多尺度表面重力波的随机输运与波相互作用：第二部分——动理学理论及海洋波应用
Stochastic Transport and Wave Interactions for Multiscale Surface Gravity Waves: Part II: Kinetic Theory and Ocean-Wave Applications
AI总结：
本文基于随机变分框架，针对深水区域表面重力波发展动理学理论，揭示随机输运在宽谱范围常超过经典四波相互作用，为业务波模型纳入输运源项提供依据。
AI中文摘要：
基于姊妹论文建立的随机变分框架，本文研究线性化随机水波系统，该系统包含与小尺度关联模式的输运动力学耦合的大尺度随机波动力学。在该框架内，针对深水区域中与未分辨随机速度场相互作用的表面重力波，本文发展了一套动理学理论。能量分析得到的波作用量动理学方程呈现两种不同机制：扩散散射机制和与Hasselmann-Zakharov理论结构相似的四次相互作用机制。在本文框架中，这些有效四次相互作用源于大尺度流动对未分辨涨落的随机输运，而非经典的内禀共振非线性。本文推导了扩散张量和有效增长率的标度律，揭示了Miles型产生-耗散机制。利用JONSWAP谱，本文对比了随机输运与经典Hasselmann相互作用的强度。对于未分辨速度方差（σᵤ≈0.1 m s⁻¹）和去相关时间（τ_c≈10 s）的实际海洋值，研究发现，在宽谱范围内，随机输运与经典四波相互作用速率相当，且常常超过后者。输运强度S=σᵤ²τ_c成为控制相互作用机制转变的关键参数。这些结果表明，未分辨的随机输运在谱演化中的作用可能比业务波模型中通常体现的要大得多，为将输运诱导源项与标准共振相互作用闭合方案一同纳入提供了动机。
英文摘要：
Building on the stochastic variational framework established in the companion paper, we investigate here the linearized stochastic water-wave system, consisting of a large-scale stochastic wave dynamics coupled to transport dynamics for the small-scale correlation modes. Within this framework, we develop, in the deep-water regime, a kinetic theory for surface gravity waves interacting with unresolved stochastic velocity fields. An energy analysis yields a wave-action kinetic equation exhibiting two distinct regimes: a diffusive scattering regime and a quartic interaction regime with structural similarities to Hasselmann--Zakharov theory. In the present framework, these effective quartic interactions arise through stochastic transport of unresolved fluctuations by the large-scale flow rather than through classical intrinsic resonant nonlinearity. Scaling laws are derived for the diffusion tensor and the effective growth rate, revealing a Miles-type production--dissipation mechanism. Using JONSWAP spectra, we then compare the strength of stochastic transport and classical Hasselmann interactions. For realistic oceanic values of unresolved velocity variance ($σ_u \approx 0.1\,\mathrm{m\,s^{-1}}$) and decorrelation time ($τ_c \approx 10\,\mathrm{s}$), stochastic transport is found to compete with, and often exceed, classical four-wave interaction rates over broad spectral ranges. The transport intensity $S=σ_u^2τ_c$ emerges as a key parameter controlling the transition between interaction regimes. These results suggest that unresolved stochastic transport may play a substantially larger role in spectral evolution than is commonly represented in operational wave models, and motivate the inclusion of transport-induced source terms alongside standard resonant interaction closures.
