On the adjoint of Laplace’s tidal equations
On the adjoint of Laplace’s tidal equations
The concept of the adjoint is regularly used in studies of both the resonances of physical systems and their response to external forcing. This report reviews the underlying theory involved in the adjoints of both differential equations and matrices and shows how the theory may be used to derive a physically meaningful adjoint to Laplace’s Tidal Equations.
Numerical models of the tides usually use a finite difference form of the tidal equations. The report investigates the adjoint properties of the finite difference equations. It shows that the are not necessarily symmetrical, i.e. the finite difference form of the adjoint tidal equations may not be the same as the adjoint of the normal finite difference equations. It also shows that, with a suitable choice of the way the boundary conditions and Coriolis terms are represented, the finite difference forms can be made symmetric.
National Oceanography Centre
Webb, D.J.
6fc412d4-f113-4e55-9e3a-dad18223a445
January 2014
Webb, D.J.
6fc412d4-f113-4e55-9e3a-dad18223a445
Webb, D.J.
(2014)
On the adjoint of Laplace’s tidal equations
(National Oceanography Centre Internal Document, 7)
Southampton, GB.
National Oceanography Centre
27pp.
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Monograph
(Project Report)
Abstract
The concept of the adjoint is regularly used in studies of both the resonances of physical systems and their response to external forcing. This report reviews the underlying theory involved in the adjoints of both differential equations and matrices and shows how the theory may be used to derive a physically meaningful adjoint to Laplace’s Tidal Equations.
Numerical models of the tides usually use a finite difference form of the tidal equations. The report investigates the adjoint properties of the finite difference equations. It shows that the are not necessarily symmetrical, i.e. the finite difference form of the adjoint tidal equations may not be the same as the adjoint of the normal finite difference equations. It also shows that, with a suitable choice of the way the boundary conditions and Coriolis terms are represented, the finite difference forms can be made symmetric.
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Published date: January 2014
Organisations:
Marine Systems Modelling
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Local EPrints ID: 361041
URI: http://eprints.soton.ac.uk/id/eprint/361041
PURE UUID: ed75bb81-1cf6-433e-8e71-f967991964d1
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Date deposited: 10 Jan 2014 16:23
Last modified: 14 Mar 2024 15:45
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Author:
D.J. Webb
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