Airflow over mountains

Abstract

CORRESPONDENCE of Bosanquet's measurements whereas Meade appears to have fitted c to the measurements themselves and even allowed a different range of values for each plant. I still feel that we must reserve judgment on which of the working theories gives the most accurate results until experimental data are available over a wider range.One object behind my analysis was to promote, in conjunction with observations of the rise of plumes, measurements of their spreading and of atmospheric turbulence, for it seems clear that there is no unique relation between these two, and that each will strongly affect the plume's elevation. Any claim to provide even an approximate treatment dispensing with one of these parameters, or its equivalent, must therefore be open to suspicion on that very account.But Meade of course does not really reduce to a ' single parameter c ' for he requires to assume values for both p and zo/Rp It is agreed that his analysis is the less elaborate when it comes to the computation of an actual example, but this is scarcely a serious consideration. Graphical or numerical integration is required in any event, and the problem is of sufficient importance to warrant the calculations being carried out once and for all to cover the relevant range of conditions.My main objection to Meade's treatment is that it turns its back on certain issues which were raised in mine, and which were there at least set on the road towards their resolution. Eq. (1) gives w as a monotonic decreasing function of z , and so excludes any case in which vertical motion is generated by buoyancy, e.g., the plumes from smoke-pots used in frost protection. Neither this nor the preceding formula contain the plume temperature or Froude number, and they therefore imply that all plumes with the same wo, Ro, zo will follow the same path, however hot they are. No indication is given of how to apply the formula when the environment is thermally stratified; presumably this might be done by adjustingp, but what are the guiding principles ?Finally it is seen from the complete solution in the M.R.P., Eq. (13), that the Eq. (3) of that paper is not satisfied : this equation here represents the condition that the temperature regime shall be in a steady state. The solution therefore does not apply to the steady state, nor indeed is it the solution of any properly formulated problem because only two basic equations have been given for the three independent variables R, 8, w.In order to extend the range of experimental data my colleague, F. K. Ball, has made measurements of plumes from burning oil-pots under a variety of wind speeds. At the larger distances downwind the smoke was too disperse to measure accurately, but at shorter distances the heights agreed very well with my theory (first phase). Thus the tentative formula Eq. (5) of my paper stands up well, without change of the constant of proportionality, to a considerable change in scale and boundary conditions. We have little evidence at all about the second phase, and the limitations of my t...

Linear theory of stratified hydrostatic flow past an isolated mountain

“…The general nature of these predictions are not strongly dependent on the hydrostatic assumption or on the choice of mountain shape, but are closely associated with the generation of three-dimensional mountain waves. The blocking criterion of Sheppard (1956), using a parcel argument, does not seem useful in this context. Furthermore, the linear theory result is quite distinct from the low Froude number result of Drazin (1961).…”

Mountain-induced stagnation points in hydrostatic flow

“…1) indicates that a low-level parcel moving along the centerline of a narrow flow-aligned ridge can rise to a great height without stagnating. Lifting is not limited to a maximum value of U,/N suggested by Sheppard (1956). This is so because the displacement field q ( x , y , z) laterally disperses so rapidly aloft that the integral of displacement above the parcel I,, remains small.…”

“…The form of this equation does not support the "kinetic energy" concept of flow stagnation proposed by Sheppard (1956). Linear theory estimates of the displacement integral are used to predict the occurrence of stagnation points as a function of hill shape and ambient shear.…”

“…The well known analysis and "kinetic energy" argument of Sheppard (1956) indicates that the lowest layer of a stably stratified fluid cannot lift over a hill without stagnating if the hill height h > U / N , regardless of the hill shape. Extending Sheppard's analysis for hydrostatic flow we find (1) the local height dependent term used by Sheppard cancels out, and (2) the critical hill height is quite dependent on hill shape.…”

Wind speed interpolation in the vicinity of the Panama Canal

“…Perry and Hollis, 2005). Jiang et al (2001) proposed a modified scheme to the surface 1/r 2 interpolation based on the potential flow concept by Sheppard (1956) for stable atmospheres which requires digital terrain data. These authors found it acceptable to apply the potential flow concept, but they also found that the actual pattern of air flow around the mountain is very complex.…”