Nonlinear tidal waves in a kind of estuary with gradually varying cross-section

Nonlinear tidal waves in a kind of estuary are studied in the paper using one-dimensional nonlinear hydrody-namic equations with friction.The estuary has exponentially varying width B=B₀e^-bx and uniform depth h.The one-dimensional hydrodynamic equations are solved by perturbation method.It was found that our solution included two special cases, Pelisenpeki's solution and Airy's solution.The former can be got by letting b=0 in our solutions, and the latter by setting b=0 and f=0 (f is linear frictional coefficient).In terms of the second-order solution, the physical mechanism of nonlinear tidal waves in estuaries with gradually varying cross-section is explored.It is shown that, under the assumption of linear friction coefficient, shallow water constituent waves consist of two parts, one is produced by shallow water nonlinear effect outside the estuary, the other is generated by shallow water nonlinear effect inside estuary.In addition, the physical mechanism of the residual tidal current and elevation are not exactly the same as that of the shallow water constituent waves. The former results from the interaction of shallow water nonlinear effect, friction and estuarine deforming effect.The latter depends chiefly on shallow water nonlinear effect. Finally, present nonlinear model is applied to the modelling of the tidal waves in the Hangzhou Bay.Seven of constituent waves (O₁, K₁,M₂, S₂, M₄,S₄, MS₄) are taken into account. It will be found that the results modelled by incident progressive waves and their Interaction agree rather well with the observations, therefore, it can be concluded that the incident progressive waves in the Hangzhou Bay are dominant.