5.6 Nourishment Sand Waves
5.6.2 Coastline Position Influence
Nourishment positions along coastlines may have significant implications on the advection-diffusion relationship given variations in relative coastline angles. The Durban coastline presents an interesting situation given that the uMngeni boundary region is slightly more diffusion influenced that the remaining two regions. Placement of nourishments at this position (pos. 3) will undergo significant diffusion which will increase advection velocities as the sand wave develops and propagates. Comparatively, nourishments placed at position 2 will experience less diffusion given the coastline orientation and will hence maintain a lower advection velocity.
This section explores the effects of different discharge positions along the Durban coastline on nourishment behaviour. In understanding how discharge positions affect nourishment waves, shore nourishment schemes may be operated optimally with retention times maximised. For this investigation, two points along the coastline served as nourishment points (pos. 2 and 3), as shown in figure 5.16a. From section 5.6.1, results showed that a single, large nourishment is not effective for maximising retention times within the domain, hence only nourishments assuming 2 waves or more will be considered in this section.
Table 5.12 Travel times for a 209,167 m3 nourishment of varying aspect ratios between multiple points along the Durban coastline. Point of application of the nourishment is position 3.
Width - L Amplitude - B B/L Pos. 3→ Pos. 2 Pos. 2 → Pos. 1 Total (m) (m) (−) (years) (years) (years)
500 47.87 0.096 2.51 1.51 4.02
1000 23.93 0.024 2.21 1.4 3.61
2000 11.97 0.0067 1.39 1.33 2.72
5.6 Nourishment Sand Waves Table 5.12 shows the time taken for a 209,167m3 nourishment placed at position 3 to reach the midpoint and end of the domain. Results expectedly show that the highest aspect ratio waves have the highest retention times within the domain. Importantly, travel times between positions 3 and 2 as compared to those between positions 2 and 1 have greater differences for higher aspect ratios. A nourishment with an aspect ratio of 0.096 takes approximately one year less to reach the end of the domain from position 2 (1.51 years) in comparison to the time taken to reach position 2 from position 1 (2.51 years). Although higher aspect ratios of nourishments produce a greater retention time, consideration must be given to the time period of successive nourishments. Larger aspect ratios placed at position 3 will take longer to reach position 2 however the following period is significantly faster. Placement of a smaller aspect ratio nourishment will result in essentially even travel times between positions, resulting in a more even distribution of sediment along the coastline. This general trend may be applied to sand waves of any volume as long as the aspect ratio is known.
Table 5.13 Travel times for a 209,167m3 nourishment of varying aspect ratios between multiple points along the Durban coastline. Point of application of the nourishment is position 2 while column 5 assumes nourishment application at position 3.
Width - L Amplitude - B B/L Pos. 2 →Pos. 1 Pos. 2 → Pos. 1 (m) (m) (−) (years) (years)
500 47.87 0.096 2.17 1.51
1000 23.93 0.024 1.98 1.4
2000 11.97 0.0067 1.71 1.33
Table 5.13 shows time taken for the same nourishments used in table 5.12 to travel from position 2 to position 1. It is evident that retention times for nourishments placed at position 2 exceed retention times for their counterpart placed at position 3 when considering travel time between position 2 and 1. This result infers that significant diffusion occurs between positions 2 and 3. Travel times may be increased between positions 1 and 2 should nourishments be re-nourished or applied entirely at point 2. Application of nourishments at position 2 will however starve the region between position 2 and 3 of nourished sediment given the dominant angle of wave approach hence consideration should be given to this.
Generally, the influence of coastline position may be significant however the impact of aspect ratio still governs sand wave behaviour. When applying diffusion dominant
rapid diffusion may result in a wave becoming advection dominated. Retention times of sand waves may be increased by placing nourishments in regions that experience lower diffusion rates or where the coastal orientation is closer to that of the dominant wave angle.
Chapter 6
Summary & Conclusions
This study comprised of five research questions with the aim of approximating the influences of varying sediment supplies on coastline evolution. A numerical one-line model was developed using existing models as a framework. This model is set apart from existing models by accounting for sand advection as well as diffusion. Calibration and validation of the longshore transport equation involved using observed wave records for the study region. Model sensitivity was also investigated. The model was then used to simulate coastline behaviour under varying sediment input circumstances to estimate sediment demands for the region. This chapter presents a summary of the results together with conclusions and recommendations.
6.1 One-line Model
What is the most effective way to simulate long term coastline evolution within reasonable timeframes?
A numerical one-line model was developed using a number of existing models as a framework. The necessary numerics of a one-line model were identified in terms of grid initialisation, wave transformations, longshore sediment transport and diffusion of sediment. Grid initialisation followed a similar method to that used by the GENESIS model developed by Hanson (1989). Longshore sediment transport was calculated using the Kamphuis (1991) formula (eqn. 2.9). Diffusion and advection were calculated using a variant of the Pelnard-Considère (1956) equation (eqn. 4.20). Fluvial sediment volumes were introduced into the model domain assuming a Gaussian distribution in plan (eqn. 4.22). Model checks involved limiting relative wave angles and the inclusion of a hard boundary in the cross-shore direction. This hard boundary ensured
adjustment of longshore transport rates based on the availability of sediment within the grid cell, developed by Hanson and Kraus (1986).
Calibration of the model involved using 18 years (reduced to 13 years) of observed wave data along the KwaZulu-Natal Coastline. The data spanned from 1992 until 2009 and was obtained from wave rider buoys situated at Durban and Richards Bay. Richards Bay data was used to supplement regions of missing data within the Durban records given their strong correlation (Corbella and Stretch, 2012b). The wave data was used in conjunction with annual estimated longshore transport rates for the Durban Bight calculated by Corbella and Stretch (2012b) to calibrate the Kamphuis (1991) longshore transport equation. The dataset was evenly split into a calibration and validation half. The one-line model was used to calculate annual longshore transport rates using a constant representative coastline angle for the region. A linear regression analysis yielded a calibration coefficient K of 0.0003078 which was found to be satisfactory when compared to the validation dataset.