“Choppy wave” model for nonlinear gravity waves

Abstract

[1] We investigate the statistical properties of a three-dimensional simple and versatile model for weakly nonlinear gravity waves in infinite depth, referred to as the ''choppy wave model'' (CWM). This model is analytically tractable, numerically efficient, and robust to the inclusion of high frequencies. It is based on horizontal rather than vertical local displacement of a linear surface and is a priori not restricted to large wavelengths. Under the assumption of space and time stationarity, we establish the complete first-and second-order statistical properties of surface random elevations and slopes for long-crested as well as fully two-dimensional surfaces, and we provide some characteristics of the surface variation rate and frequency spectrum. We establish a relationship between the so-called ''dressed spectrum,'' which is the enriched wave number spectrum of the nonlinear surface, and the ''undressed'' one, which is the spectrum of the underlying linear surface. The obtained results compare favorably with other classical analytical nonlinear theories. The slope statistics are further found to exhibit non-Gaussian peakedness characteristics. Compared to observations, the measured non-Gaussian omnidirectional slope statistics can only be explained by non-Gaussian effects and are consistently approached by the CWM.

Investigation on Doppler Spectral Characteristics of Electromagnetic Backscattered Echoes From Dynamic Nonlinear Surfaces of Finite-Depth Sea

“…Recently, Soriano et al [17] extended the Doppler spectral analysis to the two-dimensional (2-D) nonlinear surfaces on the basis of small-slope integral equation method. Nouguier et al [18] combined the so-called nonlinear "choppy wave model" (CWM) [19] with the weighted curvature approximation (WCA) probing the impact of nonlinear wave profiles on scattering from sea surfaces. Compared with other nonlinear surface models, the CWM has been proven to enjoy some desirable properties such as analytical simplicity and numerical efficiency.…”

Sea Surface Microwave Scattering at Extreme Grazing Angle: Numerical Investigation of the Doppler Shift

“…Recently, a versatile and numerically efficient weakly nonlinear model has been reintroduced [29], after the pioneering work of Pierson [34]. It was termed CWM in view of the choppy aspect of the waves it produces.…”

“…The geometrical transformation operated by the CWM induces a modification of the original prescribed spectrum, a process which is referred to as "dressing." An appropriate generation of CWM would require a preliminary step of "undressing" the reference spectrum, a procedure which is discussed in [29] and [35]. The dressing of the spectrum results in a small increase of the high-frequency components of the wavenumber spectrum but is not expected to impact significantly the shape of the normalized Doppler spectrum.…”

“…Even though these models have been shown [20], [22] to introduce additional effects which are not seen with weakly nonlinear models (such as increased Doppler spectral broadening and reverse travelling waves), their utilization in the context of microwave scattering by evolving surfaces raises numerical and conceptual issues which are not solved yet (particularly blowup of high-frequency components and nonstationarity of the power spectrum). We will therefore rely only on appropriate weakly nonlinear models, namely, the Creamer representation as well as a recent Lagrangian model, the so-called choppy wave model (CWM) [29] and its recent improvement [30]. The different hydrodynamical models are reviewed in Section II.…”

Study on Doppler spectra of two-dimensional skewed sea surfaces

“…In order to overcome the problem, Soriano [7] expanded the Creamer formulation into Taylor series and kept the first two orders, both of which can be computed using the fast Fourier transform. More recently, Nouguier presented the choppy wave model (CWM) [8] and combined the CWM with the weighted curvature approximation [9,10] to study the Doppler spectra for nonlinear surfaces at X-band. Although the Creamer (2) model and the CWM are weakly nonlinear models, they make 2-D nonlinear surface Doppler spectral analysis possible.…”