Relative importance of Terms in the Turbulent-Energy and Momentum Equations as Applied to the Problem of a Surface Roughness Change

Abstract

There are four equations which must he satisfied in a description of the flow, in the two-diinensional case, across a change in surface roughness in the neutrally-stable surface boundary layer: the horizontal and vertical momentum equations, the turbulent energy equation, and the continuity equation. Using variations on the Peterson model, the relative magnitudes of the terms in these equations are examined and the wind and shear-stress profiles predicted by each variant model are compared. The following conclusions are made: The horizontal-momentum and turbulent-energy equations are essential in a physically reasonable model of the flow. The vertical-momentum equation is less important since the pressure-gradient term in the horizontal equation of motion is relatively small except near the surface singularity. Neglect of the vertical-motion terms and thus the continuity equation does not alter the major features of the downstream wind and shear-stress profiles.