## Numerical Modelling of Irregular waves and Irregular Wave Forces with REEF3D

##### Abstract

In this study, the irregular wave generation using the numerical model REEF3D is tested and validated. The testing for the empty wave tank is done in order to test the irregular wave generation and the propagation. The influence of the different numerical and hydrodynamic parameters on the results is studied. The parameters varied are the grid size, the peak wave period, the number of linear wave components
and the length of simulation duration. Grid convergence test shows that for a coarser grids dx = 0.05 m and dx = 0.025 m, the numerical wave spectrum does not show a good match with the theory. The results with a grid size dx = 0.01 m show a very good agreement with the theoretically predicted spectrum. Thus, the grid size of dx = 0.01 m is chosen for the further testing.
Effects on the results by changing the number of linear wave components are also studied. Tests are performed for the linear wave component, N = 25 and 100. But, effects by changing the value of N do not seem to be significant. For the further testing, a value of N = 25 is chosen. Testing is also done for the different peak periods Tp = 2.50 s, 2.00 s, 1.18 s and 0.80 s. It is observed that for a higher value of the peak period, the wave spectrum is relatively narrow and all the energy is limited to the lower frequencies. As the peak wave period becomes less, the wave energy tends to spread over a wider range of the frequencies, and value of the spectrum peak is also reduced because of the widening of the spectrum. The numerical results show a good match for the higher peak wave periods but for a peak wave period Tp = 0.80 s, the results do not match with theory. This is due to the fact that the waves are shorter in this case and the grid points per wavelength are not sufficient for a good simulation. Thus, a higher grid resolution is required for this peak wave period.
Tests with a different length of simulation time show that the length of simulation affects the results as well. Tests with a shorter duration show that the waves need some time to evolve fully and to give good results. The tests with the simulation duration = 60 s, 120 s and 240 s show that the waves with higher frequencies are underrepresented for the wave gauges located at the farther locations in the working zone of the flume. Simulation duration = 500 s gives good results for all the wave gauges.
Testing is also done for the simulation duration of 1000s and 3600 s, but the results show that the improvement is not very significant and they are computational very expensive. So, for a good optimization between the accuracy and the computational time, a simulation duration of 500 s is chosen.
In the next section, the irregular wave propagation over a submerged bar is simulated. The numerical results are compared with the experimental observations. Simulations are performed for the two cases. One non-breaking wave case with a significant wave height, Hs = 0.022 m and second breaking wave case with a significant wave height, Hs = 0.05 m. Simulations with case 1 shows that the numerical model predicts accurately the hydrodynamical phenomena as observed in the experiment. The incident wave spectrum for the wave gauge located before the bar, shows that the spectrum is narrow with a single peak and most of the energy is restricted to a lower frequency range. Shoaling is expected as the wave propagates over the upslope due to decreasing water depth, this is clearly shown in the results by both experimental and numerical results. As, the wave propagates the wave spectra tends to spread over a wider range of frequencies and for the wave gauge located on the downslope of the bar, results show that the energy gets distributed more towards the higher frequencies than the lower frequencies. Also, some secondary small peaks disappear, this is shown both by the numerical and the experimental results. Simulations with case 2 show that breaking occurs, due to a larger wave height as compared to the water depth. Rest all hydrodynamic phenomena is same as in the case 1 apart from the breaking. Comparison of the last two wave gauges, which are located on the at crest before the breaking occurs and on the downslope, respectively that the dissipation of energy takes place while breaking. This is shown by the lowering of the primary peak, also more energy is distributed to the higher frequency range.
The next section of this study validates the numerical model for the wave force on a horizontal submerged cylinder. The numerical model is validated with the regular waves. The numerical wave forces for regular waves are compared with the experimental results for the same setup. Numerical model is tested for the cylinder with a diameter, D = 0.21 m. The simulations are performed for the grid sizes, dx = 0.05 m. The numerical force results show a very good agreement with the experimental force results. In the next section, a study is made for the irregular wave force. The simulations are performed for the grid sizes, dx = 0.25 m, 0.10 m and 0.05 m. The results with a grid size, dx = 0.25 m show a peak value much before than observed by the experiments and after that the spectrum decays very steeply. For the grid size, dx = 0.10 m the numerical force spectrum has a lower peak value than the experimental force spectrum. Also, the numerical spectrum is wider as compared to the experimental spectrum. Results with a grid size, dx = 0.05 m show a very good match with the experimental results. Thus, a grid size, dx = 0.05 m is chosen for the further study. Later, testing is done by varying the KC numbers by changing the value of the peak wave period, Tp. Results show that the wave spectrum with a higher value of Tp have a higher peak value as compared to the wave spectrum with lower value of Tp. Also, the spectrum is relatively narrow for higher value of Tp. Thus, it can be concluded that the longer waves tend to exert a higher wave force on a horizontal submerged cylinder. It can be inferred that the numerical model REEF3D is able to simulate the
similar behaviour as shown by the experiments for the horizontal submerged cylinder.
In the last section, a study is done on the behaviour of wave force on a vertical cylinder of diameter, D = 0.5 m for both the regular and the irregular waves. Firstly, the validation is done with the regular waves by comparing the regular wave forces with the force calculated using the Morison formula. Next, the numerical simulations are run for the irregular waves with the significant wave height, Hs = 0.03 m, the peak wave period, Tp = 1.2 s. Tests are run for the three different grid sizes, dx = 0.25 m, 0.10 m and 0.05 m. A similar shape of the spectra is shown by all the cases. Two peaks are observed in the wave force spectrum. First peak observed at lower frequency has a lower value than the second peak observed at the higher frequency. The simulation with the coarse grid, dx = 0.25 m show significantly lower peaks as compared to the fine grid results. Results with the finer grids, dx = 0.10 m and 0.05 m tend to converge and show almost the similar peaks and a similar behaviour. A grid size, dx = 0.05 m is chosen for the further study. Numerical simulations are run for different values of peak period, Tp. Three values of Tp =1.0 s, 1.2 s and 1.4 s are chosen. The results show that the waves with a higher value of Tp tend to have a higher peak value of the force spectrum. It can be inferred from this study that the longer waves will exert a higher value of force on a vertical cylinder. A study is also done to compare the regular and the irregular wave force spectrum keeping other parameters same. Two cases are studied, case 1 with the regular waves of H = 0.03 m and T = 1.2 s, which is compared with the irregular waves of Hs = 0.03 m and Tp = 1.2 s. Case 2 with the regular waves of H = 0.03 m and T = 1.0 s which is compared with the irregular waves of Hs = 0.03 m and Tp = 1.2 s. The results show that for both the cases, the regular wave force spectrum shows a higher peak value than the irregular wave force spectrum. The shape of the regular wave force spectrum is symmetric and similar to the Bell's curve. While, a irregular wave spectrum is asymmetric.
The present study concludes that the numerical model REEF3D can be successfully used to generate and study the irregular waves propagation, their interaction with a structure, the wave force calculations on the horizontal and the vertical cylinder. The numerical model is able to simulate the similar behaviour as observed in the experiments. Thus, the REEF3D can be used as a good tool to make numerical
simulations for irregular waves.