Coastal Engineering

Simple Case 1

The most simple case we could analyze was a semi-infinite breakwater in an area of constant depth. Please refer to Figure 2 below for the grid we made in SMS for STWAVE to use.

Figure 2: Semi-infinite breakwater grid.

For this model, we used a constant depth of 8 m, Hs of 2 m, theta of 90°, and T of 7 seconds. Please refer to Table 1 and Figure 3 below for the comparison of our hand calculations to the computer model.

Table 1: Simple Case Calculations compared to STWAVE's results.

Point	r (m)	L (m)	r/L	Beta (rad)	Theta (rad)	Kd	Hi (m)	Hd (m)	STWAVE	% Difference
1	21.21	55.22	0.38	0.79	1.57	0.37	2	0.74	0.62	-16.2
2	10	55.22	.181	90	1.57	.5	2	1	1.35	35

Figure 3: STWAVE results for Simple Case 1 (d = 8 m, Hs = 2 m, T = 7 sec, theta = 90°).

Simple Case 2

This next case came from one of our class homework problems. It involved an L-shaped breakwater with dimensions 250m by 400m (see Figure 4 below). The depth inside of the breakwater varied linearly from 8 m to 2 m at a point 50 m to the right of the left vertical breakwater. The wave characteristics used were the same as the previous problem with one change: theta = 45° (instead of 90°).

Figure 4: Simple Case 2.

Figure 5: Mesh of the depth contours for Simple Case 2. The different colors represent different depths, with blue representing 8m, and red representing 2m.

Although when compared to a real world example this scenario was simple, the hand calculations became quite tedious. Wave diffraction and refraction could be calculated, however wave reflection was difficult to model by hand. Therefore, the results of our hand calculations for this case are not certain.

Table 2: Results for Refraction and Diffraction for Simple Case 2.

Simple Case 2

Refraction:	Bottom slope = .0171

Break. Dist. (m)	Dx (m)	d (m)	C (m/s)	T (sec)	Lo (m)	L1 (m)	L2 (m)	L (m)	Alpha (rad)	k (1/m)	n	Kr	Ks
400	0	8.00	7.90	7.00	76.44	58.05	53.45	55.75	0.79	0.11	0.81
350.00	50.00	7.15	7.56	7.00	76.44	55.54	51.11	53.33	0.74	0.12	0.82	0.98	1.01
300.00	50.00	6.29	7.18	7.00	76.44	52.70	48.54	50.62	0.70	0.12	0.84	0.98	1.01
250.00	50.00	5.44	6.76	7.00	76.44	49.49	45.71	47.60	0.65	0.13	0.86	0.98	1.02
200.00	50.00	4.58	6.28	7.00	76.44	45.84	42.54	44.19	0.59	0.14	0.88	0.98	1.03
150.00	50.00	3.73	5.74	7.00	76.44	41.66	38.94	40.30	0.54	0.16	0.90	0.98	1.03
100.00	50.00	2.87	5.10	7.00	76.44	36.79	34.73	35.76	0.47	0.18	0.92	0.98	1.05
50.00	50.00	2.02	4.32	7.00	76.44	30.97	29.62	30.29	0.39	0.21	0.95	0.98	1.07
											average	0.98	1.03
Diffraction:

r (m)	L (m)	r/L	Beta (rad)	Theta (rad)	Kd est.
430.12	30.29	14.20	0.62	0.79	0.32

Reflection:	Kref =	.8

KsKdHi = 1.03.322 = 0.66 => H at 50 m from left end of breakwater (point A) = .66 + Href Href from drawing below ~ 0 => H = .66 m vs. STWAVE result of .4
				% Difference	=-39%

Figure 6: AutoCAD drawing of simplified wave reflection for Simple Case 2. White indicates the incident wave, blue indicates the first reflected wave, and green indicates the second reflected wave.

Figure 7: Wave height results from STWAVE.

Conclusions

These simple examples show that STWAVE produces different wave heights than our hand calculations. In the first simple case, STWAVE's result was about 16.2% lower and 35% higher than we had calculated for two different areas behind the breakwater. In the second simple case, STWAVE's result was about 39% lower than we had calculated. However, as previously stated, our hand calculations for this second case are not definite. It was noted in the Background section that STWAVE is said to have a 5% accuracy. Our results did not show this, and this could be due to quite a few reasons. The first being that the reflection coefficient that STWAVE uses may be different than what we assumed (.8). Next, STWAVE requires the spectral energy frequency to be >1, however our hand calculations assumed 1. Third, STWAVE has a much more detailed analysis of reflection than what is possible to do by hand. Finally, as noted in the background, STWAVE uses a numerical model for diffraction that is dependent on grid size. We used a different physical model in our hand calculations.