SUPERGEN Wind Wind Energy Technology Rogue Waves and their effects on Offshore Wind Foundations Jamie Luxmoore PhD student, Lancaster University SUPERGEN Wind II - 7 th training seminar 3 rd - 4 th September 2013
Rogue Waves and their effects on Offshore Wind Foundations Outline 1. What are rogue waves? 2. When and why do rogue waves form? 3. Why are they a problem for Offshore Wind Turbine Support Structures?
What are rogue waves? Formal definition: Where H S is the average height of the highest 1 / 3 of all waves in the record. Source: http://griger.blog.sme.sk/c/102744/extremne-vlny.html Accessed 2/09/11
What are rogue waves? Rogue waves can have a high peak or a deep trough ( hole in the sea ) or both. They tend to be steep on the leading edge ( wall of water ), sometimes to the point of breaking. They are usually not extreme waves. They are rare (by definition), but more common in certain conditions. They are short lived and hard to predict.
When and why do rogue waves form? Current theoretical mechanisms for generation of freak waves are divided into three groups: Spatial focusing Shallow water with suitable bathymetry or currents Dispersive focusing Used in laboratories, but not thought to be relevant in real seas Nonlinear focusing Primary mechanism in deep water
Spatial focusing Refractive focusing of wave energy by: a change in the bottom topography or a strong current can lead to a sudden local increase in the height of waves. Best known example is the Agulhas current off South Africa, but there are many other places where this can and does occur. Agulhas current
Dispersive focusing Chirp signal generated at wave maker (wave with linearly decreasing frequency) As gravity waves are dispersive (wave speed is inversely proportional to the wavelength) the later waves catch up with the earlier waves, causing an increase in wave height. Works well in a lab No physical mechanism for producing this kind of chirp has been identified in the ocean
Nonlinear focusing Nonlinear wave interactions are believed to be the most likely mechanism for generation of freak waves in the deep ocean (Kharif et al., 2009). Nonlinear four wave interactions are important in the development of the wave spectrum in deep water (three wave interactions dominate in shallow water) (Janssen, 2003) Nonlinear focusing of energy due to the Benjamin-Feir instability has been one of the most active approaches recently (Kharif and Pelinovsky, 2003).
Four wave interactions Starting from a Gaussian random wind-generated sea, the evolution of spectrum is dominated by non-linear wave interactions. In deep water this is driven by four-wave interactions three active components transfer energy to a fourth (Hasselmann, 1962) Conditions for four wave resonance
Benjamin-Feir instability (unidirectional) The Benjamin-Feir instability occurs when waves of frequency ω 0 are perturbed by sideband waves of frequency if: The Benjamin-Feir index (BFI) is the ratio of the wave steepness to the spectral bandwidth. Where ε is the wave steepness
Laboratory experiments in mutidirectional crossing seas Marintek Ocean Basin, Trondheim 50 m long, 70 m wide, 3 m deep 144 flap type wave paddles 24 twin wire wave gauges
Spectral energy density m 2 s Test variables Spectral peakedness (gamma) 0.8 0.6 0.4 0.2 1 x 10-3 Gamma = 3 Gamma = 6 Spectral energy m 2 Directional spreading (N) 4.5 x 10-5 4 3.5 3 2.5 2 1.5 1 N = 50 N = 200 N = 840 0 0 1 2 3 4 Frequency [Hz] Crossing angle (α) α 0.5 0-50 -40-30 -20-10 0 10 20 30 40 50 Directions [deg] D θ = K 2 cos N (θ θ 0 )
Exceedance probability of wave crests X Experiments Tayfun Rayleigh Second order wave crest distribution exceedance probability (Tayfun, 1980): S C > η = exp 8 H S 2 k p 2 ( 1 + 2k p η 1) 2
Exceedance probability of wave height X Experiments Rayleigh
Kurtosis Effect of directional spreading on kurtosis Unidirectional: μ 4 = π 3 BFI 2ε δ ω 2 + 3 4.4 4.2 4 Empirical Empirical + Bound Unidirectional Wind sea only Incident waves Peak frequency Empirical: π 3 BFI 2D 2 3.8 Where: 3.6 BFI 2D = 2ε/ δ ω 2 + 7.1δ θ 2 /2 3.4 3.2 3 Bound modes: μ 4 bound = 24ε 2 + 3 (Mori, Onorato and Jansen, 2011) 2.8 10-2 10-1 10 0 Directional Spreading (rad)
Why are rogue waves a problem for Offshore Wind Foundations? Simple answer: Because they are hard to predict. F Wind F Wave Rogue waves are not the largest waves, larger waves occur in extreme storms, but: Wind turbines are switched off during storms, reducing the wind load. Rogue waves may occur when the turbine is operating.
Physical model tests 1/60 th scale model studies carried out in the Total Environment Simulator in Hull and the LUREG tank in Lancaster. 50-60 m deep water Froude scaled
Physical model tests Instrumentation: Two axis load cells for bulk wave forces 8 twin wire resistance wave gauges Video for wave run-up Waves up to H = 0.3 m
Physical model results Peak wave impact forces for Monopile model
Comparison with theory Morison equation: F = η h 1 2 ρc DDu u dz + η h πd 2 ρc M u dz 4 Simplified equation (Dean & Dalrymple, 1984) gives approximation of force up to mean free surface assuming constant C D and C M. F = C D DnE cos ωt cos ωt + C M πde D tanh(kh) sin( ωt) H Ref: Dean, RG and Dalrymple, RA (1984). Water wave mechanics for engineers and scientists, World Scientific, 352 pp.
Physical model results Peak wave impact forces for Jacket structure model Monopile
Physical model results Monopile F ρd 2 U m 2 = f K, Re, kd Jacket U m = ωh/2 60% 60% Decreasing wavelength (k=2π/λ and D is constant)
Physical model results Jacket structure orientation relative to wave direction Up to 40% difference in mean peak force Complex relationship with wave height, water depth and orientation
Wave interaction with monopile Animation for test case 1045: Time history of total wave loading on monopile
Summary Rogue waves are a potential problem for offshore wind turbines due to their inherent unpredictability and the unusual structural loads that can occur. Current research is focussing on understanding the mechanisms driving rogue wave activity and improving the predictability of rogue events. Supergen research is also aiming to improve understanding of the fundamental loading mechanisms, to help predict the effects of rogue waves.
Thank you for your attention. References Kharif C & Pelinovsky E, (2003). Physical mechanisms of the rogue wave phenomenon, Euro. J. Mech. Fluids B/Fluids 22, pp. 603-634 Mori N, Onorato M & Jansen PAEM, (2011), On the Estimation of Kurtosis in Directional Sea States for Freak Wave Forecasting, J. Phys. Oceanography 41, pp.1484-1497 Kharif C, Pelinovsky E & Slunyaev A, (2009), Rogue Waves in the Ocean, Springer- Verlag, Berlin Janssen, P A, Nonlinear four-wave interactions and freak waves, Journal of Physical Oceanography, 2003, 33, 863-884 Hasselmann, K, On the non-linear energy transfer in a gravity-wave spectrum, J. Fluid Mech, Cambridge Univ Press, 1962, 12, 481-500 Tayfun, M A, Narrow-band nonlinear sea waves, Journal of Geophysical Research: Oceans (1978--2012), Wiley Online Library, 1980, 85, 1548-1552 Dean, R G & Dalrymple, R A, Water wave mechanics for engineers and scientists, Advanced series on Ocen Engineering, Vol 2, World Scientific Publishing, 1991