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Resonance characteristics of tides in branching channels

Published online by Cambridge University Press:  09 July 2013

Niels C. Alebregtse ,
H. E. de Swart  and
H. M. Schuttelaars
Niels C. Alebregtse*
Affiliation:
Institute for Marine and Atmospheric research Utrecht, Utrecht University, Princetonplein 5, 3584CC Utrecht, The Netherlands
H. E. de Swart
Affiliation:
Institute for Marine and Atmospheric research Utrecht, Utrecht University, Princetonplein 5, 3584CC Utrecht, The Netherlands
H. M. Schuttelaars
Affiliation:
Delft Institute of Applied Mathematics/Mathematical Physics, Delft University of Technology, Mekelweg 4, P.O.Box 5031, 2600 GA Delft, The Netherlands
*
†Email address for correspondence: n.c.alebregtse@uu.nl
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Abstract

Resonance characteristics of tidal waves in a network are investigated with the linearized, one-dimensional shallow water equations. The network comprises a semi-enclosed main channel with an adjacent secondary channel at an arbitrary position. Water motion is forced by a prescribed incoming wave at the entrance of the main channel. The model is used to compute the ratio of sea surface height amplitude in the presence and absence of the secondary channel. Relevance lies in the possible construction of secondary channels to reduce tidal range in the main channel. When $\mu = 2\mathrm{\pi} { l}_{b}^{\ast } / { l}_{t}^{\ast } \gtrsim \mathrm{\pi} $ (${ l}_{b}^{\ast } $ being the length of the main channel, ${ l}_{t}^{\ast } $ the tidal wavelength) and friction is weak, it is found that reduction (amplification) of the tidal range occurs for secondary channels located less (more) than a quarter wavelength from the closed end of the main channel. Furthermore, a minimum is observed halfway between the closed end and the nodal point, and a maximum a quarter wavelength further seaward. With increasing friction and/or decreasing length of the main channel, amplitude ratios become less pronounced and depend weakly on the location of the secondary channel. The mechanism responsible for amplification or reduction of the sea surface height in the main channel is identified and explained in terms of the forced wave and waves radiating away from the secondary channel.

JFM classification

Geophysical and Geological Flows: Coastal engineering Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Surface gravity waves
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 728 , 10 August 2013 , R3
Copyright
©2013 Cambridge University Press 

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