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Relationships between Tidal Dynamics and Bathymetry in Strongly Convergent Estuaries

Relationships between Tidal Dynamics and Bathymetry in Strongly Convergent Estuaries Localized analytical solutions are derived for the propagation of a single (predominant) tidal constituent in estuaries with strongly convergent triangular cross sections. The advective term is neglected, and the friction term is linearized. The solutions apply at any locality where the cross-sectional shape remains sensibly congruent and the spatial gradient of tidal elevation amplitude is small (i.e., ““synchronous””). Then, for specified tidal elevation amplitude ζζ̂ and water depth D, these solutions indicate values of tidal current amplitude û, ratio of friction to inertial terms, slope of the estuarine bed, rate of energy dissipation, and phase difference θθ between ζζ̂ and û. Illustrations of these results over a range of ζζ̂ and D provide reference frameworks to assess observed conditions at any position in any estuary satisfying the criteria cited. They may also indicate the range of parameters likely to be consistent with bathymetric equilibrium in dynamic sedimentary regimes. The ratio of friction to inertial terms is shown to be represented by tan θθ. Moreover, this ratio is further shown to be approximated by 10 ζζ̂ / D, the latter demarking the classification of shallow and deep estuaries. For shallow estuaries, by specifying a constant value of ζζ̂ , an expression for estuarine length is determined approximating 2350 D 5/4 / ζζ̂ 1/2 (m). This expression is consistent with observed values from some 50 estuaries spanning, without selection, both the entire U.K. coastline and that of the U.S. eastern seaboard. (The U.S. data are extracted from a paper relating to ““shallow, well-mixed estuaries.””) The associated scatter of the observed values is shown to be, in part, related to the influence of their prevailing sediment regime on their respective bed friction coefficients. This scatter is used to suggest a new expression relating the bed friction coefficient to the surficial mud content. Sensitivity of the solutions to changes in bed friction coefficient, mean sea level, and tidal conditions are also examined. These analyses indicate what changes in the shape and size of an estuary might follow from variations in the prevailing tidal and sedimentary regimes. These new results are assessed in the context of extensive earlier studies into tidal asymmetry in estuaries. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Physical Oceanography American Meteorological Society

Relationships between Tidal Dynamics and Bathymetry in Strongly Convergent Estuaries

Prandle, D.
Journal of Physical Oceanography , Volume 33 (12) – Apr 30, 2001
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Publisher
American Meteorological Society
Copyright
Copyright © 2001 American Meteorological Society
ISSN
1520-0485
DOI
10.1175/1520-0485(2003)033<2738:RBTDAB>2.0.CO;2
Publisher site
See Article on Publisher Site

Abstract

Localized analytical solutions are derived for the propagation of a single (predominant) tidal constituent in estuaries with strongly convergent triangular cross sections. The advective term is neglected, and the friction term is linearized. The solutions apply at any locality where the cross-sectional shape remains sensibly congruent and the spatial gradient of tidal elevation amplitude is small (i.e., ““synchronous””). Then, for specified tidal elevation amplitude ζζ̂ and water depth D, these solutions indicate values of tidal current amplitude û, ratio of friction to inertial terms, slope of the estuarine bed, rate of energy dissipation, and phase difference θθ between ζζ̂ and û. Illustrations of these results over a range of ζζ̂ and D provide reference frameworks to assess observed conditions at any position in any estuary satisfying the criteria cited. They may also indicate the range of parameters likely to be consistent with bathymetric equilibrium in dynamic sedimentary regimes. The ratio of friction to inertial terms is shown to be represented by tan θθ. Moreover, this ratio is further shown to be approximated by 10 ζζ̂ / D, the latter demarking the classification of shallow and deep estuaries. For shallow estuaries, by specifying a constant value of ζζ̂ , an expression for estuarine length is determined approximating 2350 D 5/4 / ζζ̂ 1/2 (m). This expression is consistent with observed values from some 50 estuaries spanning, without selection, both the entire U.K. coastline and that of the U.S. eastern seaboard. (The U.S. data are extracted from a paper relating to ““shallow, well-mixed estuaries.””) The associated scatter of the observed values is shown to be, in part, related to the influence of their prevailing sediment regime on their respective bed friction coefficients. This scatter is used to suggest a new expression relating the bed friction coefficient to the surficial mud content. Sensitivity of the solutions to changes in bed friction coefficient, mean sea level, and tidal conditions are also examined. These analyses indicate what changes in the shape and size of an estuary might follow from variations in the prevailing tidal and sedimentary regimes. These new results are assessed in the context of extensive earlier studies into tidal asymmetry in estuaries.

Journal

Journal of Physical Oceanography – American Meteorological Society

Published: Apr 30, 2001

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