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Identifying the critical position and river discharge for maximum tidal damping
Journal article(2019)
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Huayang Cai, Hubert H.G. Savenije, Erwan Garel, Xianyi Zhang, Leicheng Guo, Min Zhang, Feng Liu, Qingshu Yang
As a tide propagates into the estuary, river discharge affects tidal damping, primarily via a friction term, attenuating tidal motion by increasing the quadratic velocity in the numerator, while reducing the effective friction by increasing the water depth in the denominator. For the first time, we demonstrate a third effect of river discharge that may lead to the weakening of the channel convergence (i.e. landward reduction of channel width and/or depth). In this study, monthly averaged tidal water levels (2003-2014) at six gauging stations along the Yangtze River estuary are used to understand the seasonal behaviour of tidal damping and residual water level slope. Observations show that there is a critical value of river discharge, beyond which the tidal damping is reduced with increasing river discharge. This phenomenon is clearly observed in the upstream part of the Yangtze River estuary (between the Maanshan and Wuhu reaches), which suggests an important cumulative effect of residual water level on tide-river dynamics. To understand the underlying mechanism, an analytical model has been used to quantify the seasonal behaviour of tide-river dynamics and the corresponding residual water level slope under various external forcing conditions. It is shown that a critical position along the estuary is where there is maximum tidal damping (approximately corresponding to a maximum residual water level slope), upstream of which tidal damping is reduced in the landward direction. Moreover, contrary to the common assumption that larger river discharge leads to heavier damping, we demonstrate that beyond a critical value tidal damping is slightly reduced with increasing river discharge, owing to the cumulative effect of the residual water level on the effective friction and channel convergence. Our contribution describes the seasonal patterns of tide-river dynamics in detail, which will, hopefully, enhance our understanding of the nonlinear tide-river interplay and guide effective and sustainable water management in the Yangtze River estuary and other estuaries with substantial freshwater discharge.
...
As a tide propagates into the estuary, river discharge affects tidal damping, primarily via a friction term, attenuating tidal motion by increasing the quadratic velocity in the numerator, while reducing the effective friction by increasing the water depth in the denominator. For the first time, we demonstrate a third effect of river discharge that may lead to the weakening of the channel convergence (i.e. landward reduction of channel width and/or depth). In this study, monthly averaged tidal water levels (2003-2014) at six gauging stations along the Yangtze River estuary are used to understand the seasonal behaviour of tidal damping and residual water level slope. Observations show that there is a critical value of river discharge, beyond which the tidal damping is reduced with increasing river discharge. This phenomenon is clearly observed in the upstream part of the Yangtze River estuary (between the Maanshan and Wuhu reaches), which suggests an important cumulative effect of residual water level on tide-river dynamics. To understand the underlying mechanism, an analytical model has been used to quantify the seasonal behaviour of tide-river dynamics and the corresponding residual water level slope under various external forcing conditions. It is shown that a critical position along the estuary is where there is maximum tidal damping (approximately corresponding to a maximum residual water level slope), upstream of which tidal damping is reduced in the landward direction. Moreover, contrary to the common assumption that larger river discharge leads to heavier damping, we demonstrate that beyond a critical value tidal damping is slightly reduced with increasing river discharge, owing to the cumulative effect of the residual water level on the effective friction and channel convergence. Our contribution describes the seasonal patterns of tide-river dynamics in detail, which will, hopefully, enhance our understanding of the nonlinear tide-river interplay and guide effective and sustainable water management in the Yangtze River estuary and other estuaries with substantial freshwater discharge.
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 (M2, S2, N2, O1, K1) 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.
...
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 (M2, S2, N2, O1, K1) 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.
