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In this study, the problem of surface waves induced by water flow in a flow channel was investigated. The mathematical model based on the potential wave theory was established, and a new analytic solution to the corresponding initial and boundary value problem was proposed. To confirm our analytic solution, the mathematical model was applied to simulate experiments conducted in a flow channel in the laboratory. Using our analytic solution, water surface elevations and flow velocities at certain locations in the channel were compared with experimental results. Comparisons between our analytic solution and experimental results confirmed our theory that amplitudes and propagating phases are in very close agreement. Our analytic solution can be used to calculate variations in pressure and velocity along the water depth, which are expensive to calibrate and obtain in experiments. Although our analytic solution was established based on linear theory, it is very practical for applications studying the basic properties of surface elevation, velocity, and pressure of the flow field induced by water current both in space and time.

A tidal bore is a natural phenomenon usually occur in bays with large tidal waves. Sometimes this large tidal inflow are channeled deep into a river. In Indonesia, this natural phenomenon is found in the Kampar River, which is known as the tidal bore Bono. Sometimes, these tidal bore phenomena disappear, as happened to the Mascaret, tidal bore on the River Seine France. Through an understanding of the formation of tidal bore mechanism, there is hope that the tidal bore Bono in Kampar River can be preserved. In this paper, the occurrence of tidal bore Bono is simulated using the non-hydrostatic Saint-Venant equation under a staggered grid formulation. To test the accuracy of the implementation, several scenarios of hydraulic jumps were simulated first. The numerical results have shown to quantitatively confirm the analytical formula of bore height and velocity, two parameters that are important to characterize a bore wave. Further, by adopting a model that incorporates the non-hydrostatic pressure, our simulation shows the appearance of an undular bore accompanying the shock front. Finally, by using tidal current data measured along Kampar River estuary, our simulation that employs the actual river topography can show the appearance of tidal bore Bono. Our simulations were shown to be in fair agreement with the measurement.

The secondary wave field associated with undular tidal bores (known as whelps) has been barely studied in field conditions: the wave field can be strongly non-hydrostatic, and the turbidity is generally high. In situ measurements based on pressure or acoustic signals can therefore be limited or inadequate. The intermittent nature of this process in the field and the complications encountered in the downscaling to laboratory conditions also render its study difficult. Here, we present a new methodology based on LiDAR technology to provide high spatial and temporal resolution measurements of the free surface of an undular tidal bore. A wave-by-wave analysis is performed on the whelps, and comparisons between LiDAR, acoustic and pressure-derived measurements are used to quantify the non-hydrostatic nature of this phenomenon. A correction based on linear wave theory applied on individual wave properties improves the results from the pressure transducer (Root mean square error, R M S E of 0 . 19 m against 0 . 38 m); however, more robust data is obtained from an upwards-looking acoustic sensor despite high turbidity during the passage of the whelps ( R M S E of 0 . 05 m). Finally, the LiDAR scanner provides the unique possibility to study the wave geometry: the distribution of measured wave height, period, celerity, steepness and wavelength are presented. It is found that the highest wave from the whelps can be steeper than the bore front, explaining why breaking events are sometimes observed in the secondary wave field of undular tidal bores.