Linearly Stratified, Rotating Flow over Long Ridges in a Channel

The flow of a rotating, linearly stratified fluid over a long symmetric ridge in a channel is investigated experimentally. The laboratory apparatus consists of a long channel of rectangular cross section. The upper bounding surface is a transparent, horizontal plane; the lower boundary is a horizontal flexible belt. The belt serves as a false bottom of the channel and is translated parallel to its long axis. Topographic features are mounted on the belt and are towed through a salt-stratified fluid which is otherwise at rest relative to a rotating observer; the channel rests on a rotating table whose rotation axis is vertical. The most important dimensionless parameters governing the motion are the Rossby and Ekman numbers, a stratification parameter defined as the ratio of the Brunt-Vaisala frequency to the Coriolis parameter, and the geometrical parameters defining the aspect ratio of the ridge, the ridge height to channel depth ratio and the ridge to channel width ratios. An analysis is presented that demonstrates the conditions under which centrifugal effects can be neglected in such laboratory experiments. The analysis also shows the conditions under which the laboratory flows should be a good approximation to the quasigeostrophic potential vorticity equations and attendant boundary conditions for the oceans and atmosphere. This analysis is made for a general three-dimensional topographic feature; i.e. it is not restricted to a long ridge. The laboratory system seems to be an excellent vehicle for modelling oceanic flows but does not properly reproduce a non-Boussinesq term in the atmospheric equation. An analysis for an infinitely long ridge is presented. The predictions so obtained are in good qualitative agreement with the experiments. The quantitative agreement, for the range of parameters considered however, is shown to be poor and this is attributed to neglecting the effects of the lateral bounding surfaces. The experiments demonstrate that for fixed rotation, stratification and free stream speed, the streakline deflection caused by the topography decays with height. For such experiments the flow in the lower levels for positive upward rotation deflects to the left before reaching the ridge, then continues to deflect to the left on the upwind side of the ridge before beginning a rightward drift slightly upstream of the mountain crest. This rightward drift continues on the downwind side of the ridge and well downstream of the ridge itself before reaching a maximum shift, from which a leftward drift again begins. Increased rotation, other parameters being held fixed, provides stronger horizontal streakline deflections. Stronger stratification, other parameters being fixed, leads to stronger downslope winds and possibly flow separation in the lee. Various characteristics of the flow field, such as the distance upstream to which substantial streakline curvature is observed, are measured as functions of the various system parameters; comparisons with the infinite ridge theory are also made. The downstream motion is accompanied by lee waves for the major portion of the parameter space examined. The amplitude of these waves is shown to decrease with increased rotation, other parameters being held fixed. Some non-rotating experiments are conducted and these are shown to be in good agreement with the model of Long (1955) and the measured wavelengths are found to be in good agreement with linear theory and laboratory measurements made by other investigators. Measurements supporting the theory of Queney (1947) are presented which show that the horizontal wavelengths of the lee waves decrease for increased rotation, other parameters being fixed. A flow regime map based on the observed structure of the vertical wave motion is developed and it is shown that for the range of parameters considered, rotation plays only a minor role, if any.