Some notes on tidal theory and its possible relevance to a program of deep-sea tidal measurement

Heaps, N. S.

doi:10.1007/bf02233896

Cited by 4 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The dynamical equations for a tidal constituent of speed u are where the notation is as in Heaps (1969); u and u are the components of mean-depth current in the x and y directions; h(x, y ) is the sea depth; f is the tidal elevation; {' = 5 -5, with the equilibrium tide;f, u, g are constants defined in Heaps (1969); and F, G are frictional terms which we here assume are linear in hu, hu:…”

Section: The Proudman-heaps Tidal Theoremmentioning

confidence: 99%

“…l), and tidal measurements around its shore; compute the tides across the open mouth of the bay. This problem is discussed in Heaps (1969) and is formulated in terms of a single harmonic constituent of speed u. A direct calculation would require the solution of the tidal dynamical equations over the interior of the bay, and subject to boundary Y Figure 1.…”

Section: Introductionmentioning

confidence: 99%

“…An alternative approach was suggested by Proudman (1925) and extended to include linear friction by Heaps (1969). In this approach a set of auxiliary equations is introduced, together with a sequence of functions satisfying these equations with initial value boundary conditions along the open boundary of the bay.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the use of the Proudman--Heaps tidal theorem

Foreman¹,

Delves

Barrodale

et al. 1980

Geophysical Journal International

View full text Add to dashboard Cite

The Proudman-Heaps tidal theorem provides, in principle, one way of computing tides across the open boundary of a bay, given measurements round the shore; however, attempts to use the theorem numerically have so far failed. We describe in this paper the results of a theoretical and numerical investigation into the difficulties which are encountered. We show first that:(1) The mathematical model being solved is ill-posed; hence, M Z~ method, and in particular a direct use of the tidal theorem, must expect numerical difficulties.( 2 ) The direct use of the tidal theorem yields the solution of a problem close to that posed; thus, discrepancies in the solution reflect directly the ill-posedness of the problem.The ill-posedness can be countered by imposing suitable constraints, which may be either mathematical (regularity conditions on the solution) or physical (spot tidal measurements across the open mouth of the bay). We investigate the extent to which using such constraints can improve the predictive power of the method; the results obtained are not encouraging.

show abstract

Section: The Proudman-heaps Tidal Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%