Analytical solution for the Kelvin–Helmholtz instability under a submerged canopy-oscillatory flow

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 ((Formula presented.)) are higher than those from the incoming wave expressed by (Formula presented.) (Formula presented.). In addition, the analytical expression, along with the energy spectra analysis of the vertical turbulent flux of momentum ((Formula presented.)) 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.