COURSEWORK BRIEFING SHEET COURSE MODULE (and code): ASSIGNMENT TITLE: Coastal and Estuary Processes (CIVE487) Wave Theory Aims: The exercise is designed to allow students to (1) use linear wave theory for the solution of a series of simple problems of practical importance and to consider its limits of applicability and (2) carry out time domain analysis for the short-term random wave record. Details: 1. Use linear wave theory to complete the following table: Wave height, Water depth, Wave- length, H (m) d (m) L (m) Wave period, T (s) Wave celerity, C (m/s) (i) 3 5+i 40 (ii) 2 10+i 7 (iii) 1 15+i 8 i is the last digit of your student ID 2. What parameters are used to establish whether waves may be satisfactorily described by linear wave theory? [30 marks] [10 marks] 3. Classify the wave conditions in question 1 as either linear or non-linear and indicate, for the non-linear condition(s), an analytical theory (or theories) suitable for describing the waves. [10 marks] 4. For the case(s) for which linear wave theory is identified as unsuitable in question 3, note what effects the non-linearity would have on the calculated values in question 1. [10 marks] 5. Estimate the wave group velocity in a water depth of 30m if the wave period is 9s. [10 marks] 6. Estimate the wave power per unit length of wave crest in a train of regular waves if the wave height is 2m, the wavelength is 50m and the water depth is 15m. [10 marks] 7. A wave record taken during a storm is analysed by zero up crossing and contains 205 waves. The average wave height is 1.72m. Using Rayleigh distribution to i) estimate Hs, Hrms and H₁/10- ii) determine the number of wave in the record that would exceed 2.0+i/10 (i is the last digit of your student ID) [20 marks] d/Lo C d/L kd tanh kd sinh kd cosh kd n = 7007 K S 0.0000 0.0010 0.0126 0.079 0.0011 0.0132 0.083 0.0012 0.0138 0,087 0.0013 0.0144 0.091 0,0014 0.0149 0,094 0.0000 0.000 0.000 0.079 0.079 1.003 0.083 0.083 1.003 0,087 0.087 1,004 0.000 1.000 1.000 0.998 2.515 0.998 2.457 0.997 2.404 : 0.090 0,091 1.004 0.997 2.357 0.094 0.094 1.004 0.997 2,314 0.0015 0.0155 0.0016 0.0160 0.100 0.0017 0.0165 0.0018 0.0170 0.0019 0.0174 0.097 0.097 0,097 1,005 0.997 2,275 0.100 0.101 1.005 0.997 2,239 0.104 0.103 0.104 1,005 0.996 2,205 0.107 0.106 0.107 1.006 0.996 2,174 0.109 0.109 0.110 1.006 0.996 2,146 0.0020 0.0179 0.0022 0.112 0.112 0.113 1,006 0.996 2,119 0.0188 0.118 0.117 0.118 1.007 0,0024 0.995 2.069 0.0196 0,123 0,122 0.123 0.0026 1.008 0.995 2.025 0,0204 0,128 0.127 0.129 1.008 0.995 1.986 0.0028 0.0212 0.133 0.132 0.133 1.009 0.994 1,950 0,0030 0,0219 0.138 0.137 0.138 1.009 0,0032 0,994 1.917 0,0226 0.142 0.141 0.143 1,010 0,0034 0,0233 0,0036 0.993 1,887 0.147 0,146 0.147 1.011 0,993 1.859 0,0240 0.151 0.150 0.0038 0.152 1.011 0.992 1.834 0.0247 0.155 0.154 0.156 1,012 0.992 1.810 0,0040 0.0253 0.159 0.158 0,160 1,013 0.992 0.0042 0.0044 0.0266 0.167 0.0046 0,0272 0.171 0.0048 0,0278 1.787 0.0260 0.163 0.162 0,164 1,013 0.991 1,766 0.166 0,168 1.014 0.991 1.746 0.169 0.172 1.015 0.990 1.727 0.175 0.173 0,175 1.015 0.990 1,710 0,0050 0.0284 0,0055 0.178 0,176 0.179 1.016 0.990 1,693 0.0298 0,187 0.185 0.188 0,203 0,0095 0.0060 0.0311 0.195 0.0065 0.0324 0.0070 0,0336 0.0075 0,0348 0.221 1.024 0.0080 0.0360 0.226 0.222 0.228 1,026 0,0085 0,0371 0,233 0.229 0.235 1.027 0.0090 0.0382 0.240 0,236 0,242 0.0393 0.247 0.242 0.249 0.193 0.197 0,201 0.205 1.018 0,989 1.019 0.987 1.021 1.654 1,620 0,986 1,589 0,211 0.208 0,213 1.022 0,985 1,561 0,219 0,215 0.984 1,536 0.983 1.512 0.982 1.491 1,029 0.981 1.471 1.031 0.980 1.452 Linear wave theory, table of functions C d/Lo d/L kd tanh kd sinh kd cosh kd n = KS 5 0.0100 0.0403 0.253 0.248 0.256 1.032 0.979 1,435 0.0110 0,0120 0.0423 0,266 0.260 0.0443 0.278 0,269 1.036 0,271 0.282 0,0130 0.0140 0,0461 0.290 0.0479 0,282 0,294 0,977 1.403 1,039 0,975 1,375 1,042 0.973 1.350 0.301 0,292 0.306 1.046 0.971 1,327 0.0150 0.0496 0,0160 0,0513 0.322 0.0170 0,0530 0.333 0.321 0.0180 0.0546 0,312 0,302 0.317 1.049 0.969 1.307 0,312 0.328 1.052 0.967 1.288 0.339 1.056 0.965 1,271 0.343 0.330 0.350 1.059 0,963 1.255 0.0190 0,0561 0.353 0,339 0.360 1.063 0.961 1.240 0,0200 0.0576 0,362 0,347 0.370 1.066 0.959 0,0220 0.0606 1.226 0.381 0,363 0.390 1.073 0.955 0.0240 0.0634 1.201 0.398 0,379 0.409 1.080 0.951 0.0260 1.179 0.0661 0,416 0,393 0.428 1.088 0.947 0.0280 0.0688 1,159 0.432 0.407 0.446 1.095 0.943 1.141 0.0300 0.0713 0.448 0,420 0.463 1,102 0,939 1.125 0.0320 0,0738 0.464 0.0340 0,0763 0.479 0,0360 0.0787 0,0380 0,0810 0.433 0.481 1.110 0.935 1.111 0.446 0.509 0,494 0.458 0.469 0.498 0.515 1.125 0.531 1.132 1.117 0.931 1.098 0,927 1.086 0.923 1.075 0,0400 0.0833 0.0440 0.0420 0.0855 0,537 0,491 0.523 0.480 0.548 1.140 0.919 1.064 0.564 1.148 0.915 1.055 0.0877 0,551 0,501 0.580 1,156 0.911 1,046 0,0460 0,0480 0.0920 0.578 0.0899 0.565 0.512 0,595 1.164 0.908 1,038 0,521 0,611 1.172 0.904 1.030 0,0500 0.0942 0,592 0.531 0,627 1.180 0.900 0,0550 1,023 0,0993 0,624 0.554 0.665 1.201 0.890 1.007 0,0600 0,1043 0.655 0.0650 0.1092 0.686 0.0700 0,1139 0,716 0,575 0.703 1.223 0.881 0.993 0,595 0.741 1,245 0.872 0.981 0,614 0,779 1.267 0.863 0.971 0,0750 0.1186 0,745 0.632 0.816 0.0800 0.1232 0,774 0.649 0,0850 0,1277 0,803 0.665 0.0900 0,1322 0.831 0,681 0.0950 0.1366 0,858 0.695 1,291 0.854 0.962 0,854 1,315 0.845 0.955 0.892 1.340 0.836 0,948 0.929 1,365 0.827 0.968 1.392 0.942 0.819 0.937 Linear wave theory, table of functions (continued) C d/Lo d/L kd tanh kd sinh kd cosh kd n = 0.1000 0.1100 0,1410 0,886 0.1496 0,1200 0.1581 0,994 0.1300 0,1666 0.1400 0.1750 0.709 1,006 1,419 0.810 0.933 0.940 0.735 1.085 1.475 0.794 0.926 0,759 1,165 1,536 0.778 0.920 1.047 0.780 1,248 1.600 0.762 0.917 1.099 0,800 1,334 1.668 0,747 0.915 0.1500 0.1833 1.152 0,818 1.424 1.740 0,732 0.913 0.1600 0.1916 1.204 0.835 1,517 1.817 0,718 0.913 0.1700 0,2000 1.256 0.850 1.614 1,899 0.705 0.913 0,1800 0.2083 0.1900 0.2167 1.362 0.2000 0.2200 0.2421 1,309 0,864 1,716 1.986 0.692 0.914 0.877 1.823 2,079 0.680 0.916 0.2251 1,414 0.888 1.521 0.909 0,2400 0.2592 1,629 0.926 1.936 2,179 2,397 2.451 2.179 0.668 0.918 0.2600 0,2766 1.738 0.940 2.755 2,647 2,931 0.2800 0,2942 1.849 0.952 3,097 3.255 0,646 0,923 0.626 0.608 0.936 0.592 0.942 0.929 0.3000 0,3121 1.961 0,961 3,483 3.624 0.578 0.949 0,3200 0,3400 0.3486 2.190 0.3303 2,075 0,969 3,920 4,045 0,565 0,955 0,975 4,414 4.525 0.555 0.961 0.3600 0.3672 2.307 0.3800 0.3860 2,425 0.980 4,973 5.073 0.546 0.967 0.984 5,608 5,697 0.538 0.972 0,4000 0.4050 0.4200 0,4241 2,665 0.4400 0,4434 2.786 0.4600 0.4628 2,544 0.988 6,329 6,407 0.531 0.976 0.990 7.147 7.216 0.526 0.980 0.992 8.075 8.137 0.521 0.983 2,908 0.994 9.129 9.183 0,517 0.986 0,4800 0.4822 3.030 0,995 10,32 10,37 0.514 0,988 0.5000 0.5018 3.153 0,996 11,68 11,73 0.512 0.990 0,5500 0,5511 3,463 0.998 15,93 15,96 0.507 0,994 0.6000 0.6006 3.774 0,6500 0,6504 4.086 0.999 29.75 29.77 0,502 0.999 21,76 21,79 0.504 0.997 0,998 0.7000 0,7002 4.400 1,000 40.70 40,71 0.501 0,999 0.7500 0.7501 4,713 1,000 55,70 55.71 0.501 0,8000 0.8001 5.027 1.000 76,23 76,24 0.500 0,8500 0.8500 5.341 1,000 104.4 104.4 0.500 0.9000 0.9000 5,655 1.000 142,9 142,9 0.500 0.9500 0.9500 5.969 1.000 195,6 195.6 0.500 1.0000 0.999 1.000 1.000 1.000 1.000 1.0000 6.283 1.000 267.8 267,8 0,500 1.000 Linear wave theory, table of functions