A note on the imaginary part of bispectra

Masuda, Atsushi; Kuo, Yi-Yu

doi:10.1016/0198-0149(81)90063-7

Cited by 62 publications

(36 citation statements)

References 3 publications

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“…steep front faces and more gently sloped rear faces (Masuda and Kuo 1981;Elgar and Guza 1985a;Doering and Bowen 1995). The cross-shore trends in pressureand lidar-based skewness and asymmetry qualitatively are consistent with each other, and with earlier results.…”

Section: B Potential Applications Of Spatially Dense Lidar Observationssupporting

confidence: 79%

Lidar and Pressure Measurements of Inner-Surfzone Waves and Setup

Brodie

Raubenheimer

Elgar

et al. 2015

Journal of Atmospheric and Oceanic Technology

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Observations of waves and setup on a steep, sandy beach are used to identify and assess potential applications of spatially dense lidar measurements for studying inner-surf and swash-zone hydrodynamics. There is good agreement between lidar-and pressure-based estimates of water levels (r 2 5 0.98, rmse 5 0.05 m), setup (r 2 5 0.92, rmse 5 0.03 m), infragravity wave heights (r 2 5 0.91, rmse 5 0.03 m), swell-sea wave heights (r 2 5 0.87, rmse 5 0.07 m), and energy density spectra. Lidar observations did not degrade with range (up to 65 m offshore of the lidar) when there was sufficient foam present on the water surface to generate returns, suggesting that for narrow-beam 1550-nm light, spatially varying spot size, grazing angle affects, and linear interpolation (to estimate the water surface over areas without returns) are not large sources of error. Consistent with prior studies, the lidar and pressure observations indicate that standing infragravity waves dominate inner-surf and swash energy at low frequencies and progressive swell-sea waves dominate at higher frequencies. The spatially dense lidar measurements enable estimates of reflection coefficients from pairs of locations at a range of spatial lags (thus spanning a wide range of frequencies or wavelengths). Reflection is high at low frequencies, increases with beach slope, and decreases with increasing offshore wave height, consistent with prior studies. Lidar data also indicate that wave asymmetry increases rapidly across the inner surf and swash. The comparisons with pressure measurements and with theory demonstrate that lidar measures inner-surf waves and setup accurately, and can be used for studies of inner-surf and swash-zone hydrodynamics.

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Section: B Potential Applications Of Spatially Dense Lidar Observationssupporting

confidence: 79%

Lidar and Pressure Measurements of Inner-Surfzone Waves and Setup

Brodie

Raubenheimer

Elgar

et al. 2015

Journal of Atmospheric and Oceanic Technology

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“…The vertical asymmetry A of the wave signal can be obtained by integrating the imaginary part of the bispectrum (Masudo and Kuo 1981). The lower panel of Fig.…”

Section: Regular Waves Over a Submerged Bar (Dingemans Experiment 1994)mentioning

confidence: 99%

Validation of a Double-Layer Boussinesq-Type Model for Highly Nonlinear and Dispersive Waves

Chazel

Benoît

Ern

2011

Int. Conf. Coastal. Eng.

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A two-layer Boussinesq-type mathematical model has been recently introduced by the authors with the goal of modeling highly nonlinear and dispersive waves (Chazel et al. 2009). The analysis of this model has previously shown that it possesses excellent linear properties, up to kh = 10 at least, for dispersion, shoaling coefficient and vertical profile of orbital velocities. In the present work a numerical one-dimensional (1DH) version of model is developed based on a finite difference technique for meshing the spatial domain. It is then applied and verified against a set of three one-dimensional (1DH) test-cases for which either numerical or experimental reference results are available: i. nonlinear and dispersive regular waves of permanent form; ii. propagation of regular waves on a trapezoidal bar (laboratory experiments by Dingemans (1994)); iii. shoaling and propagation of irregular waves on a barred beach profile (laboratory experiments by Becq-Girard et al. (1999)). The test-cases considered in this study confirm the very good capabilities of the model to reproduce either exact solutions, high-precision numerical simulations and experimental measurements in a variety of non-breaking wave conditions and types of bottom profiles. Nonlinearity, dispersion and bathymetric effects are well accounted for by the model, which appears to possess a rather wide domain of validity while maintaining a reasonable level of complexity.

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“…The generation and amplification of these harmonics were studied and investigated by several observational and numerical studies (4)(5)(6)(7)(8). Results showed that these harmonics are bound with the spectral peak (8)(9)(10)(11). The second and third peaks of energy spectrum on two and three times of spectral peak frequency are very usual for field measurements (12,13).…”

Section: Introductionmentioning

confidence: 87%

Introduction of a Simple Cnoidal Wave Formulation Based on Nonlinear Interaction of Wave-Wave Principles

Mahmoudof

Hajivalie

2017

ijcoe

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In this study, a simple and efficient approach based on nonlinear wave interaction fundamentals is theoretically proposed to generate surface profile of the cnoidal waves. The approach includes Newton-Raphson algorithm to calculate the Ursell parameter and using a simple formulation to attain time series of cnoidal waves profile. The wave profile is determined as a superposition of limited number of cosine harmonics without encountering difficulties of using elliptic or hyperbolic functions, or any complex and complicated differential equations. It is demonstrated that a cnoidal wave profile is a result of high order self nonlinear interactions of primary frequency. Some definite energy is transmitted to higher harmonics due to nonlinear interactions. The amount of transmitted energy is controlled by Ursell parameter. The desirable accuracy determines the number of included harmonics in the proposed formulation and relative error of approach can be predicted based on Fourier and least square analysis techniques. The outputs of the proposed method are verified with cnoidal resulted from elliptic functions and the high efficiency of new approximation is revealed for engineering applications. The calculation of wave parameters such as energy flux, volume flux and radiation stress for cnoidal wave can be approximated using the proposed method. Using this approach, a physical interpretation of the Bm parameter (introduced in the first order of cnoidal wave theory) is presented. The calculation of several parameters such as velocity vectors and dynamic pressure of cnoidal waves is very simple by means of proposed approach.

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A note on the imaginary part of bispectra

Cited by 62 publications

References 3 publications

Lidar and Pressure Measurements of Inner-Surfzone Waves and Setup

Lidar and Pressure Measurements of Inner-Surfzone Waves and Setup

Validation of a Double-Layer Boussinesq-Type Model for Highly Nonlinear and Dispersive Waves

Introduction of a Simple Cnoidal Wave Formulation Based on Nonlinear Interaction of Wave-Wave Principles

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