Directional spectrum of wind waves: Part II—comparison and confirmation

Abstract

A model on the directional frequency spectrum of wind waves for deep water is introduced. The comparisons of the proposed model with other existing models show that the proposed model is very close to the JONSWAP model and DHH model for describing the developing waves under the normal spectral bandwidth, and has a better description for the transition of the unidirectional spectrum from co -4 to co -s at a position around 3cop, i.e., three time the peak frequency. Comparisons also show that the proposed model describes closely both field data measured by a four-frequency radar and a laser-optical sensor, and laboratory data measured by a laser slope gauge and an imaging optical method. The comparisons further demonstrate that the inverse spectral bandwidth as a new wave parameter is robust for describing the spectral steepness. Finally, the formula on the local spectral-peak angular frequency is confirmed using the observed two-dimensional spectra.based on the laboratory observations of Jfihne and Riemer (1990) and Klinke and Jfihne (1992). The directional spreading function, D (r k ), is given by D(r = sechZ(p~)/S sech2(t3r162 (4) with 10 [ 04408393(~p)-0567]

Directional Wave Scattering Distribution Modes Analysis and Synthesis of Random Ocean Media Roughness for SAR Electromagnetic Interactions Using Feature Fusion in Dynamic Sea States: A Survey

“…The proposed approach reduces the reliance on ocean empirical approximations and field observations [11], [35], [38], as well as the limitations of formulations [6], [22], such as dimensionality [30], [50], [55], large-scale formulations [3], [41], modulation effects [53], [68], [74], stochastic distributions [19], [42], [76], and wavenumber complexities [36], [47], [101]. In a broader context, this research extends the groundwork laid by [9], [12], [24]- [27], [29], [30], [34], [37], [42], [46], [48]- [50], [55]- [62], [64]- [65], [67], [68], [73]- [78], [80], [82], [86], [87], [91]- [94], [96], [98],…”

“…The third term in (2) accounts for a wind-generated wavefield property, serving as an additional cutoff that limit the energy-containing part of the spectrum to less than 10𝑘 [134]. As a result, the curvature spectrum oscillates at10 𝑘 [96], indicating that steep mechanically generated waves produce parasitic capillary waves in the absence of wind [134]. This highlights that long-waves, referred to as low-frequency curvature spectrum, are dependent on wave-age and fetch dependent [94].…”

“…Under steady sea state conditions with wind forcing, ocean waves generated by the wind propagate in the direction of the wind vector, with field measurements indicating that the spectral width is narrowest near the peak frequency and increases towards higher and lower frequency components [94], [96], [104], [105] , [111]. This spectral distribution pattern is influenced by various physical processes, including wind-induced energy flux, energy dissipation, and nonlinear interactions, with their relative contributions varying at different stages of wave development.…”

“…As an approach, a relative algebraic formulation of the two-scale WFS under constant sea state conditions is considered. This formulation aims to replicate the directional characteristics of ROM interactions through the utilization of angular spreading functions, hereinafter referred to as directional two-scale WFS [74], [96], [103]. The directional formulation incorporates diverse empirical metrics to achieve satisfactory agreement in both hydrodynamic and energy scatterings across a broad frequency range, spanning both above and below the peak frequency [99], [104].…”

“…The directional formulation incorporates diverse empirical metrics to achieve satisfactory agreement in both hydrodynamic and energy scatterings across a broad frequency range, spanning both above and below the peak frequency [99], [104]. Nevertheless, it is crucial to recognize that while spreading functions effectively represent the directional distribution under varying sea state conditions, they can significantly smear the essential attributes of a wavefield distribution when wind and waves interact concurrently [96], [97] [103], [104]. As a result, there is a discernible need for a more realistic synthesis of directional WFS that establishes a correlation between the two-scale WFS and the angular spreading occurring within the fetch, particularly in relation to ROM surface roughness under varying sea states.…”