# 8.2.2: Cross-shore distribution of longshore transport

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$ Figure 8.1: Example of model results (longshore current velocity $$V(x)$$, longshore transport rates $$s_y (x)$$ and transport integrated over the cross-shore $$S_y$$) computed with Unibest-CL+ (https://www.deltares.nl/en/software/unibest-cl) for a 2012 measured profile near Egmond (transect 7003850 from JARKUS, n.d.) using $$D_{50} = 200\ \mu m$$ and $$D_{90} = 300\ \mu m$$.

The cross-shore distribution of longshore sediment transport is, of course, strongly determined by the cross-shore distribution of the longshore current. The longshore current distribution on a barred beach for different wave conditions (Fig. 5.42) is repeated in Fig. 8.1a. Besides, Fig. 8.1 shows the longshore transport rates as calculated with the longshore sediment transport model Unibest-$$CL_+$$. Comparing the upper and middle panel of Fig. 8.1a while keeping Eqs. 8.2.1.1 and 8.2.1.3 in mind, we may conclude that most of the sediment stirring takes place in a relatively narrow zone on the seaward flanks of the breaker bars, where most of the wave-breaking takes place. Also note the non-linear dependency of the transport on the velocity. Figure 8.1b demonstrates that the outcomes of uncalibrated transport formulas may differ substantially. Figure 8.2: Comparison between calculated and measured cross-shore distribution of long-shore sediment transport rate for one run of the SandyDuck experiment (98/02/04). Adapted from Bayram et al. (2001). The letters indicate different models, with amongst them B: Bijker (Eq. 6.5.4.1), BI: Bailard-Inman (Sect. 6.7.2), VR: Van Rijn (Eq. 6.6.1.5 for suspended load plus separate bed load formula).

Bayram et al. (2001) analyse the cross-shore distribution of longshore sediment trans- port according to a few well-known predictive formulas and field measurements at Duck, North Carolina. Measured hydrodynamics were used as much as possible as input for the transport models. The transport models were used with standard coefficient values without further calibration. Figure 8.2 gives the result for one specific condition ($$H_{rms} = 3.18\ m, T_p = 12.8\ s$$) representative for a large transport on a barred sandy profile during a storm. The mean longshore current velocity in the surf zone was $$0.6\ m/s$$. The water depth at the most offshore measurement point was 8.6 m. The peak in the transport rate was observed some distance shoreward of the bar crest, whereas the formulas predicted the peak to occur more seaward (i.e., close to the bar crest).

For this specific run, most formulas overpredict the sediment transport. Further, the differences between the various models are rather large. The used formulas differ particularly in the way the influence of the waves has been taken into account. Besides, sensitivities to certain input parameters vary between the formulas. This could be seen from runs under different conditions that showed a different relative behaviour of the various formulas. Differences in total transports between the various transport formulas can easily be up to a factor ten! This illustrates the need for calibration of the formulations before results from computer computations can be used in specific coastal engineering cases. The data used for calibration should be representative for the considered site and hydrodynamics conditions. Examples of such calibration data are observed coastline changes following a certain ‘event’ (such as the construction of a new harbour along a coastline, or the damming of a river and the subsequent erosion of the shoreline of the river delta).

This page titled 8.2.2: Cross-shore distribution of longshore transport is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Judith Bosboom & Marcel J.F. Stive (TU Delft Open) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.