Undular Bore Due to a Low Pressure or Bottom Trough Moving at the Critical Speed

Abstract A low pressure or bottom obstacle of negative displacement moves at the critical speed along a fluid layer of constant depth. The disturbance causes a depression of the surface at its forward position. The nonlinear dynamics generates a group of short waves attached to the disturbance. The number of two to six crests have a wavelength of 5.7–12 times the water depth. The wave height increases with the decreasing wavelength. The waves of the group do not follow the dispersion properties of cnoidal waves or Stokes waves. The group is rather characterised as an undular bore. The bore develops during a travel distance of 7–15 times the length of the disturbance. Its front eventually moves ahead of the driving disturbance where the leading crest develops into a solitary wave. A short disturbance is more powerful, but generates fewer crests compared to a long one. Comparison to the generation phase of upstream waves due to a high pressure (ship) or a bottom elevation shows that the wavelength in the two cases is approximately equal.