TMA Spectrum Research Articles

Numerical investigation of the response of the hybrid wave energy converter including oscillating water column and horizontal floating cylinder to irregular waves

The main goal of this research is to investigate the effect of some geometrical parameters on an onshore Hybrid Wave Energy Converter (HWEC) including an onshore Oscillating Water Column (OWC) and a Horizontal Floating Cylinder (HFC) under regular and irregular waves. The TMA spectrum is the basis of this study. The wave spectrum is used to generate irregular waves in a numerical wave tank using Ansys-fluent software based on URANS equations. Active wave absorption is used to avoid the effect of reflected waves. Also, the SST k−ω turbulence model and the VOF scheme are used for turbulence modeling and interface tracking, respectively. The results confirm that the efficiency of the HWEC is higher than the efficiency of an OWC and the efficiency of an HFC in both regular and irregular waves. Besides, the efficiency of the HWEC in irregular waves is lower than its efficiency in regular waves. A comparison of the TMA and JONSWAP spectrum on HWEC performance shows that HWEC performance is lower on the JOANSWAP spectrum. This study shows that the use of irregular waves is essential to obtain more realistic results from analyses of the onshore HWEC performance, despite their need for high computational cost.

Spectral analysis of near-breaking wave data observed in macro-tidal environment by zero up-crossing transform method

In this study, frequency spectra were obtained by applying the Zero-Up Crossing Transform (ZUCT) and the fast Fourier transform (FFT) methods from the waveform data observed at one point of a macro-tidal beach. Their frequency spectrum conversion characteristics according to changes in water depth can be investigated and compared with the TMA spectrum applicable to shallow water. The ZUCT method is based on the reproducibility of the actual wave height and period and applies a technique that guarantees energy conservation. In particular, when the tidal level is low, the spectrum by the ZUCT method seems to show a similar shape to the TMA spectrum over the entire tidal range even if the spectrum is deformed due to partial depth-induced wave breaking. This study derived the reduction rate of the frequency spectrum by wave breaking, assuming that the wave height distribution for each frequency followed the Rayleigh distribution. Based on this, we proposed the TMA-SOON (Spectrum Operated On Nearshore), a frequency spectrum equation applicable to the nearshore zone where wave breaking occurs. Therefore, by using this formula, it is possible to estimate the incoming wave energy as well as the incoming frequency spectrum from the observation data in the wave breaking region.

Extraction of nearshore spectrum by energy-conserved zero-up crossing method and comparison with the TMA spectrum

The present study introduces the zero up-crossing transform (ZUCT) method which includes energy conservation as well as the spectrum of the desired spectral resolution (df) near shore. The wave height obtained from the zero up-crossing method cannot satisfy the variance of surface elevation because it is determined by the difference in vertical height. Therefore, this study suggests a wave height calculation method that conserves energy using the zero up-crossing period, Tz. The wave spectrum obtained by ZUCT was compared with that obtained using the conventional Fourier transform (FT). Furthermore, it also shows satisfactory similarity with the JONSWAP spectrum for a specific df. This ZUCT method was compared with the FT for the data observed in Gonghyunjin and Heukdo, which have markedly different wave characteristics. In addition, considering the observation depth (approximately 30 m), it was compared with the TMA spectrum. As a result of comparison with the TMA spectrum, it was determined that the spectral peak value was not well reproduced because of the constant applied peak enhancement factor γ of 3.3. Therefore, by presenting a method to determine the peak enhancement factor from the dimensionless spectral peak variable, the spectral peak of JONSWAP was accurately reproduced.

Numerical analysis of the response of an onshore oscillating water column wave energy converter to random waves

The main objective of this study is to investigate differences of random incident waves from regular ones in performance of wave energy converters (WEC). A numerical analysis of an onshore oscillating water column (OWC) WEC is carried out by means of the FLUENT® software, which is based on Reynolds-Averaged Navier-Stokes equations. Analyses of the efficiency of an onshore OWC device with similar characteristics of the Pico’s plant and equipped with a Wells-type turbine, located at a 10 m deep flume, subjected to random waves with TMA spectrum and regular waves are shown. The resonance occurs at an energy period T = 8.6 s with an efficiency of 62% for a root mean square wave height Hrms = 1 m in random waves, while it is observed at T = 7.1 s with 84% of efficiency for H = 1.00 m in regular waves. Differences between efficiencies of regular and random waves are significant up to around the resonant period. This study showed that the use of random incident waves is fundamental to obtain more real results of analyses of onshore OWC device performance, even considering their requirement of high simulation time.

Numerical Simulation and Large-Scale Physical Modelling of Coastal Sand Dune Erosion

Do, K.; Shin, S.; Cox, D., and Yoo, J., 2018. An international comparison of drowning in South Korea. In: Shim, J.- S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 196–200. Coconut Creek (Florida), ISSN 0749-0208.Coastal sand dune system is important in the nearshore environment for sand supply, ecosystem, and hazard mitigation. In this study, a process-based morphological model was performed and the results were compared with large-scale laboratory experimental data. Two-dimensional large-scale laboratory experiments were conducted with 1:6 geometric scale in the large wave flume (104m (L) × 3.7 m (W) × 4.6 m (D)) of the Hinsdale Wave Research Laboratory at Oregon State University (Maddux et al, 2006). Several different wave conditions were used with different water levels in this experiment including pre-storm, storm, and post storm based on random wave time series by using TMA spectrum. The data set included cross-shore Wave heights, fluid velocities, and the profile changes of the beach and dune. The process based model, XBeach (Roelvink et al., 2009) was used to simulate the nearshore hydrodynamics and bed level change during storm wave condition. Several semi-empirical parameters were used in the XBeach model to predict morphodynamic process (Roelvink et al., 2009) and recently the updated parameters (WTI settings) were suggested based on the results of field observations. The present study ran the XBeach model by using both default and WTI settings and compared with the results from the experiments. The results showed that the model results with WTI settings showed good agreement with the measured beach profile while the model results with default settings over-predicted the offshore sediment transport and dune erosion. Especially, the wave skewness (facSk) and asymmetry (facAs) gave the highest contribution to predict dune erosion.

Finite water depth effects on the performance of a wave farm

The present paper focuses on the numerical investigation and the assessment of finite water depth effects on the performance (hydrodynamic behavior and energy absorption) of a wave farm. The farm consists of nine, free floating, mutually interacting, heaving Wave Energy Converters (WECs), arranged in a 3 × 3 rectilinear grid. The WECs' Power Taking Off (PTO) mechanism, actuated from their heave motion, is modelled as a linear damping system. Linear frequency domain analysis is implemented under the action of head regular and irregular waves, while three different installation depths are examined. For defining the PTO's damping coefficient, the water depth effect on the heave radiation damping coefficient is considered. Moreover, in the case of irregular waves, an incident wave spectrum with finite depth spectral formulation (TMA spectrum) is deployed for taking into account limited water depth conditions. Constructive and destructive interactions among the WECs in terms of power absorption are appropriately quantified, and the water depth effects on the existence and the extent of these interactions are assessed. The results of the present study illustrate that water depth effects are pronounced in the case of irregular waves, where the water depth's decrease leads to a significant decrease in the WECs' response and the farm's absorbed power, especially for the smallest examined installation depth. However, the comparison of absorbed power losses with power resource losses demonstrates that although the farm's installation at smaller water depth results in significant power resource losses, the farm's capture efficiency is not so intensively reduced.

Shallow water effects on wave energy converters with hydraulic power take-off system

The effect of water depth on the power absorption by a single heaving point absorber wave energy converter, attached to a hydraulic power take-off system, is simulated and analysed. The wave energy flux for changing water depths is presented and the study is carried out at a location in the north-west Portuguese coast, favourable for wave power generation. This analysis is based on a procedure to modify the wave spectrum as the water depth reduces, namely, the TMA spectrum (Transformation spectrum). The present study deals with the effect of water depth on the spectral shape and significant wave heights. The reactive control strategy, which includes an external damping coefficient and a negative spring term, is used to maximize power absorption by the wave energy converter. The presented work can be used for making decisions regarding the best water depth for the installation of point absorber wave energy converters in the Portuguese nearshore.

Correction to a Generalized TMA Spectrum and Proposal of Highly Accurate Approximation Expressions for its Integral Quantities

We present a corrected form of a universal frequency spectrum of wind waves in finite depth water under ideal generation condition made by Yamaguchi (1988). It is a generalized form (G-TMA) of the TMA spectrum proposed by Bouws et al.(1985) as an extension of the JONSWAP spectrum in deep water. The G-TMA spectrum covers other universal deep-water spectra such as the Donelan spectrum and shallow water extensions such as the FRF spectrum. We indicate that the supposed peak frequency fp in the G-TMA spectrum is actually not the peak frequency. This is remedied in our generalized form, with a non-trivial term. In addition, we present rather accurate approximations of spectral moments in terms of total wave energy and various average frequencies.

Impact of sea breeze on wind-seas off Goa, west coast of India

After withdrawal of the Indian Summer Monsoon and until onset of the next monsoon, i.e., roughly during November–May, winds in the coastal regions of India are dominated by sea breeze. It has an impact on the daily cycle of the sea state near the coast. The impact is quite significant when large scale winds are weak. During one such event, 1–15 April 1997, a Datawell directional waverider buoy was deployed in 23 m water depth off Goa, west coast of India. Twenty-minute averaged spectra, collected once every three hours, show that the spectrum of sea-breeze-related ‘wind-seas’ peaked at 0.23 ±0.05 Hz. These wind-seas were well separated from swells of frequencies less than 0.15 Hz. The TMA spectrum (Bouwset al 1985) matched the observed seas spectra very well when the sea-breeze was active and the fetch corresponding to equilibrium spectrum was found to be 77±43 km during such occasions. We emphasize on the diurnal cycle of sea-breeze-related sea off the coast of Goa and write an equation for the energy of the seas as a function of the local wind

An approach to determining nearshore bathymetry using remotely sensed ocean surface dynamics

This paper describes a spatially one-dimensional algorithm developed to estimate water depths from remotely sensed information of the water surface, using extended Boussinesq equations. Local phase speed estimates are obtained using a least-squares approach, from spatial profiles of surface elevation/orbital velocity lagged in time. Inversion algorithms have been developed for both linearized and fully nonlinear Boussinesq equations to calculate the depth. In all cases, synthetic input data are generated using a fully nonlinear time-dependent Boussinesq model. Wave conditions including monochromatic and irregular waves are simulated in the model. Mean flow effects are included in the inversion algorithm to account for currents. For monochromatic wave conditions, there is good agreement between the actual and estimated depth and particle kinematics. The fully nonlinear method, as compared to the linearized inversion, improves the depth prediction by 10% for the test case considered. Irregular wave conditions were simulated using time series generated for a TMA spectrum with varying values of the peak enhancement factor. The error in the inverted depths increased in the deeper part of the bathymetry as the wave train become more broad-banded. For monochromatic waves in the presence of weak currents, the modified algorithm (including mean flow effects) is seen to improve the inverted depth by 10%, over the original formulation.

Nearshore waveheight during storms

This paper considers storm waves generated locally over deep water and travelling into shoaling water. The offshore (deepwater) spectrum is assumed to be of the JONSWAP form, which is approximated by the Phillips spectrum with the same H mo . This is carried ashore assuming that breaking operates to produce a constant spatial steepness. The resulting formula for H mo as a function of depth is simple, and is shown to agree well with values computed from the TMA spectrum, which is the finite-depth equivalent of the JONSWAP spectrum. The result can be used to predict 50-year maximum waveheight in finite depth, or the actual nearshore waveheight in a storm using offshore predictions from a wave forecasting model. The theory has been tested against data taken off Holderness on the Yorkshire coast in two depths. The predictions of H mo are remarkably accurate, and are apparently robust against the actual form of the spectrum not being quite as assumed. The measured spectra in the storms approximate to the TMA formula when they are under active local generation.

Estimating Wave‐Induced Bottom Velocities at Vertical Wall

A linear theory equation is presented for estimating water velocity parameters beneath reflected, two‐dimensional, irregular, nonbreaking waves as a function of the incident wave spectrum, water depth, and spatial location. The estimation procedure requires specification of wave reflection and phase shift as a function of frequency. For the special case of normally incident, unidirectional, nonbreaking irregular waves being perfectly reflected by a vertical wall, the equation provides estimates of near‐bottom (above boundary layer) fluid particle velocity parameters as a function of only the incident wave spectrum, water depth, and distance from the wall. Comparisons between laboratory fluid velocity measurements and velocity estimates based on the measured incident spectrum are good for this special case. Furthermore, the distribution of peak horizontal velocities compares well with estimates based on the Rayleigh distribution. For two cases of a TMA spectrum wherein the significant height and peak perio...

Nonlinear Properties of Random Gravity Waves in Water of Finite Depth

Abstract The weakly nonlinear theory for a stationary and homogeneous field of random gravity waves in water of finite depth is developed to the third order. This describes the second-order nonlinearities as a bound wavefield that can be expressed in terms of the freely propagating first-order waves. Expressions are obtained for the second-order spectrum and for the first nonlinear correction to the free-wave phase velocity. Calculations of these nonlinearities are made for a specified spectral form (the TMA spectrum) and also for some spectra derived from measurements. Three influences are considered: (i) the directional distribution, which spreads the interacting waves and, if narrow, will enhance the bound-wave contribution to the spectrum; (ii) the growth stage, or maturity, which is quantified by the ratio of the phase velocity at the peak frequency to the surface friction velocity and, if small, will increase the nonlinearity considerably; and (iii) the depth. Although the nonlinearity increases for...

Similarity of the wind wave spectrum in finite depth water: 1. Spectral form

A self‐similar spectral shape (the TMA spectrum) to describe wind waves in water of finite depth is presented. The parametric spectral form is depth dependent and an extension of the deep water JONSWAP spectrum. The behavior of the spectrum in frequency and wave number space is discussed. About 2800 spectra selected from three data sets (TEXEL storm, MARSEN, ARSLOE) are investigated to show the general validity of the proposal self‐similar spectral shape.