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Evaluation of tidal residual currents in a wide estuary, using a finite element method
Author(s) -
Jenkins A. D.
Publication year - 1983
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650030106
Subject(s) - finite element method , wedge (geometry) , kelvin wave , wavelength , geometry , shallow water equations , modal , mathematics , mechanics , mathematical analysis , physics , geology , materials science , meteorology , optics , polymer chemistry , thermodynamics
From the linearized, time‐independent, constant depth, shallow water tidal equations in an f ‐plane for a two‐layer estuary, two independent modal Helmholtz equations are derived. These modal equations are solved using a fifth‐degree finite element technique. The first and second space derivatives of the complex modal tidal elevations, and thus the modal currents and their first derivatives, are evaluated directly from the solution at each node of the finite element mesh. The Stokes drift, which is the major part of the residual tidal flow, is evaluated from these nodal values of the currents and their derivatives. Good agreement is obtained with the exact analytical solution for a wedge‐shaped estuary with a wedge angle of π/3, using a mesh of 64 equilateral triangles with sides approximately 1/10 of the wavelength 2πC 2 /σ of a Kelvin wave solution for the short‐wavelength mode.