 1.143 141
Fig.4.18 shows the observed and modelled transverse non dimensional concentration distributions for the single depth of 159mm and for the downstream distance 16m in the case of the over-bank flow.
The drift was initially thought to be due to the use of reflections from boundaries, which had previously not properly taken into account the transverse momentum of a particle approaching the sloped side wall of the over bank flow geometry. The particles were now reflected about the normal to the bed slope to conserve momentum (as discussed in section 4.3.3). The drift in the centroid was found to be reduced slightly (see table 4.8 above), although the systematic drift of the centroid remained.
A further investigation into the reason for the drift was undertaken, initially to see if there was any connection between the drift and the difference between the velocities in the over-bank region and those in the main channel. A simulation was undertaken whereby the random walk in the horizontal direction was left the same, but vertical steps were excluded from the trajectories so that the particles all remained at the release depth. This produced good agreement of the model centroid with the observed value. Next the particles were allowed to step vertically, but were restricted to the region of the flow no deeper than the bank top. Again the model and observed centroids were in close agreement.
The above two observations strongly suggested that the misfit in the centroid positions was not due to the relatively large difference in velocities between the in bank and over-bank regions. This velocity difference might have otherwise given rise
to the sort of drift effect discussed in chapter 2, whereby maxima in particle number densities drift away from regions of high diffusivity, or short time constants.
Having eliminated other possibilities, it was considered that the drift was associated with the asymmetric flow field faced by the particles following their release. Initially, following the injection, an equal number of particles (on average) would disperse either side of the line y = 1.05m. The particles over the main channel would be free to disperse downwards, so that there would then be relatively fewer particles close to the surface (or in the vicinity of z = 159mm at which depth the distributions were examined in detail for the over-bank flow). This would result in there being relatively more particles towards the over-bank region than in the main channel region in the simulation, whereas for the real flow, this was not observed. This facet of the real flow could be explained if the turbulence induced secondary circulation above and adjacent to the bank-top (see fig. 3.1), was increasing the mixing rate of tracer close to the bank-top, on the over-bank side, into the main channel, giving the tracer on average more opportunity to ‘escape’ into the main channel.
This effect was next attempted to be accounted for by including a transverse varying eddy viscosity as mentioned above, for the random walk, NEWJUMPB. This allowed for a greater effective eddy dispersivity in the region of the bank-top, to simulate this ‘enhanced mixing’ due to secondary circulatory cells, and was described in section 2.6.2. However, this did not produce any better agreement with the
centroids, and by all other accounts (this model was included in the sensitivity analysis above), NEWJUMPB performed badly. It was concluded that in order to investigate
this effect further, more information about the secondary advections was required, which was not available at the time of writing.
4.S.4.3 Prediction stage for over-bank flow.
The predicted spreads in the particle distributions at cross-section 7 for the models JSCALE, NSCALE and JUMP agree with the spreads in the concentration distributions to within estimated uncertainties in the data, with the remaining models deviating by between 10% and 19 % from the observations. However, it is again important to examine the vertical distributions, by inspecting the combined objective function, obj3, which was again used to list the models in decreasing order the closeness o f fit in tables 4.4 and 4.5.
4.6 Relative performances of the different models at the calibration and