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Numerical calculation of the displacements of a stratified airstream crossing a ridge of small height
Author(s) -
Sawyer J. S.
Publication year - 1960
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49708636905
Subject(s) - amplitude , ridge , constant (computer programming) , computation , physics , troposphere , function (biology) , mechanics , train , meteorology , flow (mathematics) , stream function , geology , mathematical analysis , mathematics , vortex , optics , geography , paleontology , vorticity , cartography , evolutionary biology , computer science , biology , programming language , algorithm
Numerical computations have been made of the solutions of the equation\documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{{\partial ^2 \psi }}{{\partial z^2 }} + \frac{{\partial ^2 \psi }}{{\partial x^2 }} + l^2 \psi = 0 $$\end{document} which describes the stream lines in two‐dimensional flow of small amplitude in a stratified airstream. Solutions are computed for various variations of the parameter l as a function of height. ( l 2 = gβ/ U 2 ‐ U −1 ∂ 2 U /∂ z 2 is function of the wind and temperature variations with height in the airstream). To render the mathematical problem determinate the value of l 2 is assumed to be constant above 16 km up to unlimited heights and by specifying the form of solution above 16 km consistent solutions are obtained for the troposphere little affected by the value of l 2 assumed at high levels. The solutions include lee‐wave trains which diminish in amplitude downstream as well as those of constant amplitude. The method of solution results in the former appearing on the downstream side of the ridge only. (It is assumed that waves of constant amplitude can appear only on the downstream side). Some typical displacements of the stream lines are illustrated in Figs. 3 to 10. They are similar to those computed by Queney (1947) and Scorer (1949) but it is demonstrated that lee waves may arise from variations of l 2 with height additional to those specified by these authors.