Extreme wave statistics of random waves propagating over a 3D varying bathymetry

<p>Non-uniform bathymetry may modify the wave statistics for both surface elevation and velocity field.<br>Laboratory evidence reported by Trulsen et al. (2012) shows that for a relatively long unidirectional<br>waves propagating over a sloping bottom, from deep to shallower water, there can be a local maximum<br>of kurtosis and skewness in surface elevation near the edge of the shallower side of the slope. Recent<br>laboratory experiments of long-crested irregular waves propagating over a shoal by Trulsen et al. (2020)<br>reported that the kurtosis of horizontal velocity field have different behaviour from the kurtosis of surface<br>elevation where the local maximum of kurtosis in surface elevation and horizontal velocity occur at<br>different location.<br>In present work, we utilize numerical simulation to study the evolution of skewness and kurtosis for<br>irregular waves propagating over a three-dimensional varying bathymetry. Numerical simulations are<br>based on High Order Spectral Method (HOSM) for variable depth as described in Gouin et al. (2017)<br>for wave evolution and Variational Boussinesq model (VBM) as described in Lawrence et al. (2021) for<br>velocity field calculation.</p><p> </p><p>References</p><p>GOUIN, M., DUCROZET, G. & FERRANT, P. 2017 Propagation of 3D nonlinear waves over an elliptical<br>mound with a High-Order Spectral method. Eur. J. Mech. B Fluids 63, 9–24.<br>LAWRENCE, C., GRAMSTAD, O. & TRULSEN, K. 2021 Variational Boussinesq model for kinematics<br>calculation of surface gravity waves over bathymetry. Wave Motion 100, 102665.<br>TRULSEN, K., RAUSTØL, A., JORDE, S. & RYE, L. 2020 Extreme wave statistics of long-crested<br>irregular waves over a shoal. J. Fluid Mech. 882, R2.<br>TRULSEN, K., ZENG, H. & GRAMSTAD, O. 2012 Laboratory evidence of freak waves provoked by<br>non-uniform bathymetry. Phys. Fluids 24, 097101.</p>

ROGUE WAVE ASYMMETRY IN THE DIRECT NUMERICAL SIMULATIONS OF DIRECTIONAL JONSWAP WAVES

The asymmetry between the troughs from the rear and front sides of rogue waves is the particular object of the present study. In our previous simulations of unidirectional waves the typical picture of a rogue waves possesses the trend that most of the rogue waves where characterized by deeper rear troughs. In the present work we broaden the discussion of the rogue wave front-to-crest asymmetry to the directional case. The direct numerical simulation of primitive water equations is an affordable alternative to the in-situ or laboratory measurements, in particularly when the interest is focused on the long-term evolution or on the detailed consideration of the water wave movement in space and time. In this work we simulate irregular surface waves in the hydrodynamic equations using the High-Order Spectral Method, and focus on the so-called rogue waves.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/plseXdjpE6c

On the accuracy and applicability of a new implicit Taylor method and the high-order spectral method on steady nonlinear waves

This paper presents an investigation and discussion of the accuracy and applicability of an implicit Taylor (IT) method versus the classical higher-order spectral (HOS) method when used to simulate two-dimensional regular waves. This comparison is relevant, because the HOS method is in fact an explicit perturbation solution of the IT formulation. First, we consider the Dirichlet–Neumann problem of determining the vertical velocity at the free surface given the surface elevation and the surface potential. For this problem, we conclude that the IT method is significantly more accurate than the HOS method when using the same truncation order, M , and spatial resolution, N , and is capable of dealing with steeper waves than the HOS method. Second, we focus on the problem of integrating the two methods in time. In this connection, it turns out that the IT method is less robust than the HOS method for similar truncation orders. We conclude that the IT method should be restricted to M = 4, while the HOS method can be used with M ≤ 8. We systematically compare these two options and finally establish the best achievable accuracy of the two methods as a function of the wave steepness and the water depth.

Systematic Experimental Validation of High-Order Spectral Method for Deterministic Wave Prediction

The applicability of the High-Order Spectral Method (HOSM) as a very fast non-linear method for deterministic short-term wave prediction is discussed within this paper. The focus lies on the systematic experimental validation of the HOSM in order to identify and evaluate possible areas of application as well as limitations of use. For this purpose, irregular sea states with varying parameters such as wave steepness and underlying wave spectrum are addressed by numerical simulations and model tests in the controlled environment of a seakeeping basin. In addition, the influence of the propagation distance is discussed. For the evaluation of the accuracy of the HOSM prediction, the surface similarity parameter (SSP) is utilized, allowing a quantitative validation of the results. The results obtained are compared to linear wave prediction to discuss the pros and cons of a non-linear deterministic short-term wave prediction. In conclusion, this paper shows that the non-linear deterministic wave prediction based on HOSM leads to a substantial improvement of the prediction quality for moderate and steep irregular wave trains in terms of individual waves and prediction distance.

Realistic Design Waves for Wave-in-Deck Problems

Due to subsidence, unrealistic environmental assumptions in design or other factors, many fixed offshore installations around the world are prone to large impact forces on the super-structure. Too often, unexpected damages are found, and more accurate analyses reveal the need for reinforcement to comply with the relevant rules and regulations. The common analytical practice is to compute impact forces using 5th order Stokes waves in a CFD solver, with the crest height set to the relevant return period. Using this approach implicitly introduces a series of unrealistic assumptions, and cannot necessarily be expected to produce the force of the desired return period. In the present work, we propose a framework to better estimate the true waves producing the 100-year wave-in-deck forces in a typical North Sea environment. This is done by a long-term analysis of wave-in-deck force, hierarchically using several screening filters and solvers of different complexity. The main facilitator is an efficient High-Order Spectral Method, which at the final level is used as initial and boundary conditions in CFD. The resulting waves are short crested and may break — producing very high crest velocities that are normally not accounted for in standard engineering practice.