An Analytical Approach to Determining Resonance in Semi-Closed Convergent Tidal Channels

Abstract

An analytical model is used to investigate the resonant behavior in a semi-closed channel. The main integral quantities of the tidal wave are obtained by means of a linearized one-dimensional model as a function of three dimensionless parameters, representing * Corresponding author. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. 1650009-1 H. Cai, M. Toffolon & H. H. G. Savenijecross-section convergence, friction and distance to the closed boundary. Arbitrary alongchannel variations of width and depth are accounted for by using a multi-reach approach, whereby the main tidal dynamics are reconstructed by solving a set of linear equations satisfying the continuity conditions of water level and discharge at the junctions of the sub-reaches. We highlight the importance of depth variation in the momentum equation, which is not considered in the classical tidal theory. The model allows for a direct characterization of the resonant response and for the understanding of the relative importance of the controlling parameters, highlighting the role of convergence and friction. Subsequently, the analytical model is applied to the Bristol Channel and the Guadalquivir estuary. The proposed analytical relations provide direct insights into the tidal resonance in terms of tidal forcing, geometry and friction, which will be useful for the study of semi-closed tidal channels that experience relatively large tidal ranges at the closed end.

Effects of Tidal-Forcing Variations on Tidal Properties Along a Narrow Convergent Estuary

“…Overall, the presented analytical framework is useful for describing the main tidal properties along estuaries considering various forcings (amplitude, period) at the estuary mouth and the proposed method could be applicable to other estuaries with small tidal amplitude to depth ratio and negligible river discharge. Estuaries and Coasts https://doi.org/10.1007/s12237-018-0410-y required to specify the physical drivers of tidal behavior and 10 to gain insights into their sensitivity to variations in the forc-11 ing parameters, such as the estuarine geometry, tidal wave 12 characteristics, and friction (see Cai et al 2016; van Rijn 13 2011). In line with these goals, various analytical formu-14 lations have been developed to address the most important 15 properties of tidal propagation along a channel.…”

“…Analytical solutions describing tidal dynamics along 17 estuaries are generally obtained from the derivation of 18 the linearized St. Venant equations, considering idealized 19 channel geometries (Cai et al 2016, for a brief recapit-20 ulation of the most significant contributions, see; Hoitink 21 and Jay 2016; van Rijn 2011). Following this approach, 22 many researchers have provided first-order solutions focus-23 ing on the 1D (depth-and cross-section-averaged) aspect 24 of the along channel tidal propagation.…”

“…Following Cai et al (2016), the analytical 818 solutions for a semi-closed channel were implemented to 819 explore the relationship between the tidal period (between 1 820 and 40 h) and the resonance behavior along the channel. The 821 forcing amplitude at the sea boundary was set to a constant 822 value, equal to the amplitude of the could induce distinct resonance behaviors (Dronkers 1964 …”

Frictional interactions between tidal constituents in tide-dominated estuaries

“…We note that the modified friction number χ n in Eq. (23) contains the friction coefficient K. In many applications, K is calibrated separately for each tidal constituent to account for the different friction exerted due to the combined tide, either changing K directly or through calibration of the different correction friction factors f n (see, e.g., Cai et al, 2015Cai et al, , 2016. The current study aims at avoiding the need to adjust K individually, so that only a single value of K needs to be calibrated, based on the physical consideration that friction mostly depends on bottom roughness, and the other factors (tide interaction) are to be correctly modeled.…”

Frictional interactions between tidal constituents in tide-dominated estuaries

“…(23) contains the friction coefficient K. In many applications, K is calibrated separately for each tidal constituent to account for the different friction exerted due to the combined tide, either changing K directly or through calibration of the different correction friction factors f n (see, e.g., Cai et al, 2015Cai et al, , 2016. The current study aims at 255 avoiding the need to adjust K individually, so that only a single value of K can be calibrated, which is based on the physical consideration that friction mostly depends on bottom roughness, and the other factors (tide interaction) are to be correctly modelled.…”