Bimodal Sea States Research Articles

Introducing bimodal sea-states in a hybrid model for nearshore wave processes

HySwash has been recently developed as a fast and effective hybrid method to predict nearshore wave processes under unimodal wave conditions. However, global wave climates, and especially those in the tropical regions where coral reefs are hosted, are usually exposed to multiple incoming wave systems, resulting in several energy peaks corresponding to coexisting swells and wind seas. Moreover, although the full distribution of wave runup can have a significant impact on the assessment of vulnerable low-lying tropical regions, predictive models of flooding usually synthesize wave runups to an extreme percentile value, overlooking its full distribution. To enhance the capabilities of HySwash, in the present work, the inclusion of bimodality, as well as the prediction of the complete wave runup distribution is presented. This involves adapting the sampling, selection, and interpolation algorithms together with the hydrodynamic modeling that constitutes the original HySwash methodology. The positive mathematical validation reinforces the applicability of HySwash for a variety of coastal applications. Furthermore, a comparison is conducted between extreme wave runups induced by bimodal sea states and unimodal sea states, providing insights into the impact of multimodality on wave runup extremes.

Spectral wave modeling of bimodal sea states at laboratory and coastal scales

A downshift of the wind wave peak frequency was observed in a wind wave tunnel when irregular long paddle-waves (i.e. generated mechanically with a plane wave-maker) are added in the sea state. The 3rd generation spectral wave model, TOMAWAC, is used to assess the extent at which this peak frequency downshift can take place at prototype scale in bimodal sea-state conditions involving swell and wind wave systems. Several parameterizations of the modeled physical processes are selected to numerically reproduce the laboratory experiments in the first place. Then, the model performances are further inquired in reproducing coastal observations during a specific event combining a wind wave and a swell system. Overall, a good agreement is obtained between the simulations and the observations both at laboratory and coastal scale. In particular, a set of parameterizations combining one of the latest developments in spectral wave models for the whitecapping dissipation and the nonlinear 4-wave interactions reveals high performances in reproducing the observations. Lastly, based on the performances of this latter set of parameterizations, a generic numerical domain with typical coastal scale dimensions is created to inquire the occurrence of the downshift at prototype scale. This last study reveals a wind wave peak period shift from 5 s without swell to more than 6.5 s with a 2 m high swell.

Sea Spectral Estimation Using ARMA Models.

This paper deals with the spectral estimation of sea wave elevation time series by means of ARMA models. To start, the procedure to estimate the ARMA coefficients, based on the use of the Prony’s method applied to the auto-covariance series, is presented. Afterwards, an analysis on how the parameters involved in the ARMA reconstruction procedure—for example, the signal time length, the number of poles and data used—affect the spectral estimates is carried out, providing evidence on their effect on the accuracy of results. This allowed us to provide guidelines on how to set these parameters in order to make the ARMA model as accurate as possible. The paper focuses on mono-modal sea states. Nevertheless, examples also related to bi-modal sea states are discussed.

A framework for processing wave buoy measurements in the presence of current

Waves and currents interact, with the resulting combination largely determining the loading on offshore structures and devices. Despite this, currents are often ignored and wave buoy data is processed without consideration of the current or the wave-current interaction. This data is subsequently used in design, yet sea state power, steepness, and directionality may have significant errors. Here we present a novel framework for the processing of wave buoy data to account for the effect of a current. We use a mesh adaptive direct search (MADS) algorithm to solve for the current and current-modified wave parameters simultaneously. Through 125 simulated directional wave-current sea states, we demonstrate the performance of the method under a wide range of conditions; including bimodal sea states with non-colinear current. Current speed and direction are estimated accurately for all cases (mean RMSE of 0.1179ms−1 and 0.0091 rad respectively) which enables sea state steepness and power to be estimated within ± 3%. Ignoring this current of ±2ms−1 when deriving these wave parameters results in errors up to 30%. This work demonstrates that it is possible to correctly process wave buoy measurement data to account for, and quantify, a current thus significantly reducing the uncertainty of the ocean conditions. After further validation work, the framework can be widely applied to historic datasets, correcting the wave data and providing an additional dataset of current velocities.

Reflection Analysis of Impermeable Slopes under Bimodal Sea Conditions

Understanding of the reflection characteristics of coastal seawalls is crucial for design. Wave reflection can cause difficulties in small vessel manoeuvring at harbour entrances; this can cause damage to the toe of coastal structures by scouring. Previous studies have examined the reflection characteristics of coastal seawalls under random wind-generated waves without considering the effects of wave bimodality created by the presence of swell waves. This present study focuses on the influence of random wave bimodality on the reflective characteristics of coastal seawalls. 823 experimental tests were conducted to examine the reflection performance of impermeable sloping seawalls under bimodal waves. Reflection coefficients were computed from each test. The analysis of the results suggests that both unimodal and bimodal waves give similar reflection characteristics. However, the reflection coefficient in bimodal sea states seems to be more prolonged than in the unimodal sea states. It was found that the reflection coefficients of coastal seawalls are strongly influenced by the seawall slope, the wave steepness, the relative water depth, and the surf similarity parameters. A new empirical reflection equation to describe the influence of wave bimodality on the reflection characteristics of coastal seawalls has been formulated based on this study.

Gravel beach profile response allowing for bimodal sea states

The south coast of the UK is identified as a location where significant wave swell components are present within the regional wave climate. During the winters of 2006 and 2014, several sites along the south coast of the UK were subject to significant damages where flood events were recorded. These sea states were characterised by having a double-peaked wave spectra, observing a connection between wave spectrum shape and beach response. A two-dimensional (2D) physical model study was carried out to investigate the effect of gravel beach profile response under wave spectra characterised by swell-wave and wind-wave periods in various combinations. The physical model results showed the effect of bimodal wave spectrum on beach crest erosion and were compared with the parametric model Shingle and the numerical model XBeach-G. Based on this 2D physical model study, a new parametric model, Shingle-B, was derived and an online tool developed and made available on the website for the National Network of Regional Coastal Monitoring Programmes of England. This new tool has been validated at two sites in the south of England where field data of both waves and profiles were available.

Comparison between wave generation methods for numerical simulation of bimodal seas

This paper describes an investigation of the generation of desired sea states in a numerical wave model. Bimodal sea states containing energetic swell components can be coastal hazards along coastlines exposed to large oceanic fetches. Investigating the effects of long-period bimodal seas requires large computational domains and increased running time to ensure the development of the desired sea state. Long computational runs can cause mass stability issues due to the Stokes drift and wave reflection, which in turn affect results through the variation of the water level. A numerical wave flume, NEWRANS, was used to investigate two wave generation methods: the wave paddle method, allowing for a smaller domain; and the internal mass source function method, providing an open boundary allowing reflected waves to leave the domain. The two wave generation methods were validated against experimental data by comparing the wave generation accuracy and the variance of mass in the model during simulations. Results show that the wave paddle method not only accurately generates the desired sea state but also provides a more stable simulation, in which mass fluctuation has less of an effect on the water depth during the long-duration simulations. As a result, it is suggested that the wave paddle method with active wave absorption is preferable to the internal wave maker option when investigating intermediate-depth long-period bimodal seas for long-duration simulations.

Further analysis of change in nearshore wave climate due to an offshore wave farm: An enhanced case study for the Wave Hub site

This paper addresses the use of numerical wave models for assessing the impact of offshore wave farms on the nearshore wave climate. Previous studies have investigated the effect of energy extraction by wave energy devices through the use of spectral models such as SWAN, representing a wave farm as one or more barriers within the model domain and applying a constant wave energy transmission percentage across the whole wave spectrum incident at the barrier. However, this is an unrealistic representation of the behaviour of real wave energy converters. These will exhibit frequency-dependent energy absorption characteristics that will correspond to the spectral response of the device, and may reflect its ability to be tuned to extract energy at particular frequencies. This study describes a modification of the SWAN source code to enable frequency-dependent wave energy transmission through a barrier. A detailed analysis of the wave climate at the Wave Hub wave farm site is also presented, with a particular focus on the occurrence of bimodal sea states. The modified SWAN code is used to assess how impact predictions for typically occurring sea states may differ when using frequency-dependent rather than constant wave energy transmission, with reference to a previous study using the unmodified code (Millar, Smith and Reeve, 2007 [1]). The results illustrate the dependence of the magnitude of the impact on both the response function of the devices and the spectral sea state in which they are operating.

Wave height distributions in bimodal sea states from offshore basins

The paper presents results for the distribution of wave heights from laboratory generated bimodal sea states. Data collected at the DHI offshore basin are analyzed and compared with results based on wave records from the MARINTEK offshore basin. The comparisons are done for three groups of mixed sea states: wind-sea dominated, swell-dominated and energy-equivalent, determined on the basis of the parameter sea-swell energy ratio ( SSER), which have been generated according to the model of Guedes Soares (1984). In some sea states abnormal or freak waves have been observed. The quasi-determinism theory of Boccotti is used to expand some linear narrowband models to second order, thus providing validation of the adequacy of the equations to represent the linear components of the wave heights. Also, the data are compared with the predictions of a third order model using as a nonlinear correction the coefficient of kurtosis. Due to the coexistence of wind-sea and swell, the core of the autocovariance function in some cases demonstrates a global minimum which is the second local minimum in the sequence. This can affect the fitting ability of distributions whose parameters depend on the form of the autocorrelation function or its envelope. The results for MARINTEK and DHI data show similar patterns of fit between predicted and observed exceedance probabilities for the considered classes of bimodal spectra.

Nonlinear Crest, Trough, and Wave Height Distributions in Sea States With Double-Peaked Spectra

Abstract The peak to trough distributions of nonlinear high sea waves in bimodal sea states in deep water are investigated. The statistical distribution of wave height is first analyzed by considering the Boccotti’s expression, where the parameters of the distribution are calculated for some bimodal spectra of sea states recorded in the Atlantic Ocean. The nonlinear crest and trough distributions are then obtained, particularizing for two peaked spectra the second-order Fedele and Arena expression, which depends on two parameters. The results have been finally validated by means of Monte Carlo simulations of second-order random waves with bimodal spectra.

Nonlinear High Wave Groups in Bimodal Sea States

Nonlinear effects for wave groups in bimodal sea states are investigated. The linear free surface displacement is obtained by applying the quasi-determinism theory of the highest waves, with the spectrum given by the superposition of two JONSWAP spectra. Linear groups are modeled as the sum of two groups produced by each unimodal spectrum. Nonlinear effects are given as second-order contribution to the linear free surface displacement. The structure of wave groups is then analyzed for some bimodal spectra. The linear component of wave groups shows a strong variation with respect to the classical structure with unimodal spectra, particularly in mixed seas. It is observed that the nonlinearity gives small contributions for swell dominated seas. For wind dominated sea states, the main nonlinear contribution is given by the wind wave spectral components. For mixed sea states, the interaction among the components of the wind wave spectrum and the components of the swells could give a meaningful contribution to the nonlinear profile. The strongest nonlinear effects occur when the two peaks of the spectrum are close to each other. Finally, the results are validated by means of Monte Carlo simulations of nonlinear sea waves.

Probability distributions of wave heights in bimodal seas in an offshore basin

This study aims at assessing the adequacy for describing bimodal sea states of different non-linear probability distributions that have been developed for single sea states. It is based on data collected at an offshore test basin. The measurements represent three bimodal sea states with individual unidirectional wave systems propagating at 60 ∘, 90 ∘ and 120 ∘ from each other. The wave spectra are separated into swell and wind sea components and the relative energy ratio between the areas under the associated spectral curves is estimated and is related with the statistics of the time series considered. Dependence is found between the normalized high order cumulants, which describe the non-Gaussian surface, and the predominant contribution of the wind sea energy. Furthermore, the probabilities of exceedance of the individual wave heights are estimated and compared with the Rayleigh model and with other models that take into account either the effect of spectral bandwidth or the effect of wave nonlinearities. The results are discussed with respect to three classes of sea states that reflect the relative contribution of swell and wind sea energy.

Modified Weibull-derived spectrum for deep water significant wave height estimation

The modified Weibull spectrum is utilized to calculate the zeroth spectral moment (mo) using Monte Carlo integration methods. Then significant wave height (Hs) is calculated using the formula $$ {\text{H}}_{\text{s}} = 4\sqrt {{\text{m}}_{\text{o}} } . $$ This is validated with observed buoy data and numerical wave model (WAM) predicted significant wave heights. The Weibull parameters have been calculated using energy densities from observed spectra recorded by DS5 buoy (13.80° N, 82.52° E, depth 3355.48 m) by the method of maximum likelihood (MLE).The relative root mean square error (RRMS) and relative bias error criteria show that modified Weibull spectrum estimated significant wave heights are better than those predicted by WAM model. The monthly averaged observed wave power spectra for the year 2005 recorded by deep water buoy DS5 is considered in this work. The spectra exhibit bimodal sea states for several months of the year.

Generation of Large Angle Bimodal Sea States Using One-Side Segmented Wavemaker

In the present work, we study the capabilities of a one-side segmented wavemaker to generate multidirectional sea states. We want to reproduce typical West Africa sea conditions in a rectangular basin, that is, two spectra representing swell and wind waves with ±45deg main directions relative to the basin axis. For that purpose, we study two generation techniques proposed, respectively, by Dalrymple and Molin which rely on the control of sidewall reflections in order to enlarge the testing zone. Both numerical and experimental results show that the use of such methods in combination with a one-side wavemaker provides high quality wave fields as well as large extent testing area. The Molin method appears to be more efficient in terms of wave field quality within the testing area although the tuning of its setting parameters requires more care than the Dalrymple method.

Estimation of Wind-Sea and Swell Components in a Bimodal Sea State

Methods for separating the spectral components and describing bimodal wave spectra are evaluated with reference to wave spectra from directional wave measurements made at the Maui location off the west coast of New Zealand. Two methods involve partitioning bimodal wave spectra into wind-sea and swell components and then fitting a spectral function to each component, while the third assigns an average spectral shape based on the integrated spectral parameters. The partitioning methods involve separating the wave spectrum into two frequency bands: a low-frequency peak, the swell component, and a high-frequency peak, the wind-sea. One partitioning method uses only the frequency spectrum while the other analyzes the complete frequency-direction spectrum. Comparison of the spectral descriptions and derived parameters against the measured counterparts provides insight into the accuracy of the different approaches to describing actual bimodal sea states.

Wave Height Distribution in Mixed Sea States

The statistical distribution of zero-crossing wave heights in Gaussian mixed sea states is examined by analyzing numerically simulated data. Nine different kinds of bimodal scalar spectra are used to study the effects of the relative energy ratio and the peak frequency separation between the low and high frequency wave fields on the wave height distribution. Observed results are compared with predictions of probabilistic models adopted in practice. Comparisons of the empirical data with relevant probabilistic models reveals that the Rayleigh model systematically overestimates the number of observed wave heights larger than the mean wave height, except for one of the cases analyzed. None of the models used to predict the observed exceedance probabilities is able to characterize adequately all cases of bimodal sea states examined here.