We present research on the excitation of ocean surface wind waves in non-homogeneous situations, for the case of a deep water strait in the presence of a constant wind, blowing perpendicular to the coast line. The statistical wave model used is based on the Hasselmann equation with high-wavenumbers wave-breaking dissipation, exact non-linear four-wave interaction, and ZRP (Zakharov-Resio-Pushkarev (Zakharov et al. Nonlin Process Geophys 24:581–597 2017) wind input term. At the first stage, the waves propagate in the wind direction in a step-like moving front manner, which is the combination of self-similar fetch-limited and duration-limited solutions of the Hasselmann equation. The second stage begins after intermediate self-similar linear asymptotics for wave energy is built along the fetch. Beginning with that time, the wave groups, propagating across and against the wind due to nonlinear interaction, are observed. Despite the absence of long-wave dissipation, the system asymptotically evolves into a complex quasi-stationary state, comprised of the self-similar “wind sea” in the wind direction, and quasi-monochromatic waves, radiating close to orthogonally with respect to the wind, while slightly tilting from perfectly orthogonal to the wind direction, with the angle slant increasing toward the wave turbulence origination shore line, and reaching 15^∘ close to it. The total wave energy in the asymptotic state exceeds the wave sea energy propagating along the wind by a factor of two due to the presence of quasi-orthogonal and counter the wind wave fields. Very similar turbulence structure was previously observed experimentally; this paper presents a theoretical explanation of these results.

我们目前在非均匀情况下对海面风波激发的研究，对于在恒定风速下垂直于海岸线吹行的深水海峡的情况。使用的统计波模型基于具有高波数消散，精确的非线性四波相互作用和ZRP（Zakharov-Resio-Pushkarev（Zakharov等人，Nonlin Process Geophys 24：581–597）的Hasselmann方程（2017年）风输入项。在第一阶段，海浪以风向传播，呈阶梯状移动前向方式，这是Hasselmann方程的自相似提取限制和持续时间限制解的组合。在提取过程中建立起波能量的中间自相似线性渐近性之后，阶段开始。观察到由于非线性相互作用而在风中传播并逆风传播。尽管没有长波耗散，该系统渐近地演变成复杂的准平稳状态，包括在风向上的自相似“风海”和准单色波，它们相对于辐射方向正交正交风，同时从完全正交于风向略微倾斜，并且倾斜角度朝向波浪湍流起源岸线增加，并达到15^∘靠近它。由于存在准正交且与风波场相反，渐近状态下的总波能比沿风传播的波海能大两倍。先前通过实验观察到非常相似的湍流结构。本文提出了这些结果的理论解释。