Wave Modeling Results: Baseline Observations and Modeling for the Reedsport Wave Energy Site

Offshore wave conditions along the Oregon coastline are measured at a handful of buoy locations where directional wave information is available. Most of these buoys are located in deep waters and incoming waves undergo changes as they travel from deep water onto the shelf where wave energy conversion arrays are likely to be deployed. These changes can be in the form of wave focusing or defocusing due to the presence of underwater banks, shoals, or canyons. Also, wave dissipation mechanisms such as bottom friction or wave breaking can be at play. Wave models can take into account such processes and produce predictions of the local conditions at the site of a wave energy conversion (WEC) array. Knowledge of local conditions can aid in the design of the devices for the specific local conditions to which they will be subjected and can also provide advance knowledge of wave conditions to power companies once a WEC array is in place. The work performed herein was geared towards two goals. First, transformation of the wave field from deep water to the site of the buoy deployment was assessed. Second, preliminary predictions about the potential impact of the buoys on the wave field are made. The results are discussed separately below. Note that model code used herein is freely available soft ware and can be obtained through http://www.wldelft.nl/soft/swan/. Input files specific to this work can be obtained through the author

Waves on unsteady currents

Models for surface gravity wave propagation in the presence of currents often assume the current field to be quasi-stationary, which implies that the absolute wave frequency is time invariant. However, in the presence of unsteady currents or time-varying water depth, linear wave theory predicts a time variation of the absolute wave frequency (and wavenumber). Herein, observations of wave frequency modulations from a large-scale laboratory experiment are presented. In this case, the modulations are caused by both unsteady depths and unsteady currents due to the presence of low-frequency standing waves. These new observations allow a unique and detailed verification of the theoretical predictions regarding variations in the absolute wave frequency. In addition, analytic solutions for the variations in frequency and wave height induced by the unsteady medium are found through a perturbation analysis. These solutions clarify the dependency of the wave frequency/wave height modulations on the characteristics of the unsteady medium. We also find that analytic solutions for simplified basin configurations provide an order of magnitude estimate of the expected frequency modulation effect. Finally, the importance of this phenomenon in natural situations is discussed

Physical-Environmental Effects of Wave and Offshore Wind Energy Extraction: A Synthesis of Recent Oceanographic Research

The ocean deployment of arrays of Wave Energy Converters (WEC arrays) appears likely in the near future, and deployment of offshore wind turbines has already started. These technologies tap into a potential renewable energy resource but also involve complex systems with uncertain environmental consequences that will likely scale with the size of their ocean footprint. This synthesis talk will concentrate on the potential physical effects of these array technologies. Both WEC arrays and offshore wind farms consist of sizable structures placed in the water column; hence, their mere presence is a potential environmental stressor. Possible effects on the physical environment include wave scattering and wave shadowing; added drag on the coastal current field; modifications to sediment transport (by way of the aforementioned changes to the wave and current forcing); and changes to local sediment characteristics (due to anchors and pilings). In many ways, these effects are similar to those caused by other ocean structures that have been studied for some time (e.g., offshore platforms). However, there are additional potential effects of WECs and wind turbines that require further attention. For example, extraction of wave energy by WECs could have additional environmental consequences. Similarly, offshore wind farms can alter the local wind field, in turn altering locally-generated waves. We will address effects due to wave or wind installations on the wave field, on local ocean circulation, and on sediment transport characteristics. Because WECs partially extract and scatter incident wave energy, they cause significant modifications in the near-field. In fact, if device performance can be optimized at field scales, then by definition the near-field effects will be maximized, i.e., if energy extraction is maximized the potential physical effects of WECs are also maximized. Over the past decade a sizable number of studies have applied theoretical principles using varying assumptions and simplifications to the problem of WEC-wave interactions. Some of these assumptions (e.g., “optimal” motions, monochromatic wave conditions, etc.) have now been shown to be unrealistic, and there has been a convergence toward classes of models that appear to produce reasonable estimates. While recent model studies have managed to bound the problem, significant uncertainties remain. The primary cause for the remaining uncertainties is the lack of observational studies, particularly data sets that provide spatial information about the wave field in the vicinity of in situ devices. Nonetheless, a few studies have undertaken scaled laboratory testing, and these data sets are beginning to lend confidence to the available numerical model results and shed light on the dominant processes. Once near-field effects are understood, far-field effects can be assessed. Far-field effects influence the wave field near beaches, which, in turn, influences the sand transport processes that govern the morphodynamics of the beach face. Fortunately, hydrodynamic modelling of large-scale wave propagation processes in the absence of structures is highly advanced, i.e., if given accurate incident wave conditions in the lee of an installation and bathymetry for the model domain, models can well-simulate local wave conditions, wave-driven currents and sediment transport patterns. Therefore, once near-field WEC/wave dynamics are understood, expanding our understanding to the far-field will be relatively straightforward. Nonetheless, observational studies of far-field beach modifications shoreward of an installation will help to further solidify our understanding of beach behaviour. Offshore wind farms can also potentially influence the local wind field around them. Previous studies of such modifications at land-based wind farm installations serve as a reasonable basis for predictions offshore . Any changes to offshore winds will also influence the local wave field, especially where local winds are the dominant source of waves. Such effects will be minimal near coasts where the local wave climate is dominated by incident swells generated at large distances (e.g., the U.S. West Coast). In contrast, locally generated waves are a more important component of the wave climate on the East Coast of the U.S Modification to ocean currents by an array of structures can be assessed by considering the additional frictional effects (“form” drag) caused of the array. If the drag caused by a dense of array of structures is large, circulation will be altered, which might result in reduced current velocities or the diversion of currents toward an area of less drag. Note that ocean currents already experience drag due to bottom friction; hence, the question hinges on the relative magnitude of the drag induced by structures versus the pre-existing frictional drag. Finally, any near-field modifications to the wave and circulation field (due to either WEC arrays or wind farms) will necessarily result in changes in sediment transport. Any local reduction in flow velocities can result in a reduction of the sediment carrying capacity of circulation leading to sediment accumulation at the site. Small-scale modification to a current will also likely cause bumps and holes around the pilings or anchors. These effects are similar to those observed around existing offshore structures and pilings, and can be accounted for in the design of the structures. Far-field modification of waves and associated changes in wave-induced currents can also result in changes in sediment transport patterns near beaches. Although some recent studies exist, questions regarding far-field effects on beaches are still relatively poorly addressed

Publisher's note: "Waves on unsteady currents" [Phys. Fluids 19, 126601 (2007)]

This article was originally published online and in print with an incorrect version of Fig. 1. AIP apologizes for this error. All online versions of the article have been corrected

Formulation of the undertow using linear wave theory

The undertow is one of the most important mechanisms for sediment transport in nearshore regions. As such, its formulation has been an active subject of research for at least the past 40 years. Still, much debate persists on the exact nature of the forcing and theoretical expression of this current. Here, assuming linear wave theory and keeping most terms in the wave momentum equations, a solution to the undertow in the surf zone is derived, and it is shown that it is unique. It is also shown that, unless they are erroneous, most solutions presented in the literature are identical, albeit simplified versions of the solution presented herein. Finally, it is demonstrated that errors in past derivations of the undertow profile stem from inconsistencies between (1) the treatment of advective terms in the momentum equations and the wave action equation, (2) the expression of the mean current equation and the surface shear stress, and (3) the omission of bottom shear stress in the momentum equation

Effects of wave-current interaction on shear instabilities of longshore currents

We examine the effects of wave-current interaction on the dynamics of instabilities of the surf zone longshore current. We utilize coupled models for the simulation of the incident waves and the wave-induced nearshore circulation. The coupling between the models occurs through radiation stress gradient terms (accounting for the generation of nearshore circulation) and through wave-current interaction terms (leading to the modification of the wave field by the generated circulation field). Simulations are carried out with a realistic barred beach configuration and obliquely incident waves for two frictional regimes. The results show that the shear instabilities of the longshore current have a significantly altered finite amplitude behavior when wave-current interaction effects are included for beaches with relatively high frictional damping. The primary effects are a reduction of the offshore extent of the motions and a delay of the onset of instabilities. In addition, the energy content of the motions within two surf zone widths is reduced, the propagation speed increases, and tendency to form offshore directed jets is reduced. The horizontal mixing induced by the instabilities is also reduced when wave-current interaction is considered, leading to a larger peak mean longshore current and a larger offshore current shear. These effects appear to be primarily linked to a feedback mechanism, whereby the incident wave field gains energy at locations of offshore directed currents. For more energetic shear instability fields that occur when frictional damping is small, this feedback affects the propagation speed and energy content of the instabilities near and onshore of the current peak only minimally. However, the offshore extent of the motions and the tendency to shed vortices offshore are still reduced. A reduction in the mixing due to the instabilities is evident offshore of the current peak, hence the mean longshore current profile is only affected offshore of the current peak. The inclusion of wave-current interaction significantly affects the shear instability signature observed in the shoreline runup for either frictional regime. These results indicate that the energy content and frequency extent of the shoreline response is increased markedly due to the wave-current interaction process. This effect appears to be related to variations in the forcing of the circulation that arise due to the refraction of the incident waves around offshore directed features of the circulation.Keywords: longshore currents, hydrodynamic instability, wave-current interactions, surf zone circulationKeywords: longshore currents, hydrodynamic instability, wave-current interactions, surf zone circulatio

Power Calculations for a Passively Tuned Point Absorber Wave Energy Converter on the Oregon Coast

A wave-structure interaction model is implemented, and power output estimates are made for a simplified wave energy converter operating in measured spectral wave conditions. In order to estimate power output from a wave energy converter, device response to hydrodynamic forces is computed using a boundary element method potential flow model. A method is outlined for using the hydrodynamic response to estimate power output. This method is demonstrated by considering an idealized non-resonating wave energy converter with one year of measured spectral wave conditions from the Oregon coast. The power calculation is performed in the frequency domain assuming a passive tuning system which is tuned at time scales ranging from hourly to annually. It is found that there is only a 3% gain in productivity by tuning hourly over tuning annually, suggesting that for a non-resonating wave energy converter, power output is not very sensitive to the value of the power take off damping. Interaction between wave energy converters in arrays is also considered, and results for an array of idealized point absorbers suggests that interactions are minimal when devices are placed 10 diameters apart from each other.Keywords: Annual power prediction, Wave Energy Converter Array, WAMIT, Tuning, Optimal dampin

Bathymetry correction using an adjoint component of a coupled nearshore wave-circulation model: Tests with synthetic velocity data

The impact of assimilation of wave-averaged flow velocities on the bathymetric correction is studied in tests with synthetic (model-generated) data using tangent-linear and adjoint components of a one-way coupled nearshore wave-circulation model. Weakly and strongly nonlinear regimes are considered, featuring energetic unsteady along-beach flows responding to time-independent wave-averaged forcing due to breaking waves. It is found that assimilation of time-averaged velocities on a regular grid (mimicking an array of remotely sensed data) provides sensible corrections to bathymetry. Even though the wave data are not assimilated, flow velocity assimilation utilizes adjoint components of both the circulation and wave models. The representer formalism allows separating contributions of these two components to the bathymetric correction. In a test case considered, involving a beach with an alongshore varying bar, the adjoint wave model contribution was mainly to determine the cross-shore position of the bar crest. The adjoint circulation model provided an additional contribution, mostly adding to alongshore variability in the shape of the bar. The array mode analysis reveals that there are very few modes that can be effectively corrected, given the assumed data error level. Bathymetry perturbations associated with these modes are a mixture of near-coast intensified modes as well as modes extending their influence to deep water (along the background wave characteristics). Additional tests show the utility of different observational arrays in providing the bathymetric correction.Keywords: nearshore processes, coupled wave-circulation model, variational data assimilation, bathymetry estimat

Low-frequency characteristics of wave group-forced vortices

The dynamics of vorticity motions forced by wave groups incident on an alongshore-uniform barred beach are analyzed. For both normally and obliquely incident wave groups, the potential vorticity and enstrophy equations reveal that the temporal variability of wave group–forced vortices is directly linked to the variability in the incoming wave groups rather than bottom friction, as previously hypothesized. Analysis of the lifespan of individual vortices further shows that the wave group forcing is responsible for not only the temporal variations of the vortices but also their eventual demise. Vortices in the simulations persist for 5 to 45 min, which is consistent with recent field observations. For oblique wave groups, the resulting vortices are advected by the mean current, yielding a signature in the frequency–wave number spectrum that is similar to that usually attributed to shear instabilities of the alongshore current. These results may explain previous observations of alongshore-propagating vorticity motions in the presence of a stable alongshore current. For simulations involving an unstable alongshore current, we find that the inclusion of wave group forcing results in velocity spectra that are much broader compared to the simulations that neglect wave grouping, which could explain discrepancies between previously observed and modeled spectral widths of propagating vorticity motions. Finally, the potential enstrophy balance shows that vorticity production due to wave groups may be as important as that due to the instability process and that not all low-frequency vortical motions observed during oblique wave incidence should be attributed to shear instabilities of the alongshore current.Keywords: wave groups, surf zone, vorticesKeywords: wave groups, surf zone, vortice

Nearshore Wind-Wave Forecasting at the Oregon Coast

This presentation was given as part of Oregon State University's College of Oceanographic and Atmospheric Sciences graduate student seminar series. It describes the basics of wave forecasting and then focuses on work implementing a wave forecasting system for the Oregon and Southwestern Washington Coast