Short-crested Nonlinear Random Waves Research Articles

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.

Burial and Scour of Short Cylinders and Truncated Cones Due to Long-Crested and Short-Crested Nonlinear Random Waves Plus Currents

This paper provides a practical stochastic method by which the burial and scour depths of short cylinders and truncated cones exposed to long-crested (two-dimensional (2D)) and short-crested (three-dimensional (3D)) nonlinear random waves plus currents can be derived. The approach is based on assuming the waves to be a stationary narrow-band random process, adopting the Forristall second-order wave crest height distribution representing both 2D and 3D nonlinear random waves. Moreover, the formulas for the burial and the scour depths for regular waves plus currents presented by previous published work for short cylinders and truncated cones are used.

Burial and scour of truncated cones due to long-crested and short-crested nonlinear random waves

This paper provides a practical stochastic method by which the burial and scour depths of truncated cones exposed to long-crested (2D) and short-crested (3D) nonlinear random waves can be derived. The approach is based on assuming the waves to be a stationary narrow-band random process, adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D nonlinear random waves. Moreover, the formulas for the burial and the scour depths for regular waves presented by Catano-Lopera et al. (2011) for truncated cones are used. An example of calculation is also presented.

Effects of Sand-Clay Mixtures on Scour Around Vertical Piles Due to Long-Crested and Short-Crested Nonlinear Random Waves

This note provides a practical stochastic method by which the effects of sand-clay mixtures on the maximum equilibrium scour depth around vertical piles exposed to long-crested (2D) and short-crested (3D) nonlinear random waves can be derived. This is made by using the regular wave formulas for scour depth for sand-clay mixtures by Dey et al. (2011, Scour at Vertical Piles in Sand-Clay Mixtures Under Waves,” J. Waterway, Port, Coastal, Ocean Eng., 137(6), pp. 324–331) and the stochastic method presented by Myrhaug and Ong (2013, “Scour Around Vertical Pile Foundations for Offshore Wind Turbines Due to Long-Crested and Short-Crested Nonlinear Random Waves,” ASME J. Offshore Mech. Arctic Eng., 135(1), p. 011103). Thus the present results are supplementary to those presented in the latter reference. An example calculation is provided.

Scour Around Vertical Pile Foundations for Offshore Wind Turbines Due to Long-Crested and Short-Crested Nonlinear Random Waves

This paper provides a practical stochastic method by which the maximum equilibrium scour depth around vertical piles exposed to long-crested (2D) and short-crested (3D) nonlinear random waves can be derived. The approach is based on assuming the waves to be a stationary narrow-band random process, adopting the Forristall wave crest height distribution (Forristall, 2000, “Wave Crest Distributions: Observations and Second-Order Theory,” J. Phys. Oceanogr., 30, pp. 1931–1943) representing both 2D and 3D nonlinear random waves, and using the regular wave formulas for scour depth by Sumer et al. (1992, “Scour Around Vertical Pile in Waves,” J. Waterway, Port, Coastal, Ocean Eng., 114(5), pp. 599–641). An example calculation is provided. Tentative approaches to related random wave-induced scour cases are also suggested.

Addendum to “Bottom friction and erosion beneath long-crested and short-crested nonlinear random waves”: Relevance for plug flow formation

The purpose of this note is to point out the relevance and applicability of the results in Myrhaug and Holmedal (2011) for plug flow formation beneath 2D and 3D nonlinear random waves.

Scour around spherical bodies due to long-crested and short-crested nonlinear random waves

This paper provides a practical stochastic method by which the maximum equilibrium scour depth around spherical bodies exposed to long-crested (2D) and short-crested (3D) nonlinear random waves can be derived. The approach is based on assuming the waves to be a stationary narrow-band random process, adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D nonlinear random waves, and using the regular wave formulas for scour and self-burial depths by Truelsen et al. (2005). An example calculation is provided.

Scour around vertical piles due to long-crested and short-crested nonlinear random waves plus a current

This paper provides a practical stochastic method by which the maximum equilibrium scour depth around a vertical pile exposed to long-crested (2D) and short-crested (3D) nonlinear random waves plus a current can be derived. The approach is based on assuming the waves to be a stationary narrow-band random process, adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D nonlinear random waves, and using the empirical formulas for the scour depth by Sumer and Fredsøe (2002). Comparisons are made between the present approach and the Sumer and Fredsøe (2001) data for 2D random waves plus current. An example calculation is provided.

Bottom friction and erosion beneath long-crested and short-crested nonlinear random waves

A practical approach for calculating the bottom shear stress beneath long-crested (2D) and short-crested (3D) nonlinear random waves is provided. The approach is based on assuming the waves to be a stationary narrow-band random process and by adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D nonlinear random waves. Results are presented for laminar, smooth turbulent and rough turbulent flow. Examples are also included to illustrate the applicability of the results for practical purposes using data typical for field conditions; the mobile layer thickness in sheet flow representing rough turbulent flow; erosion of mud representing smooth turbulent flow and deposition of mud representing laminar flow.

A stochastic method for wave run-up on slender circular cylinders due to long-crested and short-crested non-linear random waves

A practical stochastic method for estimating the wave run-up height on a slender vertical circular cylinder for long-crested (two-dimensional (2D)) and short-crested (three-dimensional (3D)) non-linear random waves is provided. This is achieved by using the velocity stagnation head theory in conjunction with a stochastic approach. Here the waves are assumed to be a stationary narrow-band random process. The effects of non-linear waves are included by adopting the Forristall wave crest height distribution representing both 2D and 3D non-linear random waves. A parameter study is provided and, for both 2D and 3D non-linear random waves, the wave run-up height is larger than for linear random waves. In shallow water, when the water is sufficiently shallow, the maximum wave run-up height is larger for 3D waves than for 2D waves. Comparisons are also made with measurements of the maximum wave run-up heights for 2D random waves in a finite water depth by De Vos et al., and it appears that the data are well predicted if the predictions are calibrated with the data. Therefore the present approach represents a model which can be validated against and adjusted to field data.

Drag force on a vegetation field due to long-crested and short-crested nonlinear random waves

This paper provides a practical method for estimating the drag force on a vegetation field exposed to long-crested (2D) and short-crested (3D) nonlinear random waves. This is achieved by using a simple drag formula together with an empirical drag coefficient given by Mendez et al. (1999), in conjunction with a stochastic approach. Here the waves are assumed to be a stationary narrow-band random process. Effects of nonlinear waves are included by adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D random waves.