Impulsively Started, Linearly Stratified Flow over Long Ridges

Abstract

This study is an experimental investigation of impulsively started, linearly stratified flow over long ridges of triangular and cosine-squared cross sections. The experiments employ a rigid-lid boundary confining the fluid from above. Emphasis is given to the temporal development, as well as to the fully established character of the wake. Both qualitative and quantitative measures of the characteristics of the flow are introduced and thew are studied for a wide range of the system parameters, which include the internal Froude number, Fi Reynolds number, Re ridge height to width ratio, G>d and ridge height to fluid depth ratio, Gh The governing equations for the laboratory experiments are related to those of the atmosphere. Flow regime diagrams based on the mode of the vertical wave structure are presented and the relationship of the observations to linear theory discussed. For the lowest vertical wave mode the constant phase lines of the Ice waves have a vertical slope implying total reflection of the waves by the rigid lid. At higher wave modes the constant phase lines slope upstream, indicating that some of the upward propagating momentum flux is absorbed by the lid. Experiments are presented for certain ranges of dimensionless parameter space which show the lee wave field breaking into turbulence and in certain cases subsequently relarminarizing. Observables in the tee wave pattern are introduced, including a normalized wavelength, ?/D, and wave amplitude, a/hdimensioniess downstream distance to which significant oscillatory motion in the wake occurs, L/D, and a normalized vertical location of the principal rotor, zr/h, and measurements of these for a range of system parameters are presented.