Following on from a theoretical solution to the Kelvin–Helmholtz (KH) instability under submerged canopy-oscillatory flow environments a relationship between the incoming free surface wave frequency and KH frequency was developed. The KH frequencies ($f_{KH}$) are higher than those from the incoming wave expressed by $f_{KH}$ $\approx [2.83,5.02]f_w$. In addition, the analytical expression, along with the energy spectra analysis of the vertical turbulent flux of momentum ($S_{u^{\prime }{w}^{\prime }}$) for cases when the KH dominates vertical mixing, allowed us to observe the spectral shortcut mechanism. Based on comparisons between the KH time scale and the mean horizontal transport of mass time scale, it can be concluded that the instability has no effect on the wave-induced steady current process. The instability plays an important role on vertical mixing but not on the horizontal transport of mass.

根据水下冠层振荡流动环境下开尔文-亥姆霍兹 (KH) 不稳定性的理论解决方案，开发了入射自由表面波频率与 KH 频率之间的关系。KH 频率 ($F_{ķH}$) 高于由下式表示的入射波的值$F_{ķH}$ $\approx [2.83,5.02]F_w$. 此外，解析表达式以及动量垂直湍流的能谱分析（${\mathrm{小号}}_{{你}^{\text{'}}{w}^{\text{'}}}$) 对于 KH 在垂直混合中占主导地位的情况，我们可以观察到光谱捷径机制。通过比较KH时间尺度和质量时间尺度的平均水平传输可以得出结论，不稳定性对波浪诱导的稳流过程没有影响。不稳定性对垂直混合起重要作用，但对质量的水平传输不重要。