Linking the river to the estuary: influence of river discharge on tidal damping

Abstract

The effect of river discharge on tidal damping in estuaries is explored within one consistent theoretical framework where analytical solutions are obtained by solving four implicit equations, i.e. the phase lag, the scaling, the damping and the celerity equation. In this approach the damping equation is obtained by subtracting the envelope curves of high water and low water occurrence, taking into account that the flow velocity consists of a tidal and river discharge component. Different approximations of the friction term are considered in deriving the damping equation, resulting in as many analytical solutions. In this framework it is possible to show that river discharge affects tidal damping primarily through the friction term. It appears that the residual slope, due to nonlinear friction, can have a substantial influence on tidal wave propagation when including the effect of river discharge. An iterative analytical method is proposed to include this effect, which significantly improved model performance in the upper reaches of an estuary. The application to the Modaomen and Yangtze estuaries demonstrates that the proposed analytical model is able to describe the main tidal dynamics with realistic roughness values in the upper part of the estuary where the ratio of river flow to tidal flow amplitude is substantial, while a model with negligible river discharge can be made to fit observations only with unrealistically high roughness values.Published by Copernicus Publications on behalf of the European Geosciences Union.

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

“…Note that in Table 1 η indicates the tidal amplitude, υ is the velocity amplitude, U r is the river flow velocity, ω is the tidal frequency, g is the gravity acceleration, K is the Manning-Strickler friction coefficient, r S is the storage width ratio, and c 0 is the classical wave celerity defined as definition for the estuary shape number as suggested by Cai et al (2014b) to account for the asymptotic adjustment to the river cross section, the difference being a factor (1 − A r /A), which varies with distance although it remains close to unity in the most downstream reach of the estuary.…”

“…Apart from the damping Eq. (6), the other three dimensionless equations are summarized as follows (Cai et al, 2014b).…”

“…by subtracting the envelope curves at HW and LW (for details see Cai et al, 2014b). In a Lagrangean reference frame, we assume that the velocity of a moving water particle V consists of a steady component U r , generated by the fresh water discharge, and a time-dependent constituent U t , introduced by the tidal flow:…”

“…However, as opposed to what is generally done, the cross-sectional area and stream width do not converge to zero, but to constant river-dominated values. To better represent the geometry of such funnel-prismatic estuaries, we propose the following expressions to describe the longitudinal variation of crosssectional area A and stream width B (see also Toffolon et al, 2006;Cai et al, 2014b):…”

“…In addition, we note that the decomposition of the tidally averaged friction term requires long-term measurements of velocity, which are not always available in reality. In this paper, we adopt an analytical model for tidal hydrodynamics (Cai et al, 2014b) to further study the tide-river dynamics and its impact on the residual water level in estuaries with substantial fresh water discharge. We limit the analysis to the interaction between the predominant tidal constituent (e.g.…”