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Simulation of hydraulic jumps in the presence of rotation and mountains
Author(s) -
Parrett C. A.,
Cullen M. J. P.
Publication year - 1984
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.49711046311
Subject(s) - orography , classification of discontinuities , finite difference , hydraulic jump , mathematics , rotation (mathematics) , flow (mathematics) , dimension (graph theory) , finite difference method , simple (philosophy) , mathematical analysis , geometry , meteorology , physics , pure mathematics , precipitation , philosophy , epistemology
Numerical solutions of the shallow water equations in one dimension are presented. The formation and evolution of hydraulic jumps are predicted with a simple centred finite difference model and with a model utilizing Glimm's method. Glimm's method is a special one‐dimensional method, which has been proved to converge to the physically relevant solution of a number of equations in the presence of discontinuities. The solution from it is used to check the finite difference method. Cases presented include examples of jumps produced in the presence of rotation, and a variety of jumps forced by flow over orography. It is shown that a conservative finite difference method, with the addition of artificial diffusion, converges to the correct solution for almost all cases. However, the use of multipoint filters gives poor results. At low resolution, the errors in modelling the flow induced by the orography are larger than errors caused by not resolving the shape of the orography.