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

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94870/1/jgrc8986.pd

Model-data comparisons of shear waves in the nearshore

Author Posting. © American Geophysical Union, 2005. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 110 (2005): C05019, doi:10.1029/2004JC002541.Observations of shear waves, alongshore propagating meanders of the mean alongshore current with periods of a few minutes and alongshore wavelengths of a few hundred meters, are compared with model predictions based on numerical solutions of the nonlinear shallow water equations. The model (after Özkan-Haller and Kirby (1999)) assumes alongshore homogeneity and temporally steady wave forcing and neglects wave-current interactions, eddy mixing, and spatial variation of the (nonlinear) bottom drag coefficient. Although the shapes of observed and modeled shear wave velocity spectra differ, and root-mean-square velocity fluctuations agree only to within a factor of about 3, aspects of the cross-shore structure of the observed (∼0.5–1.0 m above the seafloor) and modeled (vertically integrated) shear waves are qualitatively similar. Within the surf zone, where the mean alongshore current (V) is strong and shear waves are energetic, observed and modeled shear wave alongshore phase speeds agree and are close to both V and C lin (the phase speed of linearly unstable modes) consistent with previous results. Farther offshore, where V is weak and observed and modeled shear wave energy levels decay rapidly, modeled and observed C diverge from C lin and are close to the weak alongshore current V. The simulations suggest that the alongshore advection of eddies shed from the strong, sheared flow closer to shore may contribute to the offshore decrease in shear wave phase speeds. Similar to the observations, the modeled cross- and alongshore shear wave velocity fluctuations have approximately equal magnitude, and the modeled vorticity changes sign across the surf zone.This research was supported by the Office of Naval Research, the National Oceanographic Partnership Program, and the National Science Foundation

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

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

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

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

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

Quantifying the length-scale dependence of surf zone advection

We investigate the momentum balance in the surf zone, in a setting which is weakly varying in the alongshore direction. Our focus is on the role of nonlinear advective terms. Using numerical experiments, we find that advection tends to counteract alongshore variations in momentum flux, resulting in more uniform kinematics. Additionally, advection causes a shifting of the kinematic response in the direction of flow. These effects are strongest at short alongshore length scales, and/or strong alongshore-mean velocity. The length-scale dependence is investigated using spectral analysis, where the effect of advective terms is treated as a transfer function applied to the solution to the linear (advection-free) equations of motion. The transfer function is then shown to be governed by a nondimensional parameter which quantifies the relative scales of advection and bottom stress, analogous to a Reynolds Number. Hence, this parameter can be used to quantify the length scales at which advective terms, and the resulting effects described above, are important. We also introduce an approximate functional form for the transfer function, which is valid asymptotically within a restricted range of length scales.Keywords: Rip currents, Models, Nearshore circulation, Barred beaches, Stresses, Longshore currents, Nonlinear shear instabilities, Incident sea waves, Shallow water, Alongshore current

Data assimilation and bathymetric inversion in a two‐dimensional horizontal surf zone model

A methodology is described for assimilating observations in a steady state twodimensional horizontal (2‐DH) model of nearshore hydrodynamics (waves and currents), using an ensemble‐based statistical estimator. In this application, we treat bathymetry as a model parameter, which is subject to a specified prior uncertainty. The statistical estimator uses state augmentation to produce posterior (inverse, updated) estimates of bathymetry, wave height, and currents, as well as their posterior uncertainties. A case study is presented, using data from a 2‐D array of in situ sensors on a natural beach (Duck, NC). The prior bathymetry is obtained by interpolation from recent bathymetric surveys; however, the resulting prior circulation is not in agreement with measurements. After assimilating data (significant wave height and alongshore current), the accuracy of modeled fields is improved, and this is quantified by comparing with observations (both assimilated and unassimilated). Hence, for the present data, 2‐DH bathymetric uncertainty is an important source of error in the model and can be quantified and corrected using data assimilation. Here the bathymetric uncertainty is ascribed to inadequate temporal sampling; bathymetric surveys were conducted on a daily basis, but bathymetric change occurred on hourly timescales during storms, such that hydrodynamic model skill was significantly degraded. Further tests are performed to analyze the model sensitivities used in the assimilation and to determine the influence of different observation types and sampling schemes.Keywords: Two-dimensional horizontal surf zon