Abstract We develop asymptotic expressions for wave action density and action flux, using an extension of Kirby & Chen (1989)’s perturbation solution for weakly-sheared currents allowing for a basic flow with Froude number F = U ∕ g h = O ( 1 ) but with weak vertical shear. The accuracy of the expressions for action density and flux is established by comparison to analytic results for a current with constant shear, and to numerical results for a field case involving a buoyant ebb-tidal plume with strong vertical shear and for a case involving a numerically determined profile for a wind-driven current. We compare our results to those from recent work of Quinn et al. (2017), and find unresolved discrepancies in that prior work. We provide additional suggestions for efficiently implementing the required extensions in coupled wave/circulation models using a Taylor series expansion based on conditions at peak frequency and direction. These results generalize the previous work of Banihashemi et al. (2017) to motions in two horizontal dimensions, and cover the determination of the wave action.

中文翻译：

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垂直剪切平均流中波浪作用守恒的近似

摘要 我们开发了波作用密度和作用通量的渐近表达式，使用 Kirby & Chen (1989) 的弱剪切电流微扰解的扩展，允许基本流动具有 Froude 数 F = U ∕ gh = O ( 1 )但垂直剪切力较弱。作用密度和通量表达式的准确性是通过与具有恒定剪切力的电流的分析结果、涉及具有强垂直剪切力的浮力退潮羽流的现场情况以及涉及数值计算的情况的数值结果进行比较来确定的。确定的风驱动电流分布。我们将我们的结果与 Quinn 等人最近工作的结果进行比较。(2017)，并在之前的工作中找到未解决的差异。我们提供了额外的建议，以根据峰值频率和方向的条件使用泰勒级数展开在耦合波/环流模型中有效地实现所需的扩展。这些结果概括了 Banihashemi 等人以前的工作。(2017) 到两个水平维度的运动，并涵盖了波浪作用的确定。