Analytical description of tidal dynamics in convergent estuaries

Savenije, Hubert; Toffolon, Marco; Haas, Jennifer S.; Veling, E. J. M.

doi:10.1029/2007jc004408

Cited by 125 publications

(274 citation statements)

References 20 publications

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“…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. Furthermore, Cai et al (2012a) presented a new "hybrid" expression for tidal damping as a Table 1.…”

Section: Analytical Hybrid Modelmentioning

confidence: 99%

“…It can be demonstrated that tidal hydrodynamics is controlled by three-dimensionless parameters that depend on localized geometry and external forcing (e.g., Toffolon et al, 2006;Savenije et al, 2008), i.e., ζ the dimensionless tidal amplitude (indicating the seaward boundary condition), γ the estuary shape number (representing the effect of crosssectional area convergence) and χ the friction number (describing the role of the frictional dissipation). These parameters are defined in Table 1, where η is the tidal amplitude and K s is the Manning-Strickler friction coefficient.…”

Section: Dimensionless Parameters Local Variable Dependent Variable Tmentioning

confidence: 99%

“…where g is the acceleration due to gravity and r s the storage width ratio (e.g., Savenije et al, 2008).…”

Section: Coupled Model For Salt Intrusionmentioning

confidence: 99%

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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

Haddout

Igouzal

Maslouhi

2016

Hydrol. Earth Syst. Sci.

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Abstract. The longitudinal variation of salinity and the maximum salinity intrusion length in an alluvial estuary are important environmental concerns for policy makers and managers since they influence water quality, water utilization and agricultural development in estuarine environments and the potential use of water resources in general. The supermoon total lunar eclipse is a rare event. According to NASA, they have only occurred 5 times in the 1900s – in 1910, 1928, 1946, 1964 and 1982. After the 28 September 2015 total lunar eclipse, a Super Blood Moon eclipse will not recur before 8 October 2033. In this paper, for the first time, the impact of the combination of a supermoon and a total lunar eclipse on the salinity intrusion along an estuary is studied. The 28 September 2015 supermoon total lunar eclipse is the focus of this study and the Sebou river estuary (Morocco) is used as an application area. The Sebou estuary is an area with high agricultural potential, is becoming one of the most important industrial zones in Morocco and it is experiencing a salt intrusion problem. Hydrodynamic equations for tidal wave propagation coupled with the Savenije theory and a numerical salinity transport model (HEC-RAS software "Hydrologic Engineering Center River Analysis System") are applied to study the impact of the supermoon total lunar eclipse on the salinity intrusion. Intensive salinity measurements during this extreme event were recorded along the Sebou estuary. Measurements showed a modification of the shape of axial salinity profiles and a notable water elevation rise, compared with normal situations. The two optimization parameters (Van der Burgh's and dispersion coefficients) of the analytical model are estimated based on the Levenberg–Marquardt's algorithm (i.e., solving nonlinear least-squares problems). The salinity transport model was calibrated and validated using field data. The results show that the two models described very well the salt intrusion during the supermoon total lunar eclipse day. A good fit between computed salinity and measurements is obtained, as verified by statistical performance tests. These two models can give a rapid assessment of salinity distribution and consequently help to ensure the safety of the water supply, even during such infrequent astronomical phenomenon.

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Section: Analytical Hybrid Modelmentioning

confidence: 99%

Section: Dimensionless Parameters Local Variable Dependent Variable Tmentioning

confidence: 99%

See 1 more Smart Citation

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

Haddout

Igouzal

Maslouhi

2016

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

show abstract

“…For a predominant tide (e.g. M 2 ), the phase lag is determined by ε = π − (φ Z − φ U ), in which φ Z and φ U represent the phase of water level and velocity, respectively (Savenije et al, 2008).…”

Section: Analytical Model For Tidal Hydrodynamicsmentioning

confidence: 99%

Analytical approach for determining the mean water level profile in an estuary with substantial fresh water discharge

Cai

Savenije

Jiang

et al. 2016

Hydrol. Earth Syst. Sci.

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Abstract.The mean water level in estuaries rises in the landward direction due to a combination of the density gradient, the tidal asymmetry, and the backwater effect. This phenomenon is more prominent under an increase of the fresh water discharge, which strongly intensifies both the tidal asymmetry and the backwater effect. However, the interactions between tide and river flow and their individual contributions to the rise of the mean water level along the estuary are not yet completely understood. In this study, we adopt an analytical approach to describe the tidal wave propagation under the influence of substantial fresh water discharge, where the analytical solutions are obtained by solving a set of four implicit equations for the tidal damping, the velocity amplitude, the wave celerity, and the phase lag. The analytical model is used to quantify the contributions made by tide, river, and tide-river interaction to the water level slope along the estuary, which sheds new light on the generation of backwater due to tide-river interaction. Subsequently, the method is applied to the Yangtze estuary under a wide range of river discharge conditions where the influence of both tidal amplitude and fresh water discharge on the longitudinal variation of the mean tidal water level is explored. Analytical model results show that in the tide-dominated region the mean water level is mainly controlled by the tide-river interaction, while it is primarily determined by the river flow in the river-dominated region, which is in agreement with previous studies. Interestingly, we demonstrate that the effect of the tide alone is most important in the transitional zone, where the ratio of velocity amplitude to river flow velocity approaches unity. This has to do with the fact that the contribution of tidal flow, river flow, and tide-river interaction to the residual water level slope are all proportional to the square of the velocity scale. Finally, we show that, in combination with extreme-value theory (e.g. generalized extremevalue theory), the method may be used to obtain a first-order estimation of the frequency of extreme water levels relevant for water management and flood control. By presenting these analytical relations, we provide direct insight into the interaction between tide and river flow, which will be useful for the study of other estuaries that experience substantial river discharge in a tidal region.

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“…To explore the interaction between different constituents of the tidal flow, the quadratic velocity u|u| (where u is the velocity) is usually approximated by a truncated series expansion, such as a Fourier expansion (Proudman, 1953; z u h z Closed end Figure 1. Geometry of a semi-closed estuary and basic notation (after Savenije et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

Frictional interactions between tidal constituents in tide-dominated estuaries

et al. 2018

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Abstract. When different tidal constituents propagate along an estuary, they interact because of the presence of nonlinear terms in the hydrodynamic equations. In particular, due to the quadratic velocity in the friction term, the effective friction experienced by both the predominant and the minor tidal constituents is enhanced. We explore the underlying mechanism with a simple conceptual model by utilizing Chebyshev polynomials, enabling the effect of the velocities of the tidal constituents to be summed in the friction term and, hence, the linearized hydrodynamic equations to be solved analytically in a closed form. An analytical model is adopted for each single tidal constituent with a correction factor to adjust the linearized friction term, accounting for the mutual interactions between the different tidal constituents by means of an iterative procedure. The proposed method is applied to the Guadiana (southern Portugal-Spain border) and Guadalquivir (Spain) estuaries for different tidal constituents (M 2 , S 2 , N 2 , O 1 , K 1 ) imposed independently at the estuary mouth. The analytical results appear to agree very well with the observed tidal amplitudes and phases of the different tidal constituents. The proposed method could be applicable to other alluvial estuaries with a small tidal amplitude-to-depth ratio and negligible river discharge.

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Analytical description of tidal dynamics in convergent estuaries

Cited by 125 publications

References 20 publications

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

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

Analytical approach for determining the mean water level profile in an estuary with substantial fresh water discharge

Frictional interactions between tidal constituents in tide-dominated estuaries

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