Wave-average area morphologic change numerical modelling system, CST3D, is adopted to reproduce tombolo and salient evolution behind a detached breakwater at a laboratory. The numerical wave-average morphologic model equips the beachface slope controlling method. Beachface slope varies between two extreme values for erosion and siltation modes. The beachface slope is checked every time step, and the morphology at the beachface and flat surf terrace is modified, if necessary. The model system reproduced tombolo and salient evolution for 2 cases of Ming and Chiew’s experiments. Model results implies the length of the detached emerged structure plays an important role on formation of tombolos

Duhoon Park

Hak Soo Lim

Hyoseob Kim

Seungho Lee

English

Vibroengineering PROCEDIA

 196 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. JUN 2017, VOL. 12. ISSN 2345-0533  
Simulation of tombolo evolution by using CST3D-WA 
Hyoseob Kim1, Seungho Lee2, Duhoon Park3, Hak Soo Lim4 
1, 2, 3Kookmin University, Seoul, Republic of Korea 
4Korea Institute of Ocean Science and Technology, Ansan, Republic of Korea 
2Corresponding author 
E-mail: 1hkim@kookmin.ac.kr, 2stork@kookmin.ac.kr, 3qawsedr1991@naver.com, 4hslim@kiost.ac.kr 
Received 25 May 2017; accepted 5 June 2017 
DOI https://doi.org/10.21595/vp.2017.18673 
Abstract. Wave-average area morphologic change numerical modelling system, CST3D, is 
adopted to reproduce tombolo and salient evolution behind a detached breakwater at a laboratory. 
The numerical wave-average morphologic model equips the beachface slope controlling method. 
Beachface slope varies between two extreme values for erosion and siltation modes. The 
beachface slope is checked every time step, and the morphology at the beachface and flat surf 
terrace is modified, if necessary. The model system reproduced tombolo and salient evolution for 
2 cases of Ming and Chiew’s experiments. Model results implies the length of the detached 
emerged structure plays an important role on formation of tombolos. 
Keywords: tombolo, salient, shoreline advance, shoreline retreat morphologic change, area model. 
1. Introduction 
Tombolo or salient plays an important role to control coastal morpology. Shoreline change is 
of great interest to many coastal engineers. Korean East Sea has micro-tidal beach, and high  
waves. Beach profiles have been measured several times in 2013 and 2014 at Anmok and 
Namhangjin Beaches on the east coast of Korea [1]. Measured profiles show more or less similar 
style, see Fig. 1. Mean tidal range at the site is around 10-20 cm. The offshore-bar-average flat 
terrace also shows stable slope and depth. The beachface slope and the beachface foot level at the 
site seem very stable. The shape of the berm top and the berm body varies site by site depending 
on the land use status. The fact that beachface retains straightness between the top and the foot in 
shape, and that the beachface slope remains relatively constant throughout a year is promising 
from the engineering point of view. The offshore bar-average flat terrace also shows stable slope 
and depth. The measured beachface slope at Anmok and Namhanjin beaches are within 7° to 10° 
in 2013 and 2014, and its average value is 8.5°. It is thought that the slope is steep during eroding 
phase, and mild during siltating phase. 
 
Fig. 1. Typical beach profile style at Anmok and Namhangjin Beaches 
Many emerged or submerged detached breakwaters have been constructed to induce salients 
or tombolos, and are still under assessment on their success. It is important to reproduce or predict 
tombolo evolution behind breakwater by using a tool including numerical modelling. Ranasinghe 
et al. [2] proposed an empirical formula to distinguish erosiveness of shoreline behind submerged 
detached breakwaters, which was based on their numerical modelling results. However, their 
distingction criteria on erosion or deposition was not clearly explained. Johnson et al. [3] also 
proposed an engineering tool for design of detached breakwater, but its use is limited for 
macro-tidal coasts. 
CFD type models or Boussinesq type models could simulate sediment transport around 
SIMULATION OF TOMBOLO EVOLUTION BY USING CST3D-WA.  
HYOSEOB KIM, SEUNGHO LEE, DUHOON PARK, HAK SOO LIM 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. JUN 2017, VOL. 12. ISSN 2345-0533 197 
beachface, morphologic change up to runup height and consequent shoreline evolution, but require 
heavy computation. A simple end of simulation methods for shoreline evolution is the line models 
[4]. Line models are useful to predict long-term shoreline evolution around simple structures, but 
fail to simulate tombolo formation or spit growth which involves wild shoreline deformation 
because of their parallel or almost parallel grid system adopted. 
General wave-average area models may have merits to simulate shoreline evolution for 
arbitrary geometry. However, the difficulty in treatment of shoreward boundary has hindered the 
use of this type of approach for simulation of shoreline evolution. The major defect is that it is 
impossible to simulate morphologic change above the wave-average water level, although it is 
more or less hidden for macro-tidal environment. 
There have been a few trials to model shoreline retreat within wave-average area modelling 
approach. These include the diffusion method [5], the wet-dry cell method [6], and the cut-cell 
method [6]; these lack capabilities of simulation of shoreline advance. Another group of trials 
modelled shoreline advance as well: the fixed profile method [7], the coupling area-line method 
[8-10] and area-crossshore-alongshore transport coupling method [11-13]. The fixed profile 
method has not yet been expanded for general morphology. The coupling method runs an area 
model, and transfers output to a line or N-line models. However, it involves wild assumptions, 
and its application is limited to fairly simple morphology. Kuroiwa et al. [14, 15] included 
crossshore sediment transport and alongshore sediment transport in their area model. However, 
the cross-shore and alongshore directions are preliminarily defined at the beginning of simulation, 
and therefore the tombolo evolution with wild shoreline deformation cannot be properly  
simulated. The assumption of linear distribution of cross-shore transport rate adopted in their 
model may cause unrealishic parabolic beachface profile, and may require future adjustment. 
Kuchiishi et al. [12] and Fujiwara et al. [13] showed shoreline evolution around river mouths and 
detached breakwater by using both wave-induced and current-induced sediment transport, 
However, the nearshore wave-induced sediment transport rate requires future verification. A new 
method with management of the beachface slope to simulate the shoreline evolution of arbitrary 
shape within an area morphological model is proposed here. 
2. Beachface slope controlling method 
We assume that the beachface part of a beach profile is uniform-sloped, and the upper part of 
the terrace below the beachface foot is also nearly uniform-sloped. The shoreline may proceed in 
depositing phase or retreat in eroding phase during a certain period. If interirim model results 
reveal siltation on the lower half of the beachface and terrace so that the beachface slope becomes 
milder than the minimum one, then the temporary profile is artificially adjusted to restore the 
minimum beachface slope by moving some sediment budget on to dry zone, see Fig. 2. In the 
figure b is half of the beachface height, ߠௗ is the lower limit slope, ߠௗᇱ  is the temporary slope 
milder than the limit slope, and ߙ is the portion of the height of neutral position where both 
volumes become identical relative to the beachface height. ܣଵ should be the same as ܣଶ. We get 
ߙ = 0.25. The parameter ߙ becomes 0.25 if the profile lines are straight. 
 
Fig. 2. Beachface slope control with regard to reference height during depositing phase 
On the other hand, if interim model results reveal erosion on the lower half of the beachface 
and terrace, so that the beachface slope becomes steeper than the maximum slope, then the 
SIMULATION OF TOMBOLO EVOLUTION BY USING CST3D-WA.  
HYOSEOB KIM, SEUNGHO LEE, DUHOON PARK, HAK SOO LIM 
198 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. JUN 2017, VOL. 12. ISSN 2345-0533  
temporary profile is artificially adjusted to restore the maximum beachface slope by dumping 
some sediment volume to underwater zone, see Fig. 3. In this case the parameter ߙ is related to 
another parameter ߚ, which is a proportion of the ambient depth under erosion relative to the 
beachface height. ܣଵ and ܣଶ should be identical for sediment mass conservation. ߙ becomes 0.25 
for ߚ = 0, when the average erosion depth at surrounding bed is zero. 
 
Fig. 3. Beachface slope control with regard to reference height during eroding phase 
Shorelines are not always straight, especially around headlands or structures. Shoreline angle 
varies smoothly in space, and shoreline angle may deviate from straight line sharply around 
tombolos or salient, see Fig. 4. We want to apply the above adjustment along cross-sections, and 
we need to find the orthogonal profile for every given grid cell on the beachface. A nearly 
orthogonal profile can be found by choosing the shortest distance among many distances between 
the point of interest and the contour line of the reference level, ܼ௥, by interpolation of the depths 
of the point of interest and a cell point within a checking radius, see Fig. 5.  
 
Fig. 4. Three-dimensional morphological modification for deposition phase: shoreline advances 
 
Fig. 5. Finding control cross-section for the point of interest from many cell depths below reference level 
3. Simulation results 
Ming and Chiew [16] carried out laboratory experiments on salient or tombolo formation 
starting from plane-sloped beach, and presented their experimental results; results was divided 
into tombolos, salients, and no form. The above algorithm is adopted in a numerical modelling 
system CST3D-v2016 [17], and applied to two cases of Ming and Chiew’s laboratory experiments 
of Table 1. The numerical modeling system is semi-three-dimensional; sigma coordinated; and 
containing wave, flow, sediment transport, and morphological change sub-modules. Horizontal 
mixing of bed sediment due to wave action proportional to the number of grid points across the 
surf zone [18] is also included in the model as a smoothing process of morphology. 
SIMULATION OF TOMBOLO EVOLUTION BY USING CST3D-WA.  
HYOSEOB KIM, SEUNGHO LEE, DUHOON PARK, HAK SOO LIM 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. JUN 2017, VOL. 12. ISSN 2345-0533 199 
Table 1. Ming and Chiew’s [14] test conditions and experimental results 
Case ܤ (m) ܺ (m) ݄஻ (cm) ܺ௕ (m) ܪ଴ (cm) ଴ܶ (s) ܦ (m) ܪ଴/ܮ଴ ௗܶ (h) ܺ௦ (m) ܣ (m) 
1-7 1.50 0.90 8.00 0.50 5.00 0.85 0.335 0.044 19.0 0.900 0.557 
1-4 0.60 0.90 8.00 0.50 5.00 0.85 0.335 0.044 18.0 0.240 0.138 
The symbols in Table 1 are defined as: ܪ଴ is deep water wave height; ܪ଴/ܮ଴ is deep water 
wave steepness; ݄஻  is water depth at the breakwater; ଴ܶ  is wave period; ܮ଴  is deep water 
wavelength; ܦ is water depth in the wave basin; ௗܶ is test duration; ܤ is length of the breakwater; 
ܺ is distance of the breakwater to the initial shoreline; ܺ௕ is distance of the initial breaker line to 
the initial shoreline; ܺ௦ is distance of the salient apex to the initial shoreline; and ܣ is plan area of 
sand deposition, namely the area enclosed by the initial shoreline and the shoreward equilibrium 
shoreline. Note that the shoreline refers to the still water line. 
Model results include wave field, flow-driving force field, wave-induced current field, wave- 
average bed shear stress field under the flow and wave conditions, sediment eroding/depositing 
rate field, modified morphology by wave and current, and the accompanying modified shoreline.  
 
a) Case 1-7 
 
b) Case 1-4 
Fig. 6. Computed wave field with SWAN for Case 1-7 and 1-4:  
arrow size is wave height; arrow direction is wave direction 
 
a) Case 1-7 
 
b) Case 1-4 
Fig. 7. Computed wave-induce current field for Case 1-7 and 1-4:  
arrow size is current speed; arrow direction is current direction 
The computed wave fields using SWAN for the two cases are shown in Figs. 6. Wave height 
behind the breakwaters are small due to diffraction. The computed wave-induced current fields 
for the two cases are shown in Figs. 7. Wave-induced driving forces are strong around shoreline 
at the lee of the breakwater due to uneven wave breaker line. Wave-induced currents are strong 
behind the breakwater; forming two strong wakes, the centreline of which is heading toward the 
breakwater. Both cases show a pair of circulation cells, but the sizes of the circulation cells are 
different. The size of the circulation cells of Case 1-7 is larger, and the current speed of the case 
is weaker. Two circulation cells in the lee side of the breakwater are closer to each other for 
Case 1-4, and the fluid particle velocity and the resultant bed shear stress along the centerline 
between the two cells are larger, which hinders tombolo growth. The two wakes play an important 
role in sediment transport and morphological change around the structures. 
The smoothing step in Fig. 6(a) was added to the first intermediate morphology based on 
empirical experience. Smoothing of bed morphology represents lateral mixing of sediment due to 
SIMULATION OF TOMBOLO EVOLUTION BY USING CST3D-WA.  
HYOSEOB KIM, SEUNGHO LEE, DUHOON PARK, HAK SOO LIM 
200 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. JUN 2017, VOL. 12. ISSN 2345-0533  
wave action similar to horizontal mixing of fluid momentum. 
Computed shoreline positions for the 2 cases are shown in Figs. 8-9, which are satisfactorily 
compared with laboratory measurements in Figs. 10-11. Both the computed time evolution of the 
distance of the salient apex to the initial shoreline, (a) and the computed time evolution of the 
attachment width of the tombolo at the detached breakwater (b) show asymptotic behavior towards 
equilibrium status, see Figs. 12(a) and (b). 
 
Fig. 8. Model result: Case 1-7 
 
Fig. 9. Ming and Chiew’s result: Case 1-7 
 
 
Fig. 10. Model result: Case 1-4 
 
Fig. 11. Ming and Chiew’s result: Case 1-4 
 
 
a) Case 1-7 
 
b) Case 1-4 
Fig. 12. Computed time evolution of two lengths ܺ௦ and ௧ܹ 
4. Conclusions 
Computed shoreline evolution for the two cases of Ming and Chiew’s experiments reproduced 
measurements satisfactorily. Both tombolo and salient cases were successfully simulated by the 
model system CST3D adopting the present beachface slope controlling method, and it is believed 
that model results improve our understanding of the difference between tombolo and salient. The 
model system could further be parameterized for engineering purposes. The present beachface 
slope adjustment method work well for cases of very wide angle deformation of shoreline, which 
cannot be simulated by existing one or N line models. 
Regarding the length of a detached breakwater long breakwater helps tombolo formation. 
Modeling result clearly demonstrates that the design of an emerged breakwater should be 
SIMULATION OF TOMBOLO EVOLUTION BY USING CST3D-WA.  
HYOSEOB KIM, SEUNGHO LEE, DUHOON PARK, HAK SOO LIM 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. JUN 2017, VOL. 12. ISSN 2345-0533 201 
supported by numerical modelling to make sure that whether intended salient or tombolo would 
evolve for given structure length, depth, and distance to the initial shoreline to obtain proper 
tombolo or salient.  
Acknowledgements 
This work is a result of the research project, “Development of Coastal Erosion Control 
Technology”, funded by the Ministry of Oceans and Fisheries, Korea since 2013. 
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Simulation of tombolo evolution by using CST3D-WA

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