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FRINATEK-Fri prosj.st. mat.,naturv.,tek

Water wave modulation and wave forces with sheared currents

Alternative title: Water wave modulation and wave forces with sheared currents

Awarded: NOK 3.3 mill.

Interactions of water waves and their ambient environments, e.g., a subsurface current and a seabed which are the focus of this project, occur widely in coastal and ocean regions. They are pivotal to the spread of nutrients and pollutants, coastal erosion, and wave forces acting on fixed, moored, and floating structures. Moreover, the interactions directly affect the exchange of energy, momentum, and heat between the ocean and atmosphere, crucial to climate modeling. A wide range of practical applications in marine and offshore engineering and oceanography therefore crucially depend on realistic wave-current models, and yet theoretical and numerical predictive tools for the interactions between surface waves, a subsurface current, and a varying bathymetry are severely limited. To this end, this project intends to develop theoretical and numerical tools that are practical for investigating the effects of these interactions in different contexts. Pertinent applications of the expected results of the project mainly focus on three aspects; the possible origins of rogue waves, which are suddenly appearing and extremely large waves relative to their surroundings; Stokes drifts and trajectories of fluid particles; hydrodynamic loads on offshore vertical slender structures. To advance the understanding of rogue wave events, a statistical theoretical model has been developed for weakly nonlinear surface waves atop abrupt depth transitions (ADTs). This model is validated through comparisons with laboratory experiments and numerical simulations. Based on this model, a depth transition has been proposed as a cause for triggering rogue waves, attributing to the interaction of second-order free waves additionally released due to the ADT and linear main and second-order bound waves that are present also in the absence of the ADT. The statistical model provides a good approximation to the spatial inhomogeneity of the statistical properties of surface gravity waves atop ADTs, including excess kurtosis, skewness, and exceedance probability of the wave crest. Another possible mechanism for the generation of rogue waves is the so-called modulational instability (MI) of surface waves which refers to the phenomenon that a wave is much deviated from a periodic form due to the nonlinearity, leading to the generation of spectral sidebands and the breakup of the waveform into a form of a wave packet. In fluid dynamics, different versions of the nonlinear Schrödinger equation (NLSE) have been derived and demonstrated as a useful model for the study of MI as well as rogue wave events. The existing NLSEs have been limited to surface waves of a narrow bandwidth and of small directional spread, which are relaxed through the derivation of a new NLSE in this project. The new NLSE can be employed for the study of three-dimensional weakly nonlinear deepwater waves of an arbitrary bandwidth and of large directional spread and its capability will be further explored in future works. For the study of Stokes drifts and the roles of surface waves in transporting fluid particles, a semi-analytical model has been developed. The model can provide efficient predictions of directionally spreading weakly nonlinear surface gravity waves on an arbitrarily depth-varying current. It is numerically efficient and accurate to second order in wave steepness. It was employed to study the Stokes drifts and particle trajectories underneath a focused wave group from a broadband spectrum on an intermediate water depth. To this end, it is found that, as expected, a narrowband assumption leads to insufficient accuracy of predictions for waves of a broad bandwidth. In a deterministic context, ignoring the effects of the cross-interaction of two different monochromatic waves at second order can lead to underestimates of the Stokes drifts and, thereby, the net mean displacements of fluid particles. The coupled effects of surface waves and a depth-dependent flow are found to play an important role in the sea loads on offshore manmade structures. As a current in nature is often nonuniform in space, it is noted that a more realistic representation of the profile of a background current can contribute to a more accurate prediction of loads on offshore structures in realistic environments subject to the interaction of surface waves and a current. The proposed project has built the first few steps towards a three-dimensional theory that allows for the complex interplay of weakly nonlinear and steep surface water waves, vertically sheared currents, and a varying bathymetry. The current project is particularly relevant for countries/regions (e.g. the UK and Norway) whose coastal waters contain areas of strongly sheared currents (e.g. fjords and strong tidal currents off Scotland) and of variable depth changes, where man-made installations are present. Examples include vessels, fish farms, (fixed and floating) offshore wind turbines, and tidal turbines.

The project deals with the research topic of the complex interaction between surface waves, a depth-dependent current, and a varying bathymetry in the open ocean and coastal waters. Through the research activities, this project has led to the development of novel theories which have provided the key and complimentary steps towards the main objective for a novel theory proposed by the project. The novel mathematical modeling cover broad-band waves up to third-order in wave steepness, a semi-analytical framework for Stokes waves and particle trajectories induced by nonlinear surface gravity waves, wave action evolution for surface waves atop a depth-dependent depth in a slowly varying bathymetry, deterministic and statistical models for the formation of the extremely large wave events atop depth transitions, the shear current-modified super-harmonic and sub-harmonic surface waves, and the shear current-modified Morison equation for the hydrodynamic loads on offshore slender structures in various sea states subject to the surface waves and a depth-dependent flow. The theoretical models have contributed to advancing the physical understanding of the research topic. Customized numerical solvers using MATLAB have been produced for the implementation of the novel theories. The scripts are organized and uploaded to the GitHub repository `https://github.com/YanLi-PhD/Wave-Current-Interaction’ with the General Public License. The novel physics elucidated from the research project (alone and via collaboration) has contributed to novel physical features which produce a long-lasting impact on the safety of offshore structures in a wide range of applied fields, e.g., offshore and coastal engineering. A formation mechanism of extremely large wave events atop depth transitions has been demonstrated by mathematical modeling, and numerical and experimental observations. A new onset mechanism of wave breaking arising from the nonlinear forcing of free and bound waves of high-order harmonics has been identified with numerical and experimental observations. The coupled effects of surface waves and a depth-dependent current have been found to play an important role in the fatigue and extreme hydrodynamic loads on a bottom fixed and vertically installed monopile. The research project has greatly promoted international research collaborations and knowledge transfers between research groups based in the United Kingdom and Norway. As the FRIPRO mobility grant especially highlights the career development of the project manager (PM), it is highlighted that the PM has greatly enhanced their employability and track record with the support of this project. The PM has secured a permanent faculty position as an associate professor at a university in Norway during the implementation of the project. Continuous knowledge transfers to a research group led by the PM in Norway will be produced. The relevant impact is expected to be long-lasting.

Surface water waves, currents, and varying bathymetry widely coexist in water regions. There are extensive studies that cover two out of the three factors, but investigations that address all the three are rather limited. This project aims to develop a complex, three-dimensional theory for surface water waves over a varying current and a slowly sloping seabed, correct to – at least – second order in wave steepness. The newly developed theory creates access towards exploring physical insights into complex interactions among the three factors. Numerical implementations and real-life applications in ocean wave/circulation models and sea loads on vertical slender structures are carried out. The expected results of the project are of wide applicability, as explained below. One particular focus of this project is rogue waves, dangerous giant waves occurring suddenly out of otherwise moderately high seas. The presence of a current of shear and varying bathymetry may result in waves out of equilibrium that affects the occurrence of rogue waves. The effect of a sheared current on wave-induced forces is largely unknown, although indications are that it is considerable. All current analysis tools are either extremely expensive or inapplicable, and experiments are difficult, costly and time-consuming. This project takes the first step into this vast new field and leads to various possibilities. This project is particularly relevant to countries/regions (e.g. the UK and Norway) whose coastal waters contain areas of strongly sheared currents (e.g. fjords in Norway and strong tidal currents off Scotland, respectively) where man-made installations are present. Examples include vessels, fish farms, (floating) offshore wind turbines, and tidal turbines.

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FRINATEK-Fri prosj.st. mat.,naturv.,tek