A new analytical framework for assessing the effect of sea‐level rise and dredging on tidal damping in estuaries

Abstract

[1] This paper explores different analytical solutions of the tidal hydraulic equations in convergent estuaries. Linear and quasi-nonlinear models are compared for given geometry, friction, and tidal amplitude at the seaward boundary, proposing a common theoretical framework and showing that the main difference between the examined models lies in the treatment of the friction term. A general solution procedure is proposed for the set of governing analytical equations expressed in dimensionless form, and a new analytical expression for the tidal damping is derived as a weighted average of two solutions, characterized by the usual linearized formulation and the quasi-nonlinear Lagrangean treatment of the friction term. The different analytical solutions are tested against fully nonlinear numerical results for a wide range of parameters, and compared with observations in the Scheldt estuary. Overall, the new method compares best with the numerical solution and field data. The new accurate relationship for the tidal damping is then exploited for a classification of estuaries based on the distance of the tidally averaged depth from the ideal depth (relative to vanishing amplification) and the critical depth (condition for maximum amplification). Finally, the new model is used to investigate the effect of depth variations on the tidal dynamics in 23 real estuaries, highlighting the usefulness of the analytical method to assess the influence of human interventions (e.g. by dredging) and global sea-level rise on the estuarine environment.Citation: Cai, H., H. H. G. Savenije, and M. Toffolon (2012), A new analytical framework for assessing the effect of sea-level rise and dredging on tidal damping in estuaries,

Analytical and numerical study of the salinity intrusion in the Sebou river estuary (Morocco) – effect of the “Super Blood Moon” (total lunar eclipse) of 2015

“…Additionally, Fig. 9b shows the velocity amplitude and damping number at supermoon total lunar eclipse, which suggests that the hybrid model proposed by Cai et al (2012aCai et al ( , 2014a can well reproduce the tidal dynamics and velocity amplitude with a significant range of dam discharges.…”

“…Since 1960s there has existed a long tradition of 1-D analytical solutions for tidal dynamics in estuaries (e.g., Dronkers, 1964;Ippen, 1966;Prandle and Rahman, 1980;Leblond, 1978;Godin, 1985Godin, , 1999Jay, 1991;Savenije, 1993b;Friedrichs and Aubrey, 1994;Lanzoni and Seminara, 1998;Kukulka and Jay, 2003;Horrevoets et al, 2004;Jay et al, 2011;Cai et al, 2012a). These analytical solutions usually made assumptions to simplify or linearize the nonlinear set of equations .…”

“…They concluded that the main differences between the examined models (e.g., Savenije et al, 2008;Toffolon and Savenije, 2011;Kuijper and Van Rijn, 2011) lies in the treatment of the friction term in the momentum equation. Furthermore, Cai et al (2012a) presented a new "hybrid" expression for tidal damping as a Table 1. Definition of dimensionless parameters (Cai et al, 2015).…”

“…The proposed analytical model by Cai et al (2012a) for tidal hydrodynamics can be used to predict a variable velocity amplitude v (and hence tidal excursion E * ) for given tidal amplitude at the seaward boundary, estuary shape and friction.…”

“…Exceptions are the approaches by Horrevoets et al (2004) and Cai et al (2012b), who provided analytical solutions accounting for river discharge, based on the envelope method originally developed by Savenije (1998) (Cai et al, 2013). Recently, Cai et al (2012a) proposed a new analytical framework for understanding the tidal damping in estuaries. They concluded that the main differences between the examined models (e.g., Savenije et al, 2008;Toffolon and Savenije, 2011;Kuijper and Van Rijn, 2011) lies in the treatment of the friction term in the momentum equation.…”