ISSN:
0271-2091
Keywords:
Shallow Water Equations
;
Iterative
;
Harmonic Analysis
;
Least Squares
;
Finite Element
;
Tides
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
An iterative type harmonic finite element model is developed for solving the full non-linear form of the shallow water equations. The scheme iteratively updates time histories of the non-linear terms which are then harmonically decomposed and used as forcing terms for the linear sets of equations which result from the harmonic separation of the shallow water equations.A least-squares harmonic analysis procedure is used to decompose the non-linear forcing terms. This procedure allows for the very efficient separation of extremely closely spaced harmonics, since it is highly selective with respect to the frequencies it considers. In addition tailoring the procedure and using very specific time steps and sampling periods significantly reduces the number of time samplings points required. In conjunction with the iterative nature of our scheme, the least-squares procedure makes the scheme entirely general, allows for the direct assessment of all tidal constituents, including compound tides, and permits the clear cut and complete investigation of their mutual interaction through the non-linearities. In addition this procedure readily computes very-low-frequency or residual type circulations.The FE formulation used shows a very low degree of spurious oscillations while remaining quite simple to implement. This control on nodal oscillations is especially important due to the energy transfer mechanisms involved in this type of iterative scheme.In an example application the effects of the various non-linear overtide and compound tide type interactions are examined. It is demonstrated that not only are compound tides significant relative to the overtides, but they also influence the overtides.
Additional Material:
5 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650080706
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