A phenomenological closure model of the normal dispersive stresses

The spatial averaging of the momentum equation in obstructed environments generates dispersive stress terms that represent momentum flux induced by the spatial heterogeneity of the time-averaged flow. While previous studies ignored the dispersive stresses, recent evidences indicate that they may be significant, in particular within entry flow regions such as the leading edge of submerged vegetation in rivers and streams. The lack of available closure models makes it almost impossible to include the dispersive stresses in canopy flow models. Based on observations and theoretical considerations, we propose to model the normal component of the dispersive stress as a function of square of the double-averaged velocity. The model was tested by detailed particle image velocimetry measurements that were obtained inside and around a modeled vegetation patch, made of randomly distributed vertical thin glass plates. It was found that the normal dispersive stresses are scaled with two parameters: the relative area covered by wakes and the relative magnitude of the recirculation (negative) velocity inside the wake zones. The results indicate that prediction of the dispersive stresses is more sensitive to the wake area parameterization than that of the recirculation zone velocities. It is therefore concluded that when parameterization of the relative wake area is available, the normal dispersive stresses can be modeled and included in future flow simulations.