An Analytical Model for Sub grid Force-Equilibrium Approach in Submerged Vegetative Channel

Abstract

A new, analytical model of the vertical flow velocity profile of submerged vegetation has been developed. Velocity profile can be divided into three zones: linear zone which is closed to bed with linear velocity
distribution, logarithmic zone which involves the main channel without vegetative cover and the middle zone (transition zone) that is affected by the momentum of upper zone. For the surface layer, Prandtl’s mixing length
concept is adopted resulting in the well known logarithmic flow velocity profile. A new virtual roughness height concept is introduced for both logarithmic and vegetative zones, which accounts for the effect of vegetation on velocity distribution in these zones. From the continuity condition that both actual value and gradient of the flow velocity of the vegetation and the surface layer should be equal at the interface (z=hp), velocity at the
interface is obtained. This value is used as a reference value for obtaining velocity profile in vegetation zone using sub grid force equilibrium approach.

Keywords: Vegetated open channel flow, Force equilibrium approach, Velocity Distribution