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

Abstract

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 (fKH) are higher than those from the incoming wave expressed by fKH ≈[2.83,5.02]fw. In addition, the analytical expression, along with the energy spectra analysis of the vertical turbulent flux of momentum (Su′w′) 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.