Assessment of shallow water random wave-induced scour at the trunk section of breakwaters using deep water wind and wave conditions

This article provides a simple analytical method giving estimates of random wave-induced scour at the trunk section of vertical-wall and rubble-mound breakwaters in shallow water from deep water wind and wave conditions. Results are exemplified by using a Pierson-Moskowitz model wave spectrum for deep water wind waves with the mean wind speed at the 10 m elevation above the sea surface as the parameter. The significant value of the scour depth within a sea state of random waves is provided and an example typical for field conditions is given. The method should serve as a useful tool for assessing shallow water random wave-induced scour based on input from deep water wind and wave conditions.acceptedVersio

Time scale for scour beneath pipelines due to long-crested and short-crested nonlinear random waves plus current

This article derives the time scale of pipeline scour caused by 2D (long-crested) and 3D (short-crested) nonlinear irregular waves and current for wave-dominant flow. The motivation is to provide a simple engineering tool suitable to use when assessing the time scale of equilibrium pipeline scour for these flow conditions. The method assumes the random wave process to be stationary and narrow banded adopting a distribution of the wave crest height representing 2D and 3D nonlinear irregular waves and a time scale formula for regular waves plus current. The presented results cover a range of random waves plus current flow conditions for which the method is valid. Results for typical field conditions are also presented. A possible application of the outcome of this study is that, e.g., consulting engineers can use it as part of assessing the on-bottom stability of seabed pipelines.publishedVersio

Note on estimating bed shear stress caused by breaking random waves

This note presents a method of how the bed shear stress caused by breaking random waves on slopes can be estimated. This is obtained by adopting the Sumer et al. (2013) bed shear stress formula due to spilling and plunging breaking waves on hydraulically smooth slopes combined with the Myrhaug and Fouques (2012) joint distribution of surf similarity parameter and wave height for individual random waves in deep water. The conditional mean value of the maxima of mean bed shear stress during wave runup given wave height in deep water is provided including an example for spilling and plunging breaking random waves corresponding to typical field conditions. Another example compares the present results with one case from Thornton and Guza (1983) estimating the wave energy dissipation caused by bed shear stress beneath breaking random waves.publishedVersio

Joint description of waves and currents applied in a simplified load case

In order to perform a more accurate analysis of marine structures, joint probability distributions of different metocean parameters have received an increasing interest during the last decade, facilitated by improved availability of reliable joint metocean data. There seems to be no general consensus with regard to the approach of estimating joint probability distributions of metocean parameters and a general overview of recent studies exploring different joint models for metocean parameters is presented. The main objective of this article is twofold: first to establish a joint distribution of significant wave height and current speed and then to assess the possible conservatism in the Norwegian design standard by applying this joint distribution in a simplified load case. Based on NORA10 wave data and simulated current data, a joint model for significant wave height and current speed at one location in the northern North Sea is presented. Since episodes of wind-generated inertial oscillations are governing the current conditions at this location, a joint conditional model with current speed conditional on significant wave height is suggested. A peak-over-threshold approach is selected. The significant wave height is found to be very well modelled by a 2-parameter Weibull distribution for significant wave height exceeding 8 m, while a log-normal distribution describes the current speed well. This model is used to Monte-Carlo simulate joint significant wave heights and current speeds for periods corresponding to the ultimate and accidental limit states (ULS and ALS), i.e. 100 and 10 000 years. The possible conservatism in the Norwegian design standard is assessed by a simplified case study. The results give a clear indication that the Norwegian design standard in not necessarily conservative, neither at ULS nor ALS level.acceptedVersio

Simulated wind-generated inertial oscillations compared to current measurements in the northern North Sea

This is a pre-print of an article published in Ocean Dynamics. The final authenticated version is available online at: https://doi.org/10.1007/s10236-018-1150-zMeasured current speed data show that episodes of wind-generated inertial oscillations dominate the current conditions in parts of the northern North Sea. In order to acquire current data of sufficient duration for robust estimation of joint metocean design conditions, such as wind, waves and currents, a simple model for episodes of wind-generated inertial oscillations is adapted for the northern North Sea. The model is validated with and compared against measured current data at one location in the northern North Sea and found to reproduce the measured maximum current speed in each episode with considerably accuracy. The comparison is further improved when a small general background current is added to the simulated maximum current speeds. Extreme values of measured and simulated current speed are estimated and found to compare well. To assess the robustness of the model and also the sensitivity of current conditions from location to location, the validated model is applied at three other locations in the northern North Sea. In general, the simulated maximum current speeds are smaller than the measured, suggesting that wind-generated inertial oscillations are not as prominent at these locations and that other current conditions may be governing. Further analysis of the simulated current speed and joint distribution of wind, waves and currents for design of offshore structures will be presented in a separate paper.submittedVersio

An Overview of Wave Impact Forces on Offshore Wind Turbine Substructures

AbstractOffshore wind turbines are always subjected to highly varying aerodynamic and hydrodynamic loads which dictate the design phase of the wind turbine substructures. The breaking wave forces yield the highest hydrodynamic loads on substructures in shallow water, particularly plunging breaking waves. Due to the complex and transient nature of the impact forces, the description requires more details concerning the physical properties of breaking waves and the response of the structure. The objective of this paper is to give an overview of the previous and recent research on wave impact forces and the key issues pertaining to these forces on offshore wind turbine substructures

Scour and Burial of Spherical Bodies, Short Cylinders, and Truncated Cones Induced by Bichromatic and Bidirectional Waves

This article provides a method by which the scour and self-burial of spherical bodies, short cylinders, and truncated cones that are induced by bichromatic and bidirectional waves could be derived. The empirical scour and self-burial depth formulas for spherical bodies, short cylinders, and truncated cones are used with a bed shear stress model beneath bichromatic and bidirectional waves. Examples of the results are given for unidirectional bichromatic and bidirectional monochromatic waves. The results appear to agree qualitatively with physical expectations.acceptedVersio

SEABED SHEAR STRESS SPECTRUM FOR VERY ROUGH BEDS

ABSTRACT The spectrum of seabed shear stresses at beds with large roughness beneath ocean surface waves in finite water depth is derived by using the wave friction factor for large roughness. It is expressed in terms of the transfer function between the waves at the surface and the shear stress at the bed, and the wave spectrum in finite water depth, which is obtained by multiplying the deep water wave spectrum with a depth correction factor. The seabed shear stress spectrum for laminar flow, which is of practical interest for flow over muds, is also given as a reference case. Examples are included to illustrate the applicability of the seabed shear stress spectrum for practical purposes using data typical for field conditions, both for very rough beds and mud beds

CFD investigation on scour beneath different configurations of piggyback pipelines under steady current flow

Scour beneath piggyback pipelines laid on a sandy seabed is numerically investigated by solving two-dimensional (2D) Unsteady Reynolds-averaged Navier-Stokes (URANS) equations. The fluid flow and the sediment transport are resolved using a two-phase flow Eulerian-Eulerian numerical solver SedFoam based on the open-source code OpenFOAM. A parametric study is performed for different Shields parameters defined as θ = U2 f /(s− 1)gd50 of 0.068, 0.18 and 0.33 where Uf denotes the shear friction velocity on the seabed, the specific density of the sediment grains is s = ρs /ρf where ρs and ρf are the density of the solid and fluid phases, respectively, g is the gravitational acceleration and d50 is the median grain diameter. Scour processes beneath piggyback pipelines under steady current flow condition are studied for different gap ratios of G/D = 0, 0.15, 0.25 and 0.35 between the main cylinder and the additional ones with a diameter ratio of d/D = 0.3 between them. Mesh convergence studies based on the scour depth and the sediment profile are performed to obtain an appropriate grid resolution. A validation study is performed by comparing the scour depth of the single cylinder cases with the published experimental results obtained by Mao (1986). The effects of different θ and geometry configurations on the scour depth and the sediment profile are obtained and discussed.publishedVersio

Simulation of breaking focused waves over a slope with a cfd based numerical wave tank

Extreme wave conditions are always identified with large-amplitude breaking waves in shallow waters. Focused waves can often be used to describe extreme waves which evolve during the nonlinear wave-wave interaction, occurring at one point in space and time. Under- standing breaking focused waves has many design-related implications for the design of offshore wind turbine (OWT) substructures in shallow waters. The main objective of the paper is to model breaking focused waves over a sloping seabed and study the breaking characteristics us- ing the open-source CFD model REEF3D. The numerical model describes the two-phase flow using the incompressible Reynolds-Averaged Navier-Stokes (RANS) equations together with the continuity equation. The model uses a fifth-order WENO scheme for convection discretization and a third order Runge-Kutta scheme for time discretization along with the level set method to obtain the free surface, yielding accurate wave propagation in the numerical wave tank. Solid boundaries are accounted through the ghost cell immersed boundary method. The free surface is modeled with the level set method. Turbulence is described with the two-equation k −ω model. In the numerical wave tank, the focused waves are generated using a single flap-type maker theory. The numerical results are in good agreement with experimental results for complex free surface elevations measured at several locations along the wave tank. The numerical aspects related to the development of the breaking process are investigated together with the evolution of focusing wave group in the numerical wave tank. Further, the study also examines the free surface flow features that evolve during the breaking process