Linear Instability Theory for Frequency Assessment of Coherent Vortices in Submerged and Aside Rigid Canopies

Abstract

Two-layer system of flow through and above vegetation linked by shear flow exhibits periodic oscillations at the interface called the Kelvin-Helmholtz vortices. A dispersion relation for the vortices is derived as a function of flow and vegetation parameters and extended to aside vortices that exist in horizontally stratified flow. Nonlinearity exists in the oscillations in vertically stratified flow however is suppressed in horizontally stratified flow because of the horizontally bounded flow and depth-wise phase difference in the oscillations. The relation for both the vortex types provides a simple way to calculate vortex frequency using measurable flow and vegetation parameters. Results show that the vortex frequency for rigid plants is a function of flow hydraulics and stem density, whereas for flexible plants it is a function of the geometry of bending stems.