Understanding of WAVE hydrodynamics and its effects are important for engineers and scientists. Important insights may be gained from laboratory studies. Often the WAVEs are simulated in laboratory flumes do not have the full characteristics of real sea WAVEs. It is then necessary to present reliable methods of WAVE generation in WAVE flumes. In this paper, the results of numerically simulated water WAVEs using different methods are presented. A model was developed to simulate water WAVE profile using DSA, NAS and WNDF methods. The results showed that although DSA method provides better agreement between output and target spectra, it is associated with non realistic simulation of sea WAVEs. In the other hand WNDF method involves better stochastic WAVE characteristics if a qualitative white noise is used. It is also possible to put some controls on WAVE characteristics as input to WNDF model.

High-order nonlinearities may be an important cause of freak WAVE generation, however, it is still unclear how to stimulate the generation of freak WAVEs in deep-water RANDOM WAVEs. This study employs the modified fourth-order nonlinear Schrӧdinger equation (mNLSE) to simulate the occurrence of freak WAVEs and analyses the influence of high-order nonlinearities on the evolution of RANDOM WAVE trains described initially by the JONSWAP spectrum. In the evolution of freak WAVE generation, variations in the linear and nonlinear terms of the mNLSE are displayed with the nonlinear growth of surface elevations. For comparison, the corresponding results from the cubic nonlinear Schrӧdinger equation (CSE) and the linear Schrӧdinger equation (LSE) are also obtained. Power spectra and spectral peakedness curves in the evolution of the WAVE train are also given to analyze the potential mechanism of freak WAVE formation. Additionally, the probabilities of freak WAVE appearances are estimated for different initial parameters and different governing equations. The results show that the fourth-order nonlinearity plays an important role in the generation of freak WAVEs, but this single factor is not enough to generate freak WAVEs, and freak WAVE occurrence is the contribution of multiple factors to the unstable evolution of the WAVE train. The higher-order nonlinearity, concentrated initial RANDOM phases, larger WAVE steepness, narrower initial spectral width, and smaller sideband instability parameter can increase the probability of freak WAVE generation.

The development of marine structures for harnessing natural resources, especially clean energy technologies like offshore wind turbines, is crucial. WAVEs are a primary design force, significantly impacting the stability and performance of these structures. However, the lack of precise field data and comprehensive WAVE records poses challenges. This study proposes a novel method to generate accurate artificial WAVE records efficiently, addressing the limitations of conventional approaches that requires extensive WAVE data and time-consuming analyses. Field observations of WAVE duration and heights in the Persian Gulf were analyzed, and a modified JONSWAP spectrum, tailored to the region, was used to generate RANDOM WAVE records with fewer required WAVEs. The study also examined the impact of WAVE irregularity on structural forces by comparing forces on a vertical cylinder from the generated WAVE records and a 100-year return period WAVE. Results show that the proposed method achieves high accuracy while significantly reducing computational effort. It successfully identifies spectral peaks and generates reliable WAVE records using only 50 WAVEs, reducing engineering time by up to 90% while maintaining 97.1% accuracy. The study also introduces a relationship to estimate WAVE duration based on field data, proposing a 3-hour duration for 100-year return period WAVEs. The findings highlight the method’s effectiveness in improving WAVE load analysis for marine structures in data-scarce regions like the Persian Gulf, offering a robust framework for future research and design optimization.

Efficiency of numerical methods is an important problem in dynamic nonlinear analyses. It is possible to use of numerical methods such as beta- Newmark in order to investigate the structural response behavior of the dynamic systems under RANDOM sea WAVE loads but because of necessity to analysis the offshore systems for extensive time to fatigue study it is important to use of simple stable methods for numerical integration. The modified Euler method (MEM) is a simple numerical procedure which can be effectively used for the analysis of the dynamic response of structures in time domain. It is also very effective for response dependent systems in the field of offshore engineering. An important point is investigating the convergence and stability of the method for strongly nonlinear dynamic systems when high initial values for differential equation or large time steps are considered for numerical integrating especially when some frequencies of the system is very high. In this paper the stability of the method for solving differential equation of motion of a nonlinear offshore system (tension leg platform, TLP) under RANDOM WAVE excitation is presented. In this paper the stability criterion and the convergence of the numerical solution for critical time steps are presented.