Latent resonance in tidal rivers, with applications to River Elbe

We describe a systematic investigation of resonance in tidal rivers, and of river oscillations influenced by resonance. That is, we explore the grey-zone between absent and fully developed resonance. Data from this study are the results of a one-dimensional numerical channel model applied to a four-dimensional parameter space comprising geometry, i.e. length and depths of rivers, and varying dissipation and forcing. Similarity of real rivers and channels from parameter space is obtained with the help of a 'run-time depth'. We present a model-channel, which reproduces tidal oscillations of River Elbe in Hamburg, Germany with accuracy of a few centimetres. The parameter space contains resonant regions and regions with 'latent resonance'. The latter defines tidal oscillations that are elevated yet not in full but juvenile resonance. Dissipation reduces amplitudes of resonance while creating latent resonance. That is, energy of resonance radiates into areas in parameter space where periods of Eigen-oscillations are well separated from the period of the forcing tide. Increased forcing enhances the re-distribution of resonance in parameter space. The River Elbe is diagnosed as being in a state of anthropogenic latent resonance as a consequence of ongoing deepening by dredging. Deepening the river, in conjunction with the expected sea level rise, will inevitably cause increasing tidal ranges. As a rule of thumb, we found that 1 m deepening would cause 0.5 m increase in tidal range.