FORM AND WAVE DRAG DUE TO STABLY STRATIFIED TURBULENT-FLOW OVER LOW RIDGES

We investigate how stable stratification affects the aerodynamic force , or form drag, induced by turbulent boundary-layer now over two-dimen sional hills. Both analytical and numerical models are used to calcula te the now and thence the form drag on the hill. In the analytical mod el we use a two-layer, truncated mixing-length, turbulence model, whic h is consistent with scaling arguments and which produces reliable est imates of the form drag for the neutral now. The form drag is also cal culated analytically using an eddy-viscosity model, and the results co mpare well with values computed with the nonlinear numerical model tha t uses a similar turbulence model. The leading-order contribution to t he form drag is from a non-separated sheltering mechanism, which is si milar to the mechanism in neutral flow. Stable stratification changes the magnitude of this mechanism through several effects. For weak stra tification the predominant effect is an increase in shear in the upstr eam wind profile across a middle layer, which increases the form drag by a factor of two or more. There is indirect experimental evidence to support this finding. If the stratification is more stable, then the shear across the middle layer becomes limited because the boundary lay er has a finite depth. Then the dynamical effect of buoyancy on the pr essure perturbation becomes important and reduces the form drag, event ually to zero. For still more stable stratification, gravity waves and associated wave drag are produced. The analysis shows that the approp riate scaling velocity for wave drag is the approach-flow wind speed e valuated at the middle-layer height. The relationship between the form and wave drag components is investigated by evaluating the analytical formula for the drag on isolated hills of two idealized shapes. For w eak stratification the form drag dominates, but as the stratification becomes more stable the wave drag increases and first equals the form drag, at a value that depends on the hill shape, and then dominates.