弱黏性Dysthe理论的高阶扩展及非线性平均流阻尼的相位滞后模型
Higher-Order Extensions of Weakly Viscous Dysthe Theory and a Phase-Lag Model for Nonlinear Mean-Flow Damping
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中文总结 AI 辅助
该研究将弱黏性深水波包的多尺度分析扩展至Dysthe阶外，推导了相关可解性条件，还建立了有限调整时间的平均流响应模型，探究了非线性平均流阻尼的相位滞后修正机制。
中文摘要 AI 辅助
我们在Dias、Dyachenko和Zakharov（DDZ）的势流简化框架内，将弱黏性窄带深水波包的Carter-Govan多尺度分析扩展至Dysthe阶之外，旨在确定该框架是否会产生用于唯象修正非局域Dysthe平均流相互作用的复乘子$(1 + i\beta)$。尽管阶数计数显示直接的载波-平均流相互作用出现在六阶，但并不排除由黏性依赖的低阶谐波及非线性相互作用产生的间接五阶贡献。因此，我们推导了诱导平均流的首次修正项以及完整的五阶一阶谐波可解性条件。所得非局域项依赖于导数且不含显式黏性，从而在DDZ框架内排除了所提出的间接机制。在六阶时，对非线性黏性块的受限计算分离出一个直接的载波-平均流贡献，其算子结构与规定平均流修正的虚部相同。此外，有限调整时间模型产生了精确的、频率依赖的平均流响应，其低频展开给出乘子$1 + i\beta_{\mathrm{eff}}(\Omega)$，其中$\beta_{\mathrm{eff}}(\Omega) = \Omega\tau$。当$\Omega\tau = \mathcal O(\epsilon)$时，所得相位滞后修正出现在五阶，比主导Dysthe平均流相互作用高一个阶次。
英文摘要
We extend the Carter-Govan multiple-scales analysis of weakly viscous, narrowband deep-water wave packets beyond Dysthe order within the potential-flow reduction of Dias, Dyachenko, and Zakharov (DDZ). We seek to determine whether this framework generates the complex multiplier $(1 + iβ)$ used phenomenologically to modify the nonlocal Dysthe mean-flow interaction. Although order counting places a direct viscous carrier-mean interaction at sixth order, it does not exclude an indirect fifth-order contribution arising from viscosity dependent lower-order harmonics and nonlinear interactions. We therefore derive the first correction to the induced mean flow and the complete fifth-order first-harmonic solvability condition. The resulting nonlocal terms are derivative--dependent and contain no explicit viscosity, excluding the proposed indirect mechanism within the DDZ framework. At sixth order, a restricted calculation of the nonlinear viscous block isolates a direct carrier-mean contribution with the same operator structure as the imaginary component of the prescribed mean-flow correction. Independently, a finite-adjustment-time model yields an exact, frequency dependent mean-flow response. Its low-frequency expansion produces the multiplier $ 1 + iβ_{\mathrm{eff}}(Ω)$, with $β_{\mathrm{eff}}(Ω) =Ωτ.$ When $Ωτ= \mathcal O(ε)$, the resulting phase-lag correction enters at fifth order, one order beyond the leading Dysthe mean-flow interaction.
