Oscillations in the Roughness Sublayer, a Lagrangian Perspective

A two-equation Lagrangian stochastic dispersion model for the coupled turbulent vertical (w) and longitudinal (u) velocity increments is used to derive the vertical velocity auto-correlation Rww and the cross-correlation Ruw functions with time lag tau in the roughness sublayer above tall canopies situated on complex terrain. The necessary condition for oscillatory behavior is derived and shown to be linked to a coefficient in the pressure-mean strain interaction model. For cases where the mean wind direction originates from flat terrain, no oscillations in and are predicted or measured. On the other hand, for cases where the upwind direction originates from complex topography, damped oscillations are measured and predicted due to amplification of the mean strain rate and the pressure-mean strain interaction. The agreement between model predictions and Eulerian velocity measurements of Ruw in the RSL and their implications to flow models and RSL dispersion are discussed.