1. Nearshore circulation system
Chang Hsien Kuo
國立交通大學土木工程學系
中華民國102年4月18日

2. Surf zone (type of breakers)

3. Movement of sand on the beach
Movement parallel (↔) to shoreline
Caused by wave refraction (bending)
Each wave transports sand either upcoast or downcoast
Huge volumes of sand are moved within the surf zone
The beach resembles a “river of sand”

4. Wave set-up
Cross-shore balance of momentum

5. Wave run-up Regular wave (Miche, 1951) Irregular wave (Mase, 1989)
Surf Parameter
ξ 0 = 𝒕𝒂𝒏β 𝑯 𝟎 / 𝑳 𝟎 :

6. Longshore current and longshore drift
Longshore current = zigzag movement of water in the surf zone
Longshore drift = movement of sediment caused by longshore current

7. Nearshore circulation system
Longshore current
and Rip current
Depth-averaged momentum equations and continuity Eq.

8. Wave induced longshore current
Longuet-Higgins (1970)
Assumption:
1. Longshore homogeneity (𝑼=𝟎,𝝏𝒚=𝟎)
2.No wind forcing (Rs=0)
3. Uniform sloping bottom (d=x*tanβ)

9. Wave induced longshore current
Wave forcing
Bottom friction
紊流渦動滯度模式 (eddy viscosity model),
Reynolds stress
P: lateral mixing coefficient

10. longshore current
Wave forcing
Slope-type

11. longshore current Normalized variables and equations Special case:
p=1 (linear ratio of eddy viscosity to offshore difference) ;
q=1 (uniform slope)

12. Solution of Euler equations
Particular solution
Eigen value

13. Boundary conditions
Four conditions
Solution

14. Boundary conditions
Chang, H.K. and H.W. Hsu (1996), Longshore current on an equilibrium beach,” China Ocean Engineering, 10(2),

15. Mean longshore current
longshore current at mid-surf zone is regarded as mean longshore current
Komar and Inman, 1970
um : orbital velocity
Komar, 1979
Hbr : root-mean-square wave breaker height
Hbs : significant wave breaker height
Shore protection manual, 1984
tanβ : beach slope

16. Observed longshore current
Wave height and current at surf zone

17. Observed cross-shore current
Four conditions

18. Recent study-1
Hasaki coast of Japan

19. Recent study-1 Marine climate: height and direction of wave and wind
Longshore current

20. Recent study-1
Longshore current in northward or southward directions

21. Recent study-1 shear stress at the bottom
Wind induced shear stress at the surface

22. Recent study-1
Radiation stress
And shear stress at the bottom

23. Recent study-1
Longshore current of different season

24. Recent study-2

25. Recent study-2
Wave height variations by seven models

26. Recent study-2
Longshore current by seven models

27. Recent study-2
Comparison with measured longshore current

28. Recent study-2
Comparison with measured longshore current for spilling breaker

29. Recent study-2
Comparison with measured longshore current for plunging breaker

30. Recent study-2
Comparison with measured longshore current for some cases of Leadbetter

31. Recent study-2
Comparison with measured longshore current for some cases of DELII

32. Recent study-2
Comparison with measured longshore current for some cases of HORS

33. Recent study-2
Suggested parameters